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NuclearPhysicsNews

Nuclear Physics News is published on behalf of theNuclear Physics European Collaboration Commit-tee (NuPECC), an Expert Committee of the Euro-pean Science Foundation, with colleagues fromEurope, America, and Asia.

Volume 12/No. 3

Editor: Gabriele-Elisabeth Körner

Editorial BoardR. F. Casten, Yale R. Johnson, SurreyJ. D’Auria, Vancouver W. Kutschera, ViennaT. W. Donnelly, MIT Cambridge R. Lovas, DebrecenJ. Durell, Manchester M. Lozano, SevillaM. N. Harakeh, KVI Groningen (Chairman) I. Tanihata, RIKEN Tokyo

Editorial Office: Physikdepartment E12, Technische Universitat München,85748 Garching, Germany. Tel: +49 89 2891 2293, Fax: +49 89 2891 2298,

E-mail: [email protected].

CorrespondentsArgentina: O. Civitaresse, La Plata; Australia: A. W. Thomas, Adelaide; Austria: H. Oberhummer, Vienna; Belgium: M. Huyse, Leuven; Brasil: M. Hussein, Sao Paulo; Bulgaria: D. Balabanski, Sofia; Canada: J.-M. Poutissou, TRIUMF; K. Sharma, Manitoba; J. Simpson, Guelph; China: W. Zhan, Lanzhou; Croatia: R. Caplar, Zagreb; Czech Republic: J. Kvasil, Prague; Slovak Republic: P. Povinec, Bratislave; Denmark: K. Riisager, Århus; Finland: M. Leino, Jyväskylä;France: G. De France, GANIL Caen; B. Blank, Bordeaux; M. Guidal, IPN Orsay; Germany: K. D. Gross, GSI Darmstadt;K. Kilian, Jülich; K. Lieb, Göttingen; Greece: E. Mavromatis, Athens; Hungary: B. M. Nyako, Debrecen; India: D. K.Avasthi, New Delhi; Israel: N. Auerbach, Tel Aviv; Italy: E. Vercellin, Torino; M. Ripani, Genova; L. Corradi, Legnaro; D. Vinciguerra, Catania; Japan: J. Imazato, IEK, H. Toki, Osaka, I. Tanihata, RIKEN; Mexico: J. Hirsch, Mexico DF;Netherlands: H. Wilschut, KVI Groningen, G. van der Steenhoven, NIKHEF Amsterdam; Norway: J. Vaagen, Bergen;Poland: T. Czosnyka, Warsaw; Portugal: M. Fernanda Silva, Sacavén; Romania: A. Raduta, Bucharest; Russia: Yu.Novirov, St. Petersburg; Spain: B. Rubio, Valencia; Sweden: P.-E. Tegner, Stockholm; Switzerland: C. Petitjean, PSI Villigen;United Kingdom: B. F. Fulton, Birmingham; D. Branford, Edinburgh; USA: R. Janssens, Argonne; Ch. E. Reece, JeffersonLab; B. Jacak, Stony Brook; B. Sherrill, Michigan State Univ.; L. S. Schroeder, Lawrence Berkeley Laboratory; S. E. Vigdor,Indiana Univ.; W. C. Haxton, Seattle.

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Vol. 12, No. 3, 2002, Nuclear Physics News 1

Contents

Editorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

Laboratory PortraitNuclear Physics at Oak Ridge National Laboratory

by C. Baktash, J. Beene, V. Cianciolo, D. J. Dean, C. Gross, M. S. Smith, and G. R. Young . . . . . . . . . . . . . 0

Feature ArticlesCritical Point Symmetries in Nuclei

by Francesco Iachello . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

Density Functional Theoryby D. M. Brink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

Free Muons and Muonium: Some Achievements and Possibilities in Low Energy Muon Phsyicsby Klaus P. Jungmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

Impact and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

News and Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

Meeting Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

Facilities and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00The Nuclear Liquid-Phase Gas Transition: Studies with the ISiS Array

by V. E. Viola and K. Kwiatkowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

Investigation of the Neutronic Performance of Cold Moderators with Jessicaby K. Nüninghoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

News from NuPECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

Calendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00

NuclearPhysicsNews

Volume 12/No. 3

Cover illustration (Clockwise from upper left): The cover includes a collage of various experimentalcomponents that drive the research of the Physics Division of Oak Ridge National Laboratory. Thepictures show clockwise from the top left: a scanning electron microscope image of the carbon matrixused for ISOL targets; remote handling robot on the RIB Injector Platform; CLARION and HyBall ar-rays at the target chamber of the Recoil Mass Spectrometer; central magnet and one spectrometer armof PHENIX; central column structure of the 25-MV tandem accelerator; Daresbury Recoil Separator.

2 Nuclear Physics News, Vol. 12, No. 3, 2002

I should have known better. Acasual comment to the editor duringa conference dinner at Trento aboutthe Nuclear Physics News editorials,and here I am landed with producingthe next one. Worse still, I have tomake public my comment, at therisk of offending my older col-leagues.

The concern I voiced was thatover the last few years, too many ofthe editorials seemed to involvebackward looks to a time of betterfunding of nuclear physics and totimes when there were no pressureson “pure” research activities. Thepoint is that for the many youngermembers of our community, thepresent state of affairs is perfectlynatural and the only one they know.We (if I may put myself in thatgroup) have grown up in a period ofstatic or declining budgets, and in aclimate where society wishes to seeapplications from research. More-over, we don’t see nuclear physics asbeing treated any different fromother fields of research in this re-gard, for if we talk to our colleaguesin other areas of physics researchsuch as plasma, atomic, solid state,etc., we hear of the same pressureson funding and the favoring of ap-plications work. For the youngercommunity, the habit of lookingbackward is all very dated and of lit-tle interest. Nuclear physics operatesin the same environment and withthe same pressures as other areas ofthe physical sciences, just as it should.

Our community must take positiveaction to evolve a future strategywhich supports a balance of large,medium, and small facilities, basedboth in national laboratories and inuniversities. In the European con-text, I look to NuPECC to provide alead in these discussions.

BRIAN FULTON

editorial


The Future Please, Not the Past

The views expressed here do not represent the views and policies of NuPECC except where explicitly identified.

To avoid too much emphasis on pastreflection, perhaps more of the edi-torials should be from our youngercolleagues; as a challenge I have for-warded a few names to the editor.

There was, if I recall, anothertopic in the conversation that eve-ning. That is the growth of facilitiesat the larger laboratories at the ex-pense of facilities in smaller institu-tions and universities. Although Iwill comment on this in the contextof developments in Europe, I believethat the same comments probablyapply to our colleagues elsewhere. Inthe light of what I said at the begin-ning of this article, it is worth notingthat here again, we are really littledifferent from other areas of physicsresearch, as evidenced by the ESF forthe synchrotron community andnow the proposed ESS for the neu-tron community. The same pressureswhich drive us to aspire to largerand more expensive facilities are alsofelt by other research communities.However, we must always be awareof one important difference. Whilethe ESF, or ILL, or the proposed ESScan at any time support 20 or moregroups simultaneously, the nature ofnuclear physics facilities is such thatthey generally support only onegroup at a time. The needs of theEuropean community require far, farmore than just a few large facilities.Moreover, the scientists of the futureemerge from the Ph.D. students inuniversities, where the opportunityfor hands-on training can be given.

IntroductionOak Ridge National Laboratory

(ORNL) is the largest U.S. Depart-ment of Energy (DOE) science andengineering research laboratory. Theresearch portfolio of ORNL spans abroad range of sciences includingmaterials research, biology, compu-tational sciences, energy technology,environmental science, and nuclearphysics.

Nuclear science within thePhysics Division includes severalmajor thrust areas ranging from ex-perimental studies of nuclear struc-ture, astrophysical processes involv-ing nuclei, plasma formation usingrelativistic heavy ions, and a new re-search program in neutron science.

Nuclei offer an extremely richplayground in which to perform re-search. Increasing interest is beingplaced on understanding nucleiunder extreme conditions of isospinand excitation energy. The scientificmotivation here is to understandemergent phenomena that occurwhen we move away from stable nu-clei into regions where nuclei areweakly bound or are indeed un-bound with respect to particle decay.Nuclei also play quite importantroles in astrophysical processes suchas nova and supernova energy gener-ation and element production in theuniverse. At very high energy scales,nuclear collisions shed light on thedeconfined phase of QCD and onthe zero-baryon phase of the earlyuniverse. Finally, the nucleus is a finelaboratory where we can test thefundamental symmetries of natureand the standard model.

The Holifield Radioactive Ion Beam Facility

The low energy nuclear physicsprogram at ORNL is centered on theHolifield Radioactive Ion Beam Fa-cility (HRIBF),1 which is operated asa national facility supporting the nu-clear science research program of theU.S. DOE. The HRIBF is the onlyU.S. facility devoted to the produc-tion of radioactive ion beams (RIBs)using the isotope separator on-line(ISOL) technique and is a bridge tothe realization of the planned RareIsotope Accelerator (RIA). The ISOLtechnique, as implemented at HRIBF,is illustrated in Figure 1. An intenseion beam from the production accel-erator is used to bombard a thicktarget and create radioactive nuclei.These newly produced nuclei diffuseout of the heated target and are ion-ized and formed into a beam, whichis then mass analyzed, injected intothe post-accelerator, and finally de-livered to an experimental end sta-

tion. The HRIBF supports activeresearch programs with beams ofboth neutron-deficient and neutron-rich radioactive species. In fact, atthe present time, the HRIBF is theonly facility in the world that is ableto provide beams of medium-massneutron-rich species, such as doublymagic 132Sn, post-accelerated to en-ergies above the Coulomb barrier.Altogether, the facility acceleratesabout 80 stable beams and more than100 p- and n-rich beams (with inten-sities in excess of 103 pps) above theCoulomb barrier (see Figure 2).

Operation of the HRIBF involvesfour major components: the light ionproduction accelerator ORIC (OakRidge Isochronous Cyclotron), theRIB Injector, the 25-MV tandempost-accelerator, and several state-of-the-art experimental end stationsthat are well equipped with flexibledetector arrays and spectrometers.The layout of the facility is shown inFigure 3.

laboratory portrait


Nuclear Physics at Oak RidgeNational Laboratory

Figure 1. ISOL technique at HRIBF.

AU: Low-res artwill notprint.Pleasesupplynew art.

The production accelerator,ORIC, is a variable energy cyclotronwhich provides light ion beams withintensities in the tens of microam-pere range. The maximum beam en-ergies for protons, deuterons, 3He,and 4He are about 50 MeV, 50 MeV,120 MeV, and 100 MeV, respec-tively. The ORIC beam bombards athick target mounted on the RIB In-jector. The RIB Injector is the heartof the HRIBF, where the severestchallenges of ISOL RIB productionmust be met. It is here that the radio-active nuclei are created and ex-tracted from the production target,a process that must be accomplishedin a time commensurate with thelifetime of the species of interest.The RIB injector is comprised of ahigh voltage (300 kV) platform onwhich a target and ion source sys-tem, electrostatic beam transportsystem, a first stage mass analysissystem (M/∆M ~ 1,000), and acharge exchange cell are mounted,followed by a high resolution massseparator (isobar separator) (M/∆M ~ 20,000). The RIB is formed inthe RIB Injector ion source and sub-jected to an initial stage of massanalysis. The tandem post-accelera-

tor requires a negative-ion beam.Consequently, if the ion source pro-duces positively charged ions, acharge exchange cell is required.After being accelerated off the highvoltage platform, the negative ionspass through the high-resolutionmass analyzer and are injected intothe 25 MV tandem (which holds the

world record for tandem operatingvoltage). It is routinely used with ter-minal potentials ranging from near1 MV for astrophysics experimentsto above 24 MV for nuclear struc-ture and reaction studies. The tan-dem is folded so that the beam isbent 180 degrees inside the terminal,stripped of bound electrons by a gasor foil stripper, and perhaps strippeda second time partway down thehigh energy column. The beam maybe delivered to one of six experimen-tal end stations that contain veryversatile detector systems.

The development of radioactivebeams at HRIBF is driven by theneeds of our users. Each new beamspecies presents challenges, often re-quiring development of specializedproduction targets or ion sources.The HRIBF now routinely uses twotypes of ion sources and has severalothers in various stages of develop-ment. The Kinetic Ejection NegativeIon Source (KENIS) is a novel deviceconceived and developed at HRIBF

laboratory portrait


Figure 2. HRIBF n-rich beam production off target. For a complete list ofHRIBF beams, see www.phy.ornl.gov/hribf/users/beams.

Figure 3. Schematic layout of the Holifield Radioactive Ion Beam Facility.(Experimental equipment are described at www.phy.ornl.gov/hribf/research.)



to produce beams of halogen species(especially fluorine isotopes). TheElectron Beam Plasma Ion Source(EBPIS), based on an ISOLDE de-sign, is a general-purpose positiveion source. The EBPIS is also usedwith other target systems, e.g., a liq-uid germanium target to producebeams of As and Ga. Both positiveand negative surface ionizationsources designed for RIB’s have beendeveloped, but not yet used on line.

Production targets are a criticalpart of beam development. Eventhough the total production-beampower at HRIBF is rather low(~1kW), the power density in theproduction target can be very high.The target material must have a lowvapor pressure at the operating tem-perature (up to 2,000°C), be robustenough to withstand the power de-posited by the beam, and have a for-mat conducive to fast release of thespecies of interest. Two critical geo-metrical features are short diffusionpaths for the beam-species atomsand a highly-permeable, open struc-ture that allows atoms or moleculesto effuse out of the target quickly.We have developed a number oftarget systems for RIB production atHRIBF which meet these require-ments. An oxygen-bearing targetwas needed to produce 17,18F. Oursolution was a highly-refractoryHfO2 matrix, made up of thin (10µm) fibers. Neutron-rich RIBs areproduced at HRIBF by proton-induced fission of 238U. The targetconsists of thin layers (<10 µm) ofuranium carbide deposited on anopen-structured carbon fiber matrix(see the cover).

The nuclear reactions employedto produce RIBs generally result incomparable quantities of several iso-topes of the same mass (isobars).Some experiments can use a beamcontaining such a mixture of species,

but others require higher beam pu-rity. The ability to produce beamswhich are nearly free from isobariccontamination is a critical capabilityfor a RIB facility. The high-resolu-tion magnetic isobar separator is in-tended to fill this function; however,in many cases the quality of the neg-ative ion beam entering the separa-tor, or the small mass differencebetween adjacent isobars results ininsufficient beam purification. Insome cases, the ionization process it-self can be made species selective,such as the enhancement of alkalisby positive surface ionization, orsuppression of species that do notform negative ions in negativesources. Another technique applica-ble to light nuclei is elimination ofisobars with smaller atomic numberthan the species of interest by fullystripping the beam after accelerationbut prior to final energy analysis.Recently a new technique to purifySn and Ge beams was discovered atHRIBF, which is a variant of a chem-ical technique long employed atISOL facilities. The importance ofthis discovery follows from the criti-cal importance of pure beams of thedouble closed shell nucleus 132Sn,and the closed shell nucleus 82Ge tomany fields of RIB science. 132Sn isproduced along with a dominantbackground of 132Te and 132Se. Ifsmall quantities of sulfur are intro-duced to the production target (e.g.,as H2S), it is empirically found thatthe EPBIS produces a strong molecu-lar beam of 132SnS+, with no detec-table 132TeS+ or 132SeS+ contamina-tion. The same effect is seen with Geisotopes.

Particularly interesting radio-active beams have an intensity that isorders of magnitude lower than atypical stable beam, even after pro-duction and purification techniquesare carefully optimized. The HRIBF

has a remarkable suite of end stationsthat are well suited for RIB research.

The Recoil Mass Spectrometer(RMS) is the centerpiece of the nu-clear structure end station.2 Thisstate-of-the-art spectrometer sepa-rates reaction products from pri-mary beam and spatially separatesthe products by their mass-to-chargeratio. Many detector systems can beemployed with the RMS: CLAR-ION, an array of 11-segmentedClover Ge gamma-ray detectors;HYBALL, a 95-element CsI chargedparticle detectors which can be aug-mented by the forward array; For-ward Array, an annular array ofdouble-sided silicon strip detectorsin a ∆E-E arrangement; Microchan-nel Plate Detectors (MCP) for low-intensity beam diagnostics andcounting as well as large area posi-tion sensitive focal plane detectors;Double-sided silicon strip detectorsfor implantation and decay experi-ments such as ground state proton-and alpha radioactivity; CARDS,CLARION Ge detectors coupled tothe LSU Moving Tape Collector.

The Daresbury Recoil Separator(DRS) is the centerpiece of the astro-physics end station. The DRS filterslow-energy capture reaction prod-ucts from primary beam throughvelocity selection and momentumanalysis. The annular silicon detec-tor array SIDAR is used for chargedparticle detection. MCPs and an ion-ization chamber are used to uniquelyidentify reaction products. A win-dowless gas cell will soon be coupledto the DRS and can produce ahydrogen target equivalent to ~15ug/cm2 (1019 atoms).

The Enge Spectrograph, whichmay be operated in either vacuum orgas-filled mode, is used for reactionstudies.

The RIB On-line Test Facility(OLTF) is used to test and evaluate

laboratory portrait


the performance of RIB targets andion sources using relatively low-in-tensity beams from the tandem.Along with our two off-line ionsource test facilities, the OLFT pro-vides us with excellent tools for thedevelopment of new or more intenseRIB beams.

The HRIBF is able to bring to-gether many different experimentaltechniques because it has a largenumber of flexible, highly efficientdetector systems that are designed towork together. This detector com-patibility gives us the selectivity andefficiency to make full use of ra-dioactive and stable ion beams.

Nuclear StructureOur nuclear structure program

is centered on studies of nuclei farfrom stability. Below we shall de-scribe some highlights of our recentexperimental results, as well as pos-sible directions for future studies.

Spectroscopy of Neutron-Rich Nuclei

Modifications of shell structureand novel excitation modes are ex-

amples of fascinating new phenom-ena that are predicted to occur inneutron-rich nuclei away from thestability line. These phenomena maybe explored using a number of reac-tions with n-rich RIBs available atHRIBF. To take advantage of thesebeams, we have developed new ex-perimental techniques and a power-ful suite of specialized detectors tocope with the weak intensities andisobaric contaminations of thebeams, as well as the high back-ground resulting from their decay. Ina series of pioneering γ spectroscopyexperiments, we have used thesebeams to perform Coulomb excita-tion, fusion, and transfer reactionstudies in the A ~ 80 and A ~ 130 re-gions. The results for Coulomb exci-tation of the first 2+ states in 126,128Snand 132,134,136Te nuclei with a 12C tar-get are shown in Figure 4. The ex-perimental B(E2) value for 136Te issignificantly smaller than the valueexpected from either the systematics(right panel), or shell model calcula-tions.3 These measurements, whichmay be performed with beam inten-sities of 103 pps, will soon be ex-

tended to 130Sn and doubly-magic132Sn, as well as to A ~ 80 nucleiclose to the N = 50 line.

Transfer reactions with RIBsprovide a powerful tool to probe theevolution of single-particle states andpairing strengths as one moves fromthe stability line. We have demon-strated the feasibility of such studieswith RIBs, using complementaryheavy-ion reactions of 9Be(134Te,8Be)and 13C(134Te,12C) to populate sev-eral previously unobserved states in135Te, including a new J = 5/2 statethat is an excellent candidate for thef5/2 orbital. We plan to extend suchstudies to other nuclei in the vicinityof 132Sn, using transfer reactions in-duced by n-rich RIBs incident onboth light and heavy targets.

Our first fusion-evaporation re-action with an n-rich RIB wasperformed using beams of 118Ag(106 pps) bombarding 9Be and 12Ctargets. Data collected consisted ofgamma-HYBALL and gamma-gam-ma-recoil coincidences. Fusion-evap-oration reactions leading to theknown nuclides (e.g., the 31/2- statein 125I) were observed, together with

laboratory portrait


Figure 4. Left: gamma-ray spectra from Coulomb excitation of 134,136Te RIBs. Right: systematics of the B(E2, 0 → 2)values as a function of neutron number. Our values for Sn and Te isotopes are shown as filled circles.

previously unobserved states in123Sb. It should be possible to studymore neutron-rich nuclei such as139Ba, 141La and 143Ce in the future.

Spectroscopy of Proton-Rich Nuclei

Because of the reinforcement ofthe proton and neutron shell effects,self-conjugate nuclei and their neigh-bors play a distinctively importantrole in nuclear structure. We have re-cently explored many fascinatingphenomena along the N ~ Z line, in-cluding: (a) the possible existence ofa proton-neutron superconductivephase in heavy self-conjugate nuclei,(b) deformed and superdeformedstructures that arise from multiparti-cle-multihole excitations across thedoubly magic 40Ca and 56Ni nuclei,which help elucidate the microscopicorigin of collective rotation, and (c)discovery of proton and alpha radio-activity from deformed excitedstates.4 Spectroscopic studies of nu-clei close to 100Sn remain one of themost important and challengingareas of nuclear structure physics.We have been able to obtain, for thefirst time, information about high-spin single-particle states in 99Cdand 101,102In, which involve particle-hole excitation across the 100Sn core.This information was used to testand improve results of large-scaleshell model calculations. The aboveexperiments were performed at theGAMMASPHERE in close collabo-ration with the experimental groupsat Washington University, Lund,McMaster, ANL, LBL, and Univer-sity of Tennessee.

At the HRIBF, our studies of nu-clei beyond the particle-stabilitylimit have concentrated on protonradioactivity. Five new proton emit-ting states were discovered, withfour of them having half-lives in themicrosecond range.5 Fine structure

in proton emission has been ob-served in the decays of 141Ho, 145Tmand 146Tmgs,m. These studies havehelped elucidate the problem of pro-ton tunneling through a deformedpotential, and compositions of wavefunctions of unbound resonantstates in exotic nuclei. A novel tech-nique, based on digital signal pro-cessing, has been developed, whichallows detection of radioactive de-cays within a few hundred nano-seconds. In future, proton- andalpha-radioactive nuclei with veryshort half-lives, such as those alongthe rp-process path, will be studiedwith this technique. This work hasbeen conducted in collaborationwith researchers from 10 institutionscomprising the UNIRIB consortium.

Experimental and theoretical nu-clear structure researchers at ORNLenjoy a strong synergy, and haveworked closely together to addressseveral issues related to the structureof far-from-stability nuclei includingcalculations to interpret excitationsacross the 100Sn core, and detailedtheoretical interpretations for thestructures of proton-emitting states.

Nuclear Reaction SpectroscopyIn recent years the emphasis of

the nuclear reaction group hasshifted to lower energy reactions in-duced by RIBs, and the developmentof the experimental techniques thatwould take advantage of thesebeams efficiently.

Studies of subbarrier fusion ofheavy ions provide opportunities toexplore tunnelling through multiplebarriers. We have reconfigured theEnge split-pole spectrograph as agas-filled separator, and we arepreparing instruments for studyingfusion-evaporation and fusion-fission reactions induced by neutron-rich RIBs. Systematic studies offusion with neutron-rich nuclei can

provide important information onthe production of super-heavy ele-ments.

Breakup is an important reac-tion channel in the scattering ofweakly bound-nuclei. How breakupaffects fusion near the Coulomb bar-rier remains an open question. Tobetter understand this problem, wehave measured the breakup of 17Fproduced at HRIBF from 10 MeV/nucleon to energies slightly abovethe barrier. A large yield of strippingbreakup, which arises from the ab-sorption of the valence proton by thePb target, was observed near thegrazing angle.6

We have begun a program tostudy resonant states in light nucleiwith RIBs bombarding thick targets.With this technique, we can map acomplete excitation function in onemeasurement. Our first experimentwith a 17F beam has led to the dis-covery of the simultaneous emissionof two-protons from excited states in18Ne.7 In addition, these measure-ments provide important informa-tion regarding the quantum numbersof resonance states in light unstablenuclei that are of astrophysical in-terest.

Nuclear AstrophysicsUnstable nuclei play an influen-

tial, and in some cases dominant,role in many phenomena in thecosmos such as novae, supernovae,X-ray bursts, and other stellar ex-plosions. In the extremely hightemperatures (>108 K) of these astro-physical environments, the inter-action times between nuclei can beso short (~ seconds) that unstablenuclei formed in a nuclear reactioncan undergo subsequent reactionsbefore they decay. Sequences of nu-clear reactions occurring in explod-ing stars are therefore quite differentthan sequences occurring at lower

laboratory portrait


temperatures characteristic of oursun. Measurements of the structureand reactions of unstable nuclei aretherefore required to improve ourunderstanding of the astrophysicalorigin of atomic nuclei and the evo-lution of stars and their sometimesexplosive deaths.

At the HRIBF, we are makingsome of the first precision measure-ments of reactions needed to probethe details of exploding stars. Wehave used RIBs of 17F and 18F tostudy important reactions including14O(α,p)17F, 17F(p,γ)18Ne, and18F(p,α)15O. Our approach of meas-uring multiple reaction channels,such as 18F(p,p)18F and 18F(p,α)15O,has resulted in excellent reaction ratedeterminations. The RIBENS Col-laboration (Radioactive Ion Beamsfor Explosive Nucleosynthesis Stud-ies), consisting of 20 members at 12institutions, is carrying out these ex-periments.

Our measurement of a thin-tar-get 17F(p,p)17F excitation function tobetter determine the 17F(p,γ)18Ne re-action rate exemplifies our indirectstudies. With a low-energy, high-quality 17F beam we found the cru-cial s-wave resonance in the 17F + psystem which had not been found in30 years of studies with stablebeams. Our precision measurementof the excitation energy and totalwidth of this level resolved an or-ders-of-magnitude uncertainty in the17F(p,γ)18Ne rate at high tempera-tures.8

While most astrophysical re-actions occur at center of mass en-ergies less than 2 MeV/u, higherenergy RIBs allow us to employ indi-rect techniques. For example, wemeasured a proton transfer reaction,14N(17F, 18Ne)13C, with a higher-energy 17F beam to help determinethe direct capture rate for the17F(p,γ)18Ne reaction.Other indirect

measurements requiring higher en-ergy beams include the inverse of thereaction occurring in an astrophysi-cal environment. For example, wemade a complete measurement of theexcitation function of the 17F(p,α)14Oreaction, spanning the energy rangeneeded for X-ray bursts. This allowsa better calculation of the 14O(α,p)17Freaction rate. Measurements of elas-tic and inelastic scattering of 17F andhydrogen were also needed to con-strain the 14O(α,p)17F reaction pro-ceeding to both the ground and ex-cited states of 17F.

We also put considerable effortinto improving the rates of the18F(p,α)15O and 18F(p,γ)19Ne reac-tions9 that determine the productionof the long-lived radioactive isotope18F in novae and may serve to con-strain nova models via observations

of the decay 511-keV gamma rays.We measured 18F(p,p)18F and18F(p,α)15O, at energies correspon-ding to two important 19Ne reso-nances. We resolved a serious dis-crepancy in the literature concerningone level (Figure 5), and made thefirst statistically significant measure-ment of the strength of another. Fur-ther investigations to search for mis-sing 19Ne resonances are planned.

Future experimental work willinvolve direct measurements of cap-ture reactions with the DRS, a massspectrometer optimized for astro-physics. For example, we will meas-ure the 7Be(p,γ)8B reaction to helpunderstand measurements of thesolar neutrino flux. We also plan todirectly measure 17F(p,γ)18Ne to de-termine the gamma partial width ofthe dominant s-wave resonance.

laboratory portrait


Figure 5. Excitation functions of the 18F(p,p)18F (top) and 18F(p,α)15O(bottom) for the 665-keV 19Ne resonance.

The experimental nuclear astro-physics effort at HRIBF is closelycoupled with nuclear data evalua-tions which determine the best ratesof reactions based on all availableinformation. The new rates areavailable, and new visualizationtools are being developed to accessreaction rate information. Theserates are then incorporated intoORNL astrophysical simulations todetermine the impact of our meas-urements and to guide future experi-ments. For example, our new17F(p,γ)18Ne rate changed the pre-dicted amount of 17O synthesized byup to a factor of 3 when averagedover the entire exploding star incomparisons to some previous pre-dictions, and by up to a factor of15,000 in the hottest portions of theexplosion. Our new 18F + p rateswere also found to change theamount of 18F produced in the hotzones of novae by a factor of 3 com-pared to other estimates; this has animpact on future observational con-straints on nova models.

The Theory ProgramThe theory program covers a

broad range of science includingstudies of the quantum many-bodyproblem, astrophysics, and nuclearphenomenology related to RHICand hadronic physics. We are alsovery fortunate to enjoy significantsupport from the Joint Institute forHeavy Ion Research which funds asignificant theory visitors program.

Understanding nuclei requiresone to solve the Schrodinger equa-tion for many interacting particles.While this statement is obvious, itsimplementation has been quite diffi-cult due to the computational dif-ficulties involved in the solution ofthe problem.

The quantum many-body prob-lem may be solved in several waysand with various levels of approxi-

mation. One successful approachhas been to use quasiparticle mean-field theory that includes Skyrmeinteractions and a self-consistentpairing field. Our group has recentlyimplemented deformed Hartree-Fock-Bogoloubov calculations usingthe parallel computational facilitiesat ORNL. These facilities allow usto calculate in one day a mass anddeformation table for 3,000 nuclei,as shown in Figure 6.

We also investigate methods tosolve the quantum many-body prob-lem using quantum Monte Carloalgorithms (such as Auxiliary FieldMonte Carlo), parallel shell modeldiagonalization, and Coupled Clus-ter theory. Recently we began in-vestigations of the continuum shell-model using the Berggrencomplex-energy basis and DensityFunctional Renormalization Groupmethods. All of these efforts requiresignificant computational resources.

Our astrophysics effort prima-rily focuses on the evolution of corecollapse supernovae. The search forthe explosion mechanism of core

collapse supernovae is one of theimportant and challenging problemsin computational astrophysics. Corecollapse supernovae are among the most energetic explosions inthe Cosmos, releasing tremendousamounts of energy in the form ofneutrinos of all flavors, disruptingstars more massive than ten suns anddisseminating and producing manyof the elements in the periodic table,without which life as we know itwould not exist. Understanding theseevents requires input from numerousareas of science including nuclearand particle physics, general relativ-ity, radiation transport, and fluiddynamics. Our major contributionhere has been to fully incorporateBoltzmann neutrino transport andgeneral relativity into the simula-tions of the core collapse. We alsoincorporate nuclear structure infor-mation on weak processes in nucleiinto our core collapse simulations.

Our theory effort also focuses onthe phenomenology of RHIC colli-sions, and in particular on open-charm production and J/Ψ suppres-

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Figure 6. Chart of the even-even nuclei showing deformation. Calculationswere performed with HFB. Green: spherical. Red: prolate. Blue: oblate.From Stoitsov et al., in preparation.

AU: Fig.legendrefers tocolors.This is aB&Wmaga-zine.Pleaseupdate.Also, artis low-res.

sion that are used as probes of thesecollisions. Calculations of in-medium hadronic cross sections thatwill be important to disentangle thesignals obtained from the experi-mental program constitute a majorportion of our RHIC theory effort.

ORNL at PHENIXThe Physics Division has partici-

pated since the beginning in thePHENIX Experiment at the Brook-haven Relativistic Heavy-Ion Col-lider (RHIC). Major goals of RHICare to produce collisions in whichthe entrance-channel nucleons un-dergo a phase transition to a decon-fined state of quarks and gluons, theso-called quark-gluon plasma, tostudy this novel state of matter, tolearn about the detailed phase dia-gram of QCD, and to determine ifmore than one “partonic” phase ex-ists. PHENIX is one of the two largeexperiments located at RHIC and isdesigned particularly to detect pene-trating probes of the system pro-duced. Such penetrating probes, in-cluding direct photons and leptonpairs, are not perturbed by the final-state hadronic evolution of the cre-ated system and thus carry out in-formation from the early time of thecollision. The collision energies atRHIC are high enough that initial-state scattering of the entrance-chan-nel partons can be detected by look-ing for the resulting partons tomanifest themselves as jets havinghigh-pT particles. The energetic scat-tered partons are most likely to becreated at the start of a collision andwould find themselves propagatingthrough deconfined matter prior tohadronization.

PHENIX was conceived as apair of central-rapidity spectrome-ters that could observe photons,electrons, and identified hadrons inthe central unit of rapidity, coupledwith two endcap spectrometers that

could identify muons; a photographof the central magnet and one cen-tral spectrometer arm is shown onthe cover illustration of this issue.

The Physics Division at ORNLparticipated in the design and con-struction of the lead-glass electro-magnetic calorimeter in PHENIX.The final spectrometer arm will becompleted in the summer of 2002.Physics also designed the muon iden-tifier section of the PHENIX muonarms and has collaborated on itsconstruction, installation, and oper-ation. The Physicsand Instrumenta-tion & Controls Divisions at ORNLhave collaborated throughoutPHENIX in designing and buildingelectronics for six of the PHENIXsubsystems; this included manufac-ture of some 60,000 custom analogintegrated circuits of 6 differenttypes and design and constructionand installation of over 2,200 circuitboards for front-end electronics.

During 2001 PHENIX measuredAu-Au collisions at 200 GeV/nu-cleon pair as well as polarized pro-ton collisions at 200 GeV. Somedozen papers have been submittedfrom this first run period. One inter-

esting result, new to RHIC, is pre-sented in Figure 7. One examines therate of high-pT particle productionand compares it to the expected ratedetermined either by scaling up p-pcollisions at the same center-of-massenergy by the number of binary nu-cleon-nucleon collisions, or by scal-ing from the rates seen in peripheralAu-Au collisions. Surprisingly, theproduction rate of such high-pTevents in central Au-Au collisions isless than expected from scaling thesimpler colliding systems. This is notseen in Pb-Pb collisions at 6.5 timeslower bombarding energy at theCERN SPS, which is shown in theupper curves in Figure 7. Instead, inthat case one sees a moderate in-crease in production with ever largerpT, the so-called “Cronin effect”noted in p-A collisions, which seemsto herald only multiple-scattering ofthe partons. Instead, at RHIC, a de-pletion in rate is observed.10 This hasled to the speculation that one is ob-serving a consequence of increasedenergy loss of fast partons in a col-ored medium, perhaps the so-called“jet-quenching” which is predictedfor partons propagating in a QGP.

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Figure 7. High pT events at RHIC.

Significant further work studying thiseffect, especially via jet-jet or photon-jet correlations, is needed to estab-lish any proposed interpretation.

Neutron ScienceOak Ridge is poised to become a

world-class center for neutron re-search with the addition of a coldsource to the High Flux Isotope Re-actor (HFIR) and with the construc-tion of the Spallation NeutronSource (SNS). When completed nextyear the new HFIR (85 MW) coldsource will have a brightness (~1016

n/s/cm2/sr/eV) comparable to that atthe ILL—the brightest in the world.When the SNS (target power 1.4MW) comes on line in 2005/2006 itwill provide pulsed neutron beamsover an order of magnitude more in-tense than available at the best exist-ing spallation sources (LANSCE andISIS). Although the focus of bothprojects is on traditional neutronscattering experiments, they presentsignificant opportunities to makemajor improvements to the measure-ment of fundamental properties ofthe neutrons themselves. The PhysicsDivision is in the process of securingfunding to establish dedicated fun-damental neutron measurement fa-cilities at both HFIR and at theSNS. These facilities will enable arich variety of experiments, a signif-icant part of the emerging nationalprogram in fundamental neutronphysics.

As the simplest of all radioactivedecays the beta-decay of the freeneutron provides an excellent labo-ratory for the study of the weaknuclear interaction. Precision meas-urements of neutron decay parame-ters can be directly related to thefundamental parameters of the un-derlying quark-lepton weak inter-action and can be used to providepowerful tests of the Standard

Model (SM). A significantly im-proved measurement of the neutronelectric dipole moment could per-haps find a clear sign of time-reversalinvariance violation at a level signifi-cantly greater than SM predictions.Measurements of parity violatingquantities such as the asymmetry inthe process n + p → d + γ and neu-tron spin rotation in light nucleartargets would provide values forhadronic weak coupling constantsand would shed light on current in-consistencies.

Experiments to measure some ofthese quantities are best sited at a re-actor. Others are best sited at a spal-lation source. Both benefits are ulti-mately due to the a priori knowledgeof the neutron energy at a spallationsource (through time-of-flight infor-mation). Backgrounds are also typi-cally lower at a spallation source. Inaddition, some are best performedwith Ultra-Cold neutrons (defined ashaving low enough energy that theyare totally externally reflected, ~100neV). Such neutrons can be pro-duced by illuminating superfluid4He, which serves both as superther-mal source and as detector, with 8.9A neutrons.

SummaryDuring the last 10 years the

Physics Division at ORNL hasstrengthened its position as a worldleader in nuclear physics: the HRIBfacility came on line and now pro-duces excellent, high-quality ra-dioactive beams for both nuclearstructure and astrophysics research.Research activities at HRIBF are en-hanced by a strong external-userscommunity and our unique asset, theJoint Institute for Heavy-Ion Re-search.11 We have established astrong effort in theoretical researchin both nuclear structure and astro-physics phenomena. The Phenix col-

laboration began last year to pro-duce exciting data that will shedlight on the formation and proper-ties of the quark-gluon plasma.

We also look forward to a brightfuture. We anticipate significant sci-ence coming from HRIBF during thenext ten years, and new scientificdiscoveries emanating from ourfledgling program in neutron scienceto our theoretical programs in nu-clear science and astrophysics.

AcknowledgmentOak Ridge National Laboratory

is managed by UT-Battelle LLC,under contract number DE-AC05-00OR22725, for the U.S. Depart-ment of Energy.

References1. For further information see http://

www.phy.ornl.gov/hribf/2. C. J. Gross et al., Nucl. Instrum. and

Methods in Phys. Res. A 450, 12(2000).

3. D. C. Radford et al., Phys. Rev. Lett.88, 222501 (2002).

4. D. Rudolph et al., Phys.Rev. Lett.80, 3018 (1998); 86, 1450 (2001).

5. K. Rykaczewski et al., Nucl. Phys.A682, 270c (2001).

6. F. Liang et al., Phys. Rev. C65,O51603(R) (2002).

7. J. Gomez del Campo et al., Phys.Rev. Lett. 86, 43 (2001).

8. ASTRO2: D. W. Baradayan et al.,Phys. Rev. Lett. 83, 45 (1999).

9. D. W. Bardayan et al., Phys. Rev.C63 (2001) 065802.

10. K. Adcox et al., Phys. Rev. Lett. 88,022301 (2002).

11. For further information see http://web.utk.edu/~bingham/jihir.html.

Contributors to this article include:

C. BAKTASH, J. BEENE, V. CIANCIOLO,D. J. DEAN, C. GROSS, M. S. SMITH,

AND G. R. YOUNG

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IntroductionRecently, a new concept, called “critical point sym-

metry,” has been introduced to elucidate the nature ofquantum phase transitions in many-body systems [1],[2]. In a series of experiments at several Laboratoriesboth in the United States and in Europe (the A. W.Wright Nuclear Structure Laboratory of Yale University,the University of Köln in Germany, the LaboratoriNazionali di Legnaro in Italy, the Institut Laue-Langevinin Grenoble, France), strong evidence for the occurrenceof these symmetries in nuclei has been found [3], [4].

Shape Phase TransitionsSeveral many-body systems (nuclei, molecules,

atomic clusters, macromolecules, polymers, etc.) displayphase transitions whenever the geometric configurationof the system changes. For example, in molecules, phasetransitions occur whenever the structure changes fromlinear to non-linear or from planar to a-planar or from ageometry with point group C to one with point groupC�. These phase transitions are called “shape” phasetransitions. One of the best studied cases of shape phasetransitions is that occurring in nuclei, where the geomet-ric configuration changes from spherical to quadrupoledeformed either with or without axial symmetry. Phasetransitions are described in terms of sharp changes insome quantity, called the order parameter, describing thestructure of the system, as a function of another quan-tity, called the control parameter. The order parameterfor shape phase transitions in nuclei is the quadrupoledeformation β. (There is another order parameter asso-ciated with distortions from axial symmetry, sin γ, butthis will not be discussed here.) For quantum phasetransitions the control parameter is the value of the di-mensionless coupling constant that appears in front ofthe interaction driving the transitions (in nuclei thequadrupole-quadrupole interaction). Figure 1 shows theexperimental values of B(E2;2+ → 0+) ~ β2 as a functionof the valence neutron number for some rare-earth nu-clei. The sudden jump at valence neutron number ~6 isindicative of a phase transition. (The control parameteris related to the number of valence particles.)

Although nuclei are finite systems and thus cannotexhibit phase transitions in the true sense of the word,nonetheless phase transitions can be defined in the clas-sical limit in which the number of particles, N, goes toinfinity. Numerical simulations of quantum phase transi-tions within the framework of algebraic models (the In-teracting Boson Model in Nuclear Physics [5], [6] andthe Vibron Model in Molecular Physics [7], [8]) showthat, even for small systems, the order parameter in-creases sufficiently fast as a function of the controlparameter to be able to detect experimentally “shape”phase transitions (Figure 2). The only difference betweenfinite and infinite systems is that in infinite systems thereis a discontinuity in some quantity while in finite systemsthe discontinuity is smoothed out. (This statement ap-plies also to other phase transitions in nuclei, such as theliquid-gas transition, and to other finite quantum sys-tems. It has been verified experimentally in molecules bymeasuring the specific heat of small water droplets withN ~ 10.)

Quantum phase transitions are best studied bymeans of algebraic models. In condensed matter physics,the Ising model, for example, has provided a deep un-derstanding of phase transitions in spin systems. The

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Critical Point Symmetries in NucleiFRANCESCO IACHELLOCenter for Theoretical Physics, Sloane Laboratory, Yale University

Figure 1. Experimental B(E2; 2+ → 0+) values as a func-tion of neutron number for some rare-earth nuclei,showing a sudden jump at neutron number 90, indica-tive of a shape phase transition.

shape phase structure of nuclei was indeed studied in theearly 80’s within the framework of the classical limit [9],[10], [11] of the Interacting Boson Model [5], [6]. (Thephase structure of nuclei when the proton-neutron de-gree of freedom is included was also studied, but will notbe presented here.) The situation is best discussed interms of a phase diagram [12], as shown on the left inFigure 3. Here the three dynamic symmetries of the In-teracting Boson Model, U(5), SU(3), and O(6), areschematically shown at the vertices of a triangle, calledCasten’s triangle. The classical limit of these symmetriesshows that they correspond to spherical shape, U(5), de-formed shape with axial symmetry, SU(3), and deformedshape without axial symmetry (the so-called γ-unstableshape), O(6).

The studies performed in the 80’s demonstrated thatthere is a line of first-order transitions ending in a pointof second-order transitions separating the spherical fromthe deformed “phase” (Figure 3) [9], [12]. The order ofthe phase transition is defined here in the usual way(Ehrenfest classification); that is, if the energy of theground state as a function of the control parameter isdiscontinuous at the critical point, the phase transition issaid to be of zeroth order, if the first derivative is dis-continuous it is said to be first order, if the second deriv-ative is discontinuous it is said to be second order, etc.(This is in the classical limit N → ∞.) For first-order

transitions, there is a region of coexistence of the twophases, well known from thermodynamic phase transi-tions (liquid-gas, for example). This region is alsoschematically shown in Figure 3. The coexistence regionshrinks to a point at the second order transition.

Several experimental studies performed in the 80’sshowed that indeed the situation described by Figure 3 iswhat actually happens in nuclei [6]. For example, the oc-currence of a first-order shape transition in nuclei can bedetected by plotting the derivative of the ground stateenergy, i.e., the separation energy, here the two-neutronseparation energy, S2n, as a function of the control pa-rameter (or a function of it, here the valence neutronnumber). This quantity is discontinuous in a first-ordertransition. Figure 4 shows the experimental values forthe Sm isotopes. The occurrence of a first-order transi-tion is clearly visible.

Critical Point SymmetriesIn understanding the nature of phase transitions an

important question is what is the structure of the spec-trum of a system at the critical point of a second-orderphase transition or in the coexistence region of a first-order transition. This question has been extensively in-vestigated within the framework of algebraic models. Asalready shown in 1978 [13], the Interacting BosonModel provides an accurate description of shape phasetransitions in nuclei. Recent calculations [14], [15] haveconfirmed that the entire transition region can be welldescribed by simple algebraic Hamiltonians. However,the description of the critical region is obtained by nu-merical diagonalization of the Hamiltonian. One maywonder whether the nature of the spectrum at the criti-cal point can be understood from general argumentsbased on some “symmetry” of the problem. This ques-tion has not been investigated, except from some generalstatements within the framework of quantum field theo-ries, where the structure at the critical point is associatedwith conformal invariance. Without going into details ofwhat conformal invariance in quantum field theory is,the net results of these arguments is that the “symmetry”of the problem reduces the number of parameters by oneand the properties of the system at the critical point aregiven only in terms of a scale.

Recently, I have suggested that, within the frame-work of quantum mechanics (i.e., a Schrödinger-likeequation), the structure of the spectrum at the criticalpoint can be associated with Euclidean invariance withina certain domain [1]. The physical argument for this sug-gestion is that at the critical point of a second-order tran-sition the potential as a function of some coordinate

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Figure 2. The order parameter ⟨nd⟩ ~ β2 a function of thecontrol parameter η for various numbers of particles N,for the second-order spherical to γ-unstable transition(U(5) to O(6)). From numerical diagonalization of theInteracting Boson Model Hamiltonian. Courtesy of N. V.Zamfir.

(here β) is flat and it can be approximated by a constant(in one dimension a square-well potential). The Hamil-tonian for a flat potential is just the kinetic energy, whichis invariant under Euclidean transformations. Twomajor consequences of this suggestion (referred hereafteras “critical point symmetry”) are that the spectrum of

the system at the critical point of a second-order transi-tion is given in terms only of a scale parameter, and,most importantly, the energy eigenvalues and other ob-servables both for first- and second-order transitions canbe given in explicit analytic form.

The suggestion of a possible occurrence of criticalpoint symmetries in nuclei has stimulated considerablework both theoretical and experimental. On the theoret-ical side, a detailed investigation of the structure of nu-clei in the critical region of second- and first-order shapetransitions has been initiated. As mentioned above, crit-ical point symmetries are analyzed best within the frame-work of a differential (Schrödinger-like) equation. In thecase of collective quadrupole shapes in nuclei, a conven-ient differential equation is the Bohr equation [16]. Twosituations have been so far investigated:

(i) The structure of the spectrum at the critical pointof the second-order transition between U(5) and O(6)(spherical to γ-unstable transition), called E(5) [1]. It hasbeen found that the spectrum is given by the simple for-mula

E(s,τ) = A1(xs,τ )2,

where xs,τ is the sth zero (s = 1, 2, 3, . . .) of the Besselfunction Jτ+3/2(z) of half-integer order τ + 3/2. The quan-tum number τ(τ = 0, 1, 2, . . .) labels the irreducible rep-resentations of O(5), which is an exact symmetry forspherical and γ-unstable nuclei. This formula explicitly

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Figure 3. Left-hand side: Schematic representation of thephase structure of the Interacting Boson Model-1. Thethree dynamic symmetries of this model are placed at thevertices of the triangle. Adapted from Feng, Gilmore andDeans [12]. Right-hand side: Schematic representation ofthe results obtained recently [1], [2]. The two new “sym-metries” are placed on the side of the triangle and in thecoexistence region. The dynamic symmetry U(5) that canbe also obtained as a solution of the Bohr Hamiltonianis placed at one of the vertices of the triangle.

Figure 4. Experimental values of the two-neutron sepa-ration energies, S2n, as a function of neutron number, in-dicative of a first-order shape phase transition.

tally in 152Sm it lies at 5.62 times; see Figure 6. The ver-ification of parameter-independent (universal) propertiesis evidence for the occurrence of “critical point sym-metries” in nuclei. There is no a priori reason (in bothmicroscopic and macroscopic models) why the ratio ofvibrational to rotational excitation energies should be5.67. It is a consequence of a “critical point symmetry,”wherein the energies of states are given by zeros of Besselfunctions of a particular order. The evidence presented in[4] has been reinforced by an even more recent experi-ment in 150Nd by Krücken et al [20] and it appears to ex-tend to the set of nuclei 150Nd-152Sm-154Gd-156Dy, lyingon the line of first-order transitions in the phase diagramof Figure 3. Experiments are being planned to elucidatethe nature of this phase transition even further, both inthe rare-earth region and in other regions of the periodictable.

Implications for Other FieldsThe concept of “critical point symmetry” is being

applied to other fields, most notably molecular physics.Here the transition from linear to non-linear shapes hasbeen studied and the corresponding formulas applied tothe analysis of spectra of several molecules. It has beenfound [21] that fulminic acid, HCNO, lies very close tothe critical point of a second-order shape phase transi-

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Figure 5. Comparison between the excitation energiesof states in the ground state band of the set of nuclei150Nd-152Sm-154Gd-156Dy as a function of the angularmomentum L and the corresponding expression forX(5). The difference between the data and either theharmonic vibrator, E(L) = aL, or the axial rotor, E(L) =bL(L + 1), should be noted. The extent to which thedata agree with the new formula E(L) = A2(xs,L)2 is anindication of the occurrence of “new symmetries.”

shows that the spectrum is given in terms only of a scaleparameter, A1.

(ii) The structure of a portion of the spectrum in thecoexistence region of the first-order phase transition be-tween U(5) and SU(3) (spherical to deformed with axialsymmetry), called X(5) [2]. This phase transition is muchmore complex than the transition from spherical to γ-un-stable shape for two reasons: (a) the transition is firstorder; (b) the transition involves simultaneously twovariables, β and γ. In nuclei, however, the potential humpseparating the two coexisting minima is very small (see,for example, Figure 4 of [17]) and the transition can betreated effectively as a second order. Also, the two vari-ables can be (approximately) decoupled. The portion ofthe spectrum involving the variable β is given by the for-mula

E(s,L) = A2(xs,L)2

where xs,L is the sth zero (s = 1, 2, 3, . . .) of the Besselfunction Jv(z) with

v = � + �1/2

.

Note that the order here is an irrational number. L is theangular momentum quantum number (L = 0, 2, 4, . . .)of each state and again energy levels are given in termsof a single scale, A2.

Both predictions have recently been tested by a seriesof experiments performed at various laboratories.

(i) Casten and Zamfir [3] have shown that the spec-trum of 134Ba (as well as its E2 transition rates) can wellbe described by the E(5) formula. A search for other nu-clei lying at the critical point of the second-order spher-ical to γ-unstable transition is currently under way. Can-didates are some isotopes of Xe, Pd [18], and Ru [19].

(ii) The region of coexistence of the first-order spher-ical to axially deformed transition has received most ofthe attention, in view of its intricate nature and the factthat it is easily accessible in rare-earth nuclei, Nd-Sm-Gd-Dy. Casten and Zamfir [4] have shown that the βpart of the spectrum in 152Sm (as well as its E2 transitionrates) can be described very well by the X(5) formula.The agreement between the formula and data is not lim-ited to the behavior of the energies of the ground stateband (s = 1) with L, shown in Figure 5, but it extendsalso to the location of the β-vibrational excitation. Inthis case, the X(5) spectrum contains a parameter-inde-pendent prediction that has been verified experimentally:the energy of the first excited 0+ level is predicted to beat 5.67 times the energy of the first 2+ state. Experimen-

9–4

L(L + 1)––3

tion between linear and non-linear (bent) configurations.This molecule thus plays the role in molecular physicsthat 134Ba plays in nuclear physics. The same conceptcan, in principle, be used for a variety of systems includ-ing atomic clusters, macromolecules, and polymers. Forsecond-order transitions, in n ≥ 2 dimensions, spectraare given by the universal formula [22]

E(s,τ) = A(xs,τ)2,

where xs,τ is the sth zero of Jv(z) with v = τ + (n – 2)/2 (in-teger or half-integer). From this point of view, symme-tries at the critical point are another example of symme-tries theoretically introduced and experimentally foundin nuclear physics and later used in other fields.

Open ProblemsThe introduction of the new concept of “critical

point symmetries” opens up a wealth of problems. (i)The derivation of the equations given above has beendone in the limit N → ∞. In nuclei, the number of parti-cles is finite. This problem has been investigated byCaprio, who has found that finite N effects are not im-

portant for the low-lying states [23] for the case of E(5).(ii) Also, in nuclei, the transition operator cannot be sim-ply taken as linear in the variable β, but β2 terms are im-portant. This problem has been solved by Arias [24],who has calculated the β2 contribution to E2 transitionrates and found in 134Ba better agreement with experi-ment. (iii) The description given above for the U(5) –SU(3) transition is only in terms of one variable β. Theinclusion of the γ degree of freedom in a consistent fash-ion has been investigated and the corresponding formu-las will be published soon [25]. (iv) The coupling be-tween β and γ degrees of freedom needs to be studiedand introduced in this context (it was studied years agowithin the context of the Interacting Boson Model). (v)The effect on the spectra of the small hump in the po-tential description of the first-order, U(5) – SU(3), shapephase transition needs to be investigated (again, this ef-fect has been studied within the context of IBM [17]).(vi) Finally, the connection between the differential real-ization of critical point symmetries and their algebraiccounterparts needs to be investigated. This connectionwill allow one to describe both types of symmetries, theusual dynamical symmetries, U(5), SU(3), SO(6), and

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Figure 6. Comparison between the energy and transition rates of the β part of the spectrum of 152Sm and X(5). FromCasten and Zamfir [4]. The two experimental ratios E(02)/E(21) = 5.62 and E(41)/E(21) = 3.01 should be comparedwith the parameter free predictions of X(5), 5.67 and 2.91, respectively, and are a measure of how well the “criti-cal symmetry” is realized in these nuclei.

the “critical point symmetries,” E(5) and X(5), withinthe same framework. At the moment, they lie on differ-ent parameter spaces, as shown schematically on theright-hand side of Figure 3.

ConclusionsIn conclusion, a new concept, “critical point symme-

tries,” has been introduced. This concept produces newbenchmarks (explicit solutions in terms of quantumnumbers) for studies of nuclear spectra, in which the so-lutions for energy levels and transition rates are param-eter free, except for an overall scale. The occurrence ofcritical point symmetries has been experimentally estab-lished in nuclei. This finding has been made possible bythe development of very sensitive γ-ray detector systems,such as the YRAST-Ball at Yale, and of techniques formeasuring nuclear level lifetimes with Döppler-basedmethods. These have allowed a much more accurateanalysis of the spectra of nuclei. It is yet another exam-ple of how the improvement of experimental techniquesthat has been occurring in nuclear physics is providing adeeper understanding of physics and of how theoreticalideas developed in nuclear physics have a wide range ofapplication to other quantum systems.

AcknowledgementsThis work was supported in part under D.O.E. Con-

tract No. DE-FG02-91ER-40608.

References1. F. Iachello, Phys. Rev. Lett. 85, 3580 (2000).2. F. Iachello, Phys. Rev. Lett. 87, 052502 (2001).3. R. F. Casten and N. V. Zamfir, Phys. Rev. Lett. 85, 3584

(2000).4. R. F. Casten and N. V. Zamfir, Phys. Rev. Lett. 87, 052503

(2001).5. F. Iachello, in Nuclear Structure and Spectroscopy, H. P.

Blok and A. E. L. Dieperink, eds. (Scholar’s Press, Amster-dam, 1974), p. 163; A. Arima and F. Iachello, Phys. Rev.Lett. 35, 1069 (1975).

6. F. Iachello and A. Arima, The Interacting Boson Model(Cambridge University Press, Cambridge, 1987).

7. F. Iachello, Chem. Phys. Lett. 78, 581 (1981).8. F. Iachello and R. D. Levine, Algebraic Theory of Mole-

cules (Oxford University Press, Oxford, 1995).9. A. E. L. Dieperink, O. Scholten and F. Iachello, Phys. Rev.

Lett. 44, 1747 (1980).10. J. Ginocchio and M. Kirson, Phys. Rev. Lett. 44, 1744

(1980).11. A. Bohr and B. R. Mottelson, Phys. Scr. 22, 468 (1980).12. D. H. Feng, R. Gilmore and S. R. Deans, Phys. Rev. C23,

1254 (1981).

13. O. Scholten, F. Iachello and A. Arima, Ann. Phys. (N. Y.)115, 325 (1978).

14. J. E. Garcia-Ramos, C. De Coster, R. Fossion, and K.Heyde, Nucl. Phys. A688, 753 (2001).

15. N. V. Zamfir, P. von Brentano and R. F. Casten, to be pub-lished.

16. A. Bohr, Mat. Fys. Medd. K. Dan. Vidensk Selsk. 26, No.14 (1952).

17. F. Iachello, N. V. Zamfir and R. F. Casten, Phys. Rev. Lett.81, 1191 (1998).

18. N. V. Zamfir, M. A. Caprio, R. F. Casten, C. J. Barton,C. W. Beausang, Z. Berant, D. S. Brenner, W. T. Chou, J. R. Cooper, A. A. Hecht, R. Krücken, H. Newman, J. R.Novak, N. Pietralla, A. Wolf and K. E. Zyromski, Phys.Rev., in press (2002).

19. A. Frank, C. E. Alonso, and J. M. Arias, Phys. Rev. C65,014391 (2001).

20. R. Krücken, B. Albanna, C. Bialik, R. F. Casten, J. R.Cooper, A. Dewald, N. V. Zamfir, C. J. Barton, C. W. Beau-sang, M. A. Caprio, A. A. Hecht, T. Klug, J. R. Novak, N.Pietralla, P. von Brentano, to be published.

21. F. Perez-Bernal and P. Vaccaro, in preparation.22. F. Iachello, in Testimonios por Marcos Moshinsky, A.

Frank and K. B. Wolf, eds., A. Sanchez, Mexico (2001),p.107.

23. M. A. Caprio, Phys. Rev. C, in press (2002).24. J. Arias, Phys. Rev. C63, 034308 (2001).25. F. Iachello, in preparation.

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FRANCESCO IACHELLO

AU: Pleaseupdate #’s15, 18, 20,21, 23, 25,if possible.

IntroductionDensity functional theory (DFT) in quantum chem-

istry is a method for calculating ground state propertiesof atoms and molecules from first principles. It was in-vented by Walter Kohn and his collaborators Pierre Ho-henberg and Lu Sham in 1964 and 1965 and has beendeveloped to the level where it is accurate enough to playan important role in atomic physics, in chemistry, andeven in biochemistry. Kohn shared the Nobel Prize inChemistry in 1998 in recognition for this important con-tribution. One of the aims of this article is to explain thebasic ideas behind the Kohn-Sham density functionalmethod. Another is to compare it with Skyrme Hartree-Fock theory in nuclear physics, which dates back to pa-pers published by Tony Skyrme in 1957. A third is toreview some recent developments.

An atom or a molecule consists of electrons and a nu-cleus or nuclei interacting by Coulomb forces and awave function which satisfies the Schrödinger equation.In principle it should be possible to solve this equationand to calculate properties of the atom or molecule fromfirst principles. As pointed out by Dirac in 1929 thedifficulty lies in the fact that, except for the simplestsystems, the Schrödinger equation is too complex to besolved. This is because the wave function is a multi-dimensional function depending on the positions andspins of all the electrons and nuclei.

The Born-Oppenheimer approximation gives a bigsimplification to the theory of molecular structure. Thenuclei in a molecule move slowly compared with theelectrons, and the Born-Oppenheimer approximation as-sumes that the electron wave functions can be calculatedfor fixed positions of the nuclei. The equilibrium shapeof the ground state of the molecule is obtained by mini-mizing the energy with respect to the positions of thenuclei. The Hartree-Fock approximation is another sim-plification. The wave function of an atom or moleculewith n electrons is approximated by an antisymmetrizedproduct of single electron wave functions. The antisym-metrization ensures that the restrictions imposed by thePauli principle are satisfied. It depends only on n singleparticle wave functions, one for each electron. The Har-

tree-Fock approximation includes the effects of Paulicorrelations, but not other many-body correlations.

Density functional theory takes a different tack. Itfocuses on the electron density ρ(r), which is a functionof one position variable r rather than the electron wavefunction Ψ(r1σ1, r2σ2, . . . , rnσn) which is a function ofthe positions and spins of each of the n electrons andargues that the ground state energy of the molecule is de-termined by ρ(r).

An approximation to the quantum mechanics ofelectrons in an atom was suggested in 1927 by Thomasand Fermi. They argued that the ground state energy ofthe electrons in an atom could be approximated by afunction of the electron density

E[ρ(r)] = EKTF[ρ(r)] + EC[ρ(r)]. (1)

The first term in (1) is the Thomas-Fermi approxi-mation to the kinetic energy of the electrons; the secondIn Thomas-Fermi theory, the kinetic energy of the elec-trons is approximated by

EKTF[ρ(r)] = (3π2)2/3�d3rρ(r)5/3 (2)

with the constraint that the atom contains n electrons

�d3rρ(r) = n. (3)

The Thomas-Fermi approximation for the Coulombenergy is

EC[ρ(r)] =��d3rd3r�

+ �d3r . (4)

The first term is the electron-electron Coulomb in-teraction and the second represents the Coulomb inter-action of the electrons with the nucleus of the atom. Theequilibrium ground state energy and density are ob-tained by minimizing E[ρ] in (1) with respect to ρ(r)subject to the constraint in (2). Thomas-Fermi theory

Ze2ρ(r)––r

e2ρ(r)ρ(r�)–––

r – r�

3–5

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Density Functional TheoryD. M. BRINK

Department of Physics, Oxford University

AU:Pleasecompletethesentence.

predicts a scaling behaviour for bulk properties ofatoms. For example, the radius of an atom is propor-tional to Z-1/3. Heavy atoms are smaller than light ones.

The Kohn-Sham density functional theory for anatom can be thought of as an extension of the Thomas-Fermi model. In practical terms the energy functional inKohn-Sham theory is similar to (1) but makes a betterapproximation to the kinetic energy and includes an ex-change-correlation energy.

Kohn-Sham Density Functional TheoryThe starting point of the Kohn-Sham density func-

tional method is the theorem of Hohenberg and Kohn[1] published in 1964, which gave the theoretical foun-dation of their approach. The Hamiltonian for an atomor molecule contains the kinetic energy of the electrons,the Coulomb interaction between the electrons and aone-body potential v(r) which includes the Coulomb in-teraction energy of the electrons with the nuclei, andpossibly an external field. Hohenberg and Kohn provedthat the exact ground state electron density uniquelyspecifies v(r). Since the Coulomb interaction are knownit was concluded that the ground state density ρ(r) spec-ifies the hamiltonian and therefore all the properties ofthe ground state. Stated another way, they proved the ex-istence of a functional E[ρ], which gives the exactground state energy for a given ground state density. Theminimizing E[ρ] is a variational principle which gives theexact ground state energy and density and, indirectly, themany electron ground state wave function.

Of course, all this is too good to be true. The diffi-culty is that specifying the functional E[ρ] would requirea complete solution of the quantum mechanical many-body problem for the atom or molecule. Kohn and Sham[2] bypassed this problem by using physical argumentsto fix an approximate energy functional which is re-markably good. Their energy functional consists of threeparts:

E[ρ] = EK[ρ] + EC[ρ] + EXC[ρ]. (5)

The single particle density matrix is written in diagonalform

ρ(r, r�) = �i

niφi(r)φi*(r�). (6)

The eigenstates φ(r) of the single particle density ma-trix form an orthonormal set of single particle states andthe Pauli principle requires that the occupation numbers

ni ≤ 2. The total number of electrons is Σi ni = Z. Thekinetic energy of the electrons is

EK[ρ] = ni �i

ni � d3r∇φi(r)2. (7)

This expression for the kinetic energy is exact but theoccupation numbers are unknown. In their 1965 paperKohn and Sham [2] assumed that the eigenstates are ei-ther fully occupied (ni = 2) or unoccupied (nI = 0). Otherchoices are possible. The remaining term in (5) is the ex-change-correlation energy. It can be calculated exactlyfor a uniform electron gas for any density ρ. Kohn andSham made the local density approximation and wrote

EXC[ρ] = � d3rρ(r)εXC(ρ(r)), (8)

where εXC(ρ(r)) is the exchange correlation energy den-sity for an electron density ρ(r). Now that the energyfunctional is specified, the ground state energy and elec-tron density can be computed by minimizing the energyfunctional with respect to the eigenstates φi of the singleparticle density matrix with the constraint (3) on thetotal number of electrons. This yields a set of equationsfor the single particle wave functions which are similarto Hartree-Fock equations.

The Kohn-Sham density functional theory resemblesHartree-Fock theory but there are important differences.Hartree-Fock theory is based on a Slater determinantwave function which is an approximation to the many-electron wave function. There is no Slater determinantwave function in Kohn-Sham theory. With Hartree-Focktheory one imagines that there should be corrections dueto zero point fluctuations. In Kohn-Sham DFT these arealready included. Hartree-Fock theory uses a non-localexpression for the exchange energy calculated with theSlater determinant wave function and there is nothing toinclude the effects of many-electron correlations. Kohn-Sham density functional theory includes the correlationenergy and the exchange energy in a local density ap-proximation.

Big advances in density functional methods havebeen made during the past 15–20 years. In a recent re-view on the application of DFT to transition metal prob-lems Koch and Hertwig [3] wrote:

It is beyond doubt that approximate DFT has ad-vanced in only a few years from and exotic methodhardly known to the average quantum chemist to oneof the most attractive tools in computational quantum

�2–2m

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AU: Wehave both“Sham”and“Scham”;editorchangedall to“Sham”through-out--OK?

chemistry and, in particular, to transition metal chem-istry. The reason for this is that DFT methods are notonly highly efficient, they are capable of giving resultswhich are in most cases superior to those obtainedwith much more demanding conventional ab initiomethods.

In their article they discuss the exotic moleculesCr(CO)6, Mo(CO)6, W(CO)6, and give results for bondlengths, bond dissociation energies, and molecular vi-brational frequencies. The theoretical results agree withexperiment to within a few percentage points. There aretwo main reasons for recent advances. One is the devel-opment of powerful numerical methods for representingthe wave functions and solving the Kohn-Sham equa-tions so that quite large molecules can be studied.Another is the development of accurate semi-empiricalexpressions for the exchange-correlation energy.

There is a multitude of applications in physics andchemistry. Some chemical applications have been re-viewed by Ching-Han Hu and D. P. Chong [4]. On the more physical side Yabana and Bertsch [5] haveapplied the time-dependent local-density approximation(TDLDA), a time-dependent version of density func-tional theory, to calculate the optical response for mole-cules like carbon chains, polyenes, benzine, and C60.Natatsukasa, Yabana, and Bertsch have used TDLDA tocalculate the shift and broadening of absorption lines ofCs atoms embedded in superfluid helium.

Skyrme’s Energy Functional for Nuclear Structure

The interaction between nucleons has been studiedintensively and is now quite well known. Potentialswhich have been fitted to nucleon-nucleon scatteringdata, and when supplemented by appropriate three-bodyforces, can describe the properties of nuclear matter andlight nuclei. For example, Pieper et al. [6] have added apion exchange three-nucleon interaction to the Argonnev18 realistic two-nucleon interaction and have calculatedthe energies of 17 bound or narrow resonance states ofnuclei with 3 ≤ A ≤ 8. The calculations use the Green’sfunction Monte Carlo method which gives an almostexact solution of the A-nucleon problem. The calcula-tions reproduce the observed energies with an rms error<1%. It is also possible with realistic forces to calculateproperties of heavier nuclei. Even though realistic nu-clear forces are very complicated, effective forces havebeen derived from them which can be used for shellmodel calculations in certain regions of the periodictable. For example, Elgaroy et al. [7] have calculated the

excitation energies of 2+ states in even Sn isotopes with102 ≤ A ≤ 130 with a realistic force. Martinez-Pinedo etal. [8] have made full fp-shell model studies of A = 47,48, and 49 nuclei.

In view of the success of density functional theoryfor atoms and molecules one can ask if an analogous the-ory exists for nuclei. A derivation of a density functionaldirectly from the realistic nucleon-nucleon force is aproject for the future but there is a phenomenologicalapproach, nuclear Hartree-Fock theory with an effectiveinteraction, which resembles Kohn-Sham theory andwhich has been very successful in calculating propertiesof nuclear ground states. About 45 years ago Skyrme [9]introduced an effective nucleon-nucleon interaction andwas able to calculate some of the properties of nuclearmatter and light nuclei in a very simple way. His inter-action was written as a potential:

V = �i<j

vij + �i<j<k

vijk(3) (9)

containing two-body and three-body parts. Skyrme jus-tified his three-body force by the following physical ar-gument: “The potential used in our analysis must con-tain 3-body, and generally many-body, terms whichdescribe the way in which the interaction between twoparticles is influenced by the presence of others; the twobody terms alone should be related closely to the scat-tering between free nucleons.” In 1970 Vautherin andBrink [10] noticed that Skyrme’s interaction was veryconvenient for making Hartree-Fock calculations ofground state properties of closed shell nuclei. ThisSkyrme Hartree-Fock theory leads to a density func-tional and a set of self-constant equations. They can besolved to give the binding energy of a nucleus, the mat-ter and charge density of the ground state, and variousother properties. Skyrme Hartree-Fock theory for nucleihas many similarities with Kohn-Sham DFT for atomsand molecules. The contribution of electron correlationsin Kohn-Sham theory is included by a term added to thedensity functional. The three-body force plays a similarrole in Skyrme Hartree-Fock theory.

To simplify calculations Skyrme used a short-rangeapproximation for the two-body interaction

v12 = t0(1 + x0Pσ)δ(r1 – r2) + . . . + v12so. (10)

The leading term is a δ-function potential with strengtht0 and a spin exchange term with strength x0. The dotsindicate terms which give the leading finite range correc-tions with strengths and spin-dependence fixed by pa-

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rameters t1x1t2x2. There is also a short-range spin-orbitinteraction between nucleons v12

so with a strength W0.Skyrme’s three-body force is also a zero range interaction

vijk(3) = t3δ(r1 – r2)δ(r1 – r3).

The energy functional of a nucleus in SkyrmeHartree-Fock theory is the expectation value of the ef-fective interaction with a wave function represented by asingle Slater determinant Φ. The explicit form of the en-ergy functional is

E[ρ, τ, J] = ⟨ΦT + VΦ⟩ =�H(r)d3r, (11)

where the energy density H(r) is a sum of kinetic and po-tential energy contributions each depending on densitieswhich are expressed in terms of the single particle statesφi(r) defining Φ

ρ(r) = �φi(r)2, τ(r) = �∇φ i(r)2,

J(r) = �φi*(r)l.σφi(r). (12)

Here ρ(r) is the nucleon density and is analogous to theelectron density in Kohn-Sham theory. The density τ(r)determines the contribution of the kinetic energy to thetotal energy and J(r) is a spin-orbit density associatedwith the spin-orbit term in Skyrme’s effective interaction.

We write the total energy density H(r) as a sum ofthree parts: H+(r) depending on the total nucleon densi-ties, H-(r) depending on the differences between neutronand proton densities, and HC(r) containing the Coulombrepulsion between the protons. The first part is

H+(r) = τ + a0ρ2 + a1(∇ρ)2

+ a2ρτ + a3ρ3 + aso Jρ. (13)

The term proportional to τ in H+(r) represents the ki-netic energy of the nucleons. It has the same form in theKohn-Sham theory. The coefficients ai can be expressedin terms of the parameters of Skyrme’s effective inter-action; a0 = 3t0/8$, a1 = (9t1 – 5t2)/64, a2 = (3t1 + 5t2)/16,a3 = t3/16, aso = 3W0/4. The term proportional to ρ2

comes from the zero range part of the two-body poten-tial and the two terms depending on (∇ρ)2 and ρτ arefinite range corrections. The ρ3 term is the contributionof the three-body force. In modern versions of theSkyrme interaction the three-body force is replaced by adensity-dependent two-body force and the ρ3 term is re-

�2–2m

1–r

placed by a ρ2+α term where 0 < α ≤ 1. The second partH-(r) of H(r) depends on differences of the proton andneutron densities are

H-(r) = b0(ρp – ρn)2 + b1(∇ρp – ∇ρn)

2 + . . . . (14)

There are five terms in H- analogous to the terms in H+.Only two are written explicitly in (14). The coefficientsb0, b1, . . . depend on parameters in Skyrme’s effective in-teraction.

Combinations of terms in (13) and (14) have a sim-ple physical significance. The strengths of the ρ2, the ρτ,and the ρα terms in (13) fix the binding energy, the den-sity and compressibility of symmetric nuclear matter.The term proportional to Jρ fixes the spin-orbit cou-pling. The (∇ρ)2 term is large at the nuclear surface andis important for fixing the surface energy of a nucleus.The ρτ term is an exchange term and gives the nucleonsan effective mass. The term b0(ρn – ρp)

2 in (14) influencesthe symmetry energy of nuclear matter and b1(∇ρp –∇ρn)

2 contributes to the surface symmetry energy.Many improvements in the choice of the parameters

in the Skyrme interaction have been made since 1970.One was the replacement of the three-body interactionby a density-dependent two-body interaction. Two oth-ers relate to the symmetry energy and isospin propertiesand to the spin-orbit interaction. The first is importantfor applications to neutron-rich nuclei. In 1981 Fried-man and Pandharipande [11] made a variational calcu-lation of the equation of state for neutron matter withthe v14 interaction and a semi-realistic three-body force.Modern Skyrme parametrizations aim to fit this equa-tion of state as well as properties of stable nuclei with theexpectation that these interactions should be good forneutron-rich nuclei. A second improvement concerns thespin-orbit contribution. With the spin-orbit force usedby Vautherin and Brink [10] the strengths of the spin-orbit contribution asoJρ to the density H+ and bso(Jn –Jp)(ρn – ρp) to H- were related and depended only on theparameter W0. Nuclear radii for sequences of isotopesobtained by measuring by isotope shifts in atomsshowed characteristic feature at neutron closed shells N= 82 and N = 126 which was not reproduced by SkyrmeHartree-Fock calculations with the interactions then inuse. Sharma et al. [12], with experience from relativisticmean field theory, pointed out that the situation could beimproved by fitting aso and bso independently.

A Skyrme energy functional SkX developed byBrown [13] depends on just 12 parameters, the 10 ai andbi in (13), (14), the parameter α giving the exponent of

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the density-dependent term, and a parameter xc whichfixes the strength of an approximation to the exchangepart of the Coulomb interaction. It fits the Friedman andPandharipande [11] equation of state for nuclear matterand the experimental binding energies of 11 double-closed shell nuclei (16O, 24O, 34Si, 40Ca, 48Ca, 48Ni, 68Ni,88Sr, 100Sn, 132Sn, and 208Pb). This list includes severalwhich are far from the line of β-stability. Brown’s pa-rameter set also gives a good fit to about 40 single par-ticle energy levels in these nuclei, the rms radii of the fiveclosed shell nuclei which have been measured, and themeasured charge distributions of 40Ca, 90Zr, and 208Pb.Another interaction with improved isospin properties,intended for applications to nuclei far from β-stability,was developed recently by Chabanat et al. [14].

Skyrme Hartree-Fock theory has also been used tocalculate other nuclear properties. Extensions involvingrandom phase approximation or time-dependentHartree-Fock have been very successful in describinggiant resonances: dipole, monopole, quadrupole, andGamow-Teller. Well-deformed nuclei can be treated bythe deformed Hartree-Fock method. The first paperusing the Skyrme interaction for deformed nuclei waspublished by Vautherin [15] in 1973. A recent reference[16] uses the Chabanat et al. [14] interaction and con-tains an application to rotational bands and fission bar-riers in a transuranic element. Extensions to nuclei awayfrom closed shells and especially to deformed nuclei re-quire a generalization of the Skyrme energy functional toinclude a pairing force between nucleons. A very neatand simple generalization combining Hartree-Fock witha BCS pairing interaction was worked out by Vautherinin his 1973 paper [15]. Duguet et al. used Hartree-Fock-Bogoliubov theory and the Lipkin-Nogami approximateparticle number projection.

Summary and OutlookHartree-Fock and density functional theory are very

similar in their practical applications, but the underlyingphilosophy is different. The focus in Hartree-Fock is theSlater determinant wave function which is an approxi-mation to the many particle wave function. The anti-symmetry of the wave function ensures that the Pauliexclusion principle is satisfied. According to the Hohen-berg-Kohn theorem the fundamental entity in densityfunctional theory is the single particle density. In theKohn-Sham applications it is rather the single particledensity matrix which, in principle, is associated with theexact many particle wave function. The Pauli exclusionprinciple is imposed by requiring that the eigenvalues of

the single particle density matrix (single particle occupa-tion numbers) do not exceed unity. The single particlewave functions in HF theory specify the Slater determi-nant wave function, while in density functional theorythey are the eigenfunctions of the one-particle densitymatrix. In HF the occupation numbers are either zero orone, while in density functional theory fractional occu-pation is the norm. In Kohn-Sham theory occupationnumbers are chosen to be zero or unity to simplify thecalculations.

Skyrme Hartree-Fock theory occupies the middleground. Sometimes it may be better to stress the Hartree-Fock aspects. Then the Slater determinant wave functionis an approximation to a more exact many particle wavefunction and is open to improvement by calculatinghigher order effects which are not included in the effec-tive interaction. If, on the other hand, one thinks of it asa density functional theory, then improvements of thetheory would result from choosing a better density func-tional. Vautherin’s application [15] of Skyrme’s inter-action to deformed nuclei is an interesting example. Hemodified Skyrme’s density functional to include pairingin a constant gap BCS approximation. From the Har-tree-Fock point of view he should have improved thetheory by making a Hartree-Fock-Bogoliubov extensionand then do particle number projection, etc. From thedensity functional point of view he made an improve-ment to the density functional. A better single particledensity matrix comes out of the theory and there is nonecessity to project particle number. It gives fractionaloccupation numbers to single particle states and yields atheory which can be used to describe deformed nuclei.

Looking at Skyrme’s Hartree-Fock theory, or othermean field theories with effective interactions, from adensity functional point of view might give a new per-spective and could lead to new and interesting ways ofthinking about nuclear structure.

References1. P. Hohenberg and W. Kohn, “Inhomogeneous electron

gas,” Phys. Rev. B136, 864 (1964).2. W. Kohn and L. J. Sham, “Self-consistent equations in-

cluding exchange and correlation effects,” Phys. Rev.A140, 1133 (1965).

3. W. Koch and R. H. Hertwig, “Density functional theory,Applications to transition metal problems,” Encyclopaediaof Computational Chemistry (ed. Paul v.R. Schleyer), JohnWiley and Sons, New York, 1998, p. 689.

4. Ching-Han Hu and D. P. Chong, “Density functional ap-plications,” Encyclopaedia of Computational Chemistry

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(ed. Paul v.R. Schleyer), John Wiley and Sons, New York,1998, p. 664.

5. K. Yabana and G. F. Bertsch, “Time-dependent localdensity approximation in real time: Application to con-jugated molecules,” Int. J. Quantum Chem. 75, 55 (1999).

6. S. C. Pieper, V. R. Pandharipande, R. B. Wiringa and J.Carlson, “Realistic models of pion exchange three-nucleoninteractions,” Phys. Rev. C64, 014001 (2001).

7. O. Elgaroy, T. Engeland, M. Hjorth-Jensen and E. Osnes,“Pairing correlations in nuclear systems, from infinite mat-ter to finite nuclei,” International Journal of ModernPhysics, B15, 1501 (2001).

8. G. Martinez-Pinedo, A. P. Zuker, A. Poves, E. Caurier,“Full pf shell study of A = 47 and A = 49 nuclei,” Phys.Rev. C55, 187 (1997).

9. T. H. R. Skyrme, “The nuclear surface,” Philos. Mag. 1,1043 (1956); “The effective nuclear potential,” Nucl.Phys. 9, 615 (1959).

10. D. Vautherin and D. M. Brink, “Hartree-Fock calculationswith Skyrme’s interaction,” Phys. Lett. 32B, 149 (1970);Phys. Rev. C5, 626 (1972).

11. B. Friedman and V. J. Pandharipande, “Hot and cold: Nu-clear and neutron matter,” Nucl. Phys. A361, 502 (1981).

12. M. M. Sharma, G. Lalazissis, J. Konig and P. Ring, Phys.Rev. Lett. 74, 3744 (1995).

13. B. A. Brown, “New Skyrme interaction for normal and ex-otic nuclei,” C58, 220 (1998).

14. E. Chabanat, P. Bonche, P. Haensel, J. Meyer and R. Schaeffer, “A Skyrme interaction from subnuclear toneutron star densities,” Nucl. Phys. A627, 710 (1997);Nucl. Phys. A635, 231 (1998).

15. D. Vautherin, “Hartree-Fock calculations with Skyrme’sinteraction: Axially deformed nuclei,” Phys. Rev. C7, 296(1973).

16. T. Duguet, P. Bonche and P. H. Heenen, “Rotational prop-erties of 252No, 253No and 254No: Influence of pairing cor-relations,” Nucl. Phys. A679, 427 (2001).

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IntroductionThe Standard Model (SM) is a theory framework,

which allows an accurate description of all confirmedmeasurements in particle physics up to the turn of thecentury. However, many observations are left withoutdeeper explanations. Among those are the fundamentalfermion mass spectrum, the origins of parity and CP vi-olation, the fact of exactly three particle generations,and many more. A variety of speculative models hasbeen invented, in order to suggest physical interpreta-tions of such not yet understood features contained inthe SM.

Muons (µ-) and their antiparticles (µ+), the chargedleptons in the second generation of fundamental fermi-ons, have no internal structure down to dimensions of10-18 m as shown in high energy lepton scattering exper-iments. They may therefore be regarded as point-like ob-jects. The behaviour of muons can be described withinstandard theory with sufficient accuracy for all high pre-cision experiments that have been carried out on them.

Muons are therefore important and central tools in avariety of research programs: The dominant µ+ decayinto a positron (e+), muon anti-neutrino, and electronneutrino (µ+ → e+ν–µνe) yields the best value for the weakinteraction Fermi coupling constant GF. The insensitivityof muons to strong interactions makes muons importantprobes of nucleon properties in deep inelastic high-en-ergy scattering. Muonic atom spectroscopy has givenvery reliable values for nuclear parameters, in particularnuclear charge radii. Searches for as yet unobservedlepton number violating decays have yielded numerousbounds on crucial parameters in speculative models.High precision measurements of the electromagnetic in-teractions of free muons and such bound in the muo-nium atom (M = µ+e-)—the hydrogen-like bound state ofa positive muon and an electron (e-)—have establishedstringent tests of standard theory, which includes in par-ticular Quantum Electrodynamics (QED). The excellentagreements between measurements and this underlyingtheory has contributed significantly to today’s view uponQED as the best available field theory. This solid confi-dence allows us in return to extract most accurate valuesof fundamental constants such as the muon mass mµ,

muon magnetic moment µµ, and magnetic anomaly aµ,and the electromagnetic fine structure constant α.

In many muon experiments a limitation has beenreached by now which is determined by the availableparticle fluxes at today’s sources. For new acceleratorfacilities, such as the recently approved Japanese HadronProject (JHP), a next generation of experiments has al-ready been proposed. In addition to the exploitation ofhigher fluxes with established approaches, novel tech-niques will be introduced to the field. This promises anexpansion into new regions and can be expected to resultin significant progress in exploring fundamental inter-actions and symmetries in physics (Table 1) [1].

In this article we will focus mainly on measurementsof electromagnetic properties of the free muon and onspectroscopy of the muonium atom.

MuoniumThe close confinement of the bound state in the

muonium atom offers excellent opportunities to exploreprecisely fundamental electron-muon interactions. Sincethe effect of all known fundamental forces in this systemare very well calculable within bound state QED, it ren-ders both the possibility to extract precise constants aswell as the possibility to search very sensitively for yetunknown interactions between these leptons. In contrastto natural atoms and ions as well as to artificial atomicsystems, which contain hadrons, muonium has the ad-vantage of being free of complications arising from thefinite size and the internal structure of any of its con-stituents. Therefore, the system is particularly suited forsearching new and yet unknown forces in nature.

In the muonium atom (Figure 1) the most precisespectroscopy measurements can be performed on theground state hyperfine structure splitting [2] and the 1s-2s energy interval [3]. Such experiments have beencompleted very recently after reaching limitations givenby the quantities of available muons at the late LosAlamos Meson Physics Facility (LAMPF) in Los Alamos,USA, and at the Rutherford Appleton Laboratory (RAL)in Chilton, United Kingdom. These two transitions areexperimentally favoured because they involve the 1sground state in which the atoms can be produced with

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Free Muons and Muonium: Some Achievements andPossibilities in Low Energy Muon PhysicsKLAUS P. JUNGMANN

Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen

the highest yields. For accurate measurements the atomsneed to be at low, ideally thermal velocities in the labo-ratory. The efficient conversion of an energetic µ+ beaminto M is a key element in all experiments.

Muonium ProductionThe best-known mechanism to produce muonium is

e- capture after stopping µ+ in a suitable noble gas, whereyields of 80 (10)% can be achieved for krypton. Muonsat accelerator facilities are born in weak pion decaysand parity violation in this process causes the muonbeams to be polarized. The moderation processes in-volve dominantly the electric interaction and there is nomuon depolarization. In strong axial magnetic fields (B >> 0.16 T) M is formed with a well-defined ensembleaverage of the muon spin direction.

Muonium atoms at thermal velocities in vacuum canbe obtained by stopping µ+ close to the surface of a tar-get consisting of fine SiO2 powder. The atoms are formedthrough e- capture and a fraction of a few percent ofthem diffuses through the target surface into the sur-rounding vacuum. Additional cooling with, e.g., lasertechniques would not provide any significant advan-tages. Due to the τµ = 2.2 µs muon lifetime the naturalline width of all transitions has a lower limit at ∆νnat =(π . τµ)

-1 = 145 kHz and cooling could not provide amuch more advantageous line width. This thermal Mproduction technique has become an essential prerequi-site for Doppler-free two-photon laser spectroscopy ofthe 12S1/2 – 22S1/2 interval ∆ν1s2s at KEK in Tsukuba,Japan, and with significantly higher precision at RAL. Itwas also the key to a sensitive search for a conversion ofM into its anti-atom M

_at the Paul Scherrer Institut (PSI)

in Villigen, Switzerland.

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Table 1. Some muon physics experiments where significantly enhanced accuracy can be expected at intensivemuon sources. The prospected future accuracies have been estimated for a (pulsed) 4 MW protonaccelerator facility [1]. The gain in precision arises not only from improved statistics. In many casesnovel concepts and techniques can be applied.

Type of Possible Present Possible experiment Physics issue experiments Accuracy future accuracy

“Classical” rare Lepton number violation; µ+e- → µ-e+ 8.1 × 10-11 <10-13 (novel concept)and forbidden New Physics searches µ → e γ 1.2 × 10-11 <10-15 (novel techniques)decays µ → eee 1.0 × 10-12 <10-16 (novel techniques)

µ-N → e-N 6.1 × 10-13 <10-18 (novel method)

Muonium Fundamental constants ∆νHFS 12 × 10-9 <5 × 10-9 (exploit. statistics)spectroscopy mµ, µµ, α, qµ; ∆ν1s2s 1 × 10-9 <10-11 (novel concept)

weak interactions,muon charge

Muon moments Standard Model tests; gµ – 2 1.3 × 10-6 <10-7 (exploit. statistics)New Physics searches; µ electric dipole 3.4 × 10-19 ecm <5 × 10-26 ecm (novel concept)T, CP, CPT tests moment

Muonic atoms Nuclear parameters; µ- atoms Depends on Depends on system (novelnuclear charge radii; Radioactive system not yet ideas involving particle traps)weak interactions µ- atoms performed

Figure 1. Muonium energy levels for principal quantumnumbers n = 1 and n = 2.

Ground State Hyperfine StructureThe most recent experiment at LAMPF had a Kr gas

target inside of a microwave cavity at typically atmos-pheric density and in a homogeneous magnetic field of1.7 T. Microwave transitions between the two energeti-cally highest, respectively two lowest, Zeeman sublevelsof the n = 1 state at the frequencies ν12 and ν34 (Figure 2)involve a muon spin flip. Due to parity violation in theweak interaction muon decay process the e+ from µ+ de-cays are preferentially emitted in the µ+ spin direction.This allows a detection of the spin flips through a changein the spatial distribution of the decay e+. As a conse-quence of the Breit-Rabi equation, which describes thebehaviour of the M ground-state Zeeman levels in amagnetic field B, the sum of ν12 and ν34 equals at anystrength of B the zero field splitting ∆νHFS. For suffi-ciently well known B the difference of these two fre-quencies yields the magnetic moment µµ.

The latest LAMPF experiment [2] has utilized thetechnique of “Old Muonium,” which allowed us toreduce the line width of the signals below half of the“natural” line width ∆νnat (Figure 3). For this purpose anessentially continuous muon beam was chopped by anelectrostatic kicking device into 4 µs long pulses with 14µs separation. Only decays of atoms which had been in-teracting coherently with the microwave field for periodslonger than several muon lifetimes were detected.

The magnetic moment was measured to be µµ =3.183 345 24(37) (120 ppb), which translates into amuon-electron mass ratio mµ/me = 206.768 277(24) (120

ppb). The zero-field hyperfine splitting is determined tobe ∆νHFS(exp) = 4 463 302 765(53) Hz (12 ppb), whichagrees well with the theoretical prediction of ∆νHFS(theo)= 4 463 302 563(520)(34)(<100) Hz (120 ppb). Here,the first quoted uncertainty is due to the accuracy towhich mµ/me is known, the second error is from theknowledge of α as extracted from Penning trap meas-urements of the electron magnetic anomaly, and thethird uncertainty corresponds to estimates of uncalcu-lated higher order terms. Among the non QED contri-butions is the strong interaction through vacuum polar-ization loops with hadrons, which adds 250 Hz and aparity conserving axial vector–axial vector weak interac-tion which is –65 Hz.

For the muonium hyperfine structure the compari-son between theory and experiment is possible with al-most two orders of magnitude higher precision than fornatural hydrogen because of the not sufficiently knownproton charge and magnetism distributions. For hydro-gen the achieved some six orders of magnitude higherexperimental precision (in hydrogen maser experiments)can therefore unfortunately not be exploited for a betterunderstanding of fundamental interactions.

Among the possible exotic interactions, which couldcontribute to ∆νHFS, is muonium-antimuonium conver-sion [4] (see below). Here, an upper limit of 9 Hz couldbe set from an independent experiment described below.

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Figure 2. Muonium ground state hyperfine structureZeeman splitting.

Figure 3. Samples of conventional and “old muonium”resonances at frequency ν12. The narrow “old” lines ex-hibit a larger signal amplitude. The signals were ob-tained with magnetic field sweep (left column, magneticfield in units of proton NMR frequencies) and by mi-crowave frequency scans (right column) [2].

Recently, generic extensions of the SM, in which bothLorentz invariance and CPT invariance are not assumed,have attracted widespread attention in physics. Diurnalvariations of the ratio (ν12 – ν34)/(ν12 + ν34) are pre-dicted. An upper limit could be set from a reanalysis ofthe LAMPF data at 2 × 10-23 GeV for the Lorentz andCPT violating parameter. In a specific model by Kostel-cky and co-workers a dimensionless figure of merit forCPT tests is sought by normalizing this parameter to theparticle mass. In this framework ∆νHFS provides a signif-icantly better test of CPT invariance than electron g-2and the neutral Kaon oscillations [5].

The hyperfine splitting is proportional to α2 . R∞with the very precisely known Rydberg constant R∞.Comparing experiment and theory yields α-1 = 137.035996 3(80) (58ppb). If R∞ is decomposed into even morefundamental constants, one finds ∆νHFS ∝ α4 . me/h. Withh/me as determined in measurements of the neutron deBroglie wavelength we have α-1 = 137.036 004 7(48) (35ppb). In the near future a small improvement in this fig-ure can be expected from ongoing determinations ofh/me in measurements of the photon recoil in Cs. A bet-ter determination of the muon mass, e.g., will result in afurther improvement and may contribute to resolvingthe situation of various poorly agreeing determinationsof the fine structure constant, which is important inmany different fields of physics.

It should be mentioned that the present agreementbetween α as determined from M hyperfine structureand from the electron magnetic anomaly is generallyconsidered the best test of internal consistency of QED,as one case involves bound state QED and the other oneQED of free particles.

The results from the LAMPF experiment are mainlystatistics-limited and improve the knowledge of both∆νHFS and µµ by a factor of three over previous measure-ments. This gain could be significantly surpassed at a fu-ture high flux muon source.

The 1s-2s Interval in MuoniumIn muonium the 1s-2s energy difference is essentially

given by the relevant quantum numbers, R∞ and a re-duced mass correction. Therefore, this transition may beregarded ideal for a determination of the muon-electronmass ratio. QED corrections are well known for theneeds of presently possible precision experiments and donot play an important role here.

Doppler-free excitation of the 1s-2s transition hasbeen achieved in pioneering experiments at KEK and atRAL. In all these experiments two counter-propagatingpulsed laser beams at 244 nm wavelength were em-ployed to excite the n = 2 state. The successful transi-tions were then detected by photo-ionization with a

third photon from the same laser field. The released µ+

was then registered on a microchannel plate detector.The accuracy of the early measurements was limited

by the ac-Stark effect and rapid phase fluctuations (fre-quency chirps), which were inherent properties of thenecessary pulsed high power laser systems. The key fea-ture for the latest high accuracy measurement at RALwas a shot by shot measurement of the spatial laserintensity profile as well as the time dependences of the laser light intensity and phase. This together with anewly developed theory of resonant photo-ionization [6]allowed a shot-by-shot prediction of the transition prob-ability as a basis for the theoretical line shape (Figure 4).

The latest RAL experiment [3] yields ∆ν1s2s(exp) = 2455 528 941.0(9.8) MHz in good agreement with a the-oretical value ∆ν1s2s(theo) = 2 455 528 935.4(1.4) MHz.The muon-electron mass ratio is found to be mµ + /me- =206.768 38(17). Alternatively, with mµ + /meas ex-tracted from the M hyperfine structure, a comparison ofexperimental and theoretical values can be interpreted interms of a µ+ – e- charge ratio, which results as qµ + /qe- +1 = –1.1(2.1) × 10-9. This is the best verification ofcharge equality in the first two generations of particles.The existence of one single universal quantized unit ofcharge is solely an experimental fact and no underlyingsymmetry could yet be revealed. The interest in such aviewpoint arises because gauge invariance assures chargequantization only within one generation of particles.

Major progress in the laser spectroscopy of M can beexpected from a continous wave laser experiment, where

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Figure 4. Muonium 1s-2s signal. The frequency scalecorresponds to the offset of the laser system base fre-quency from a molecular iodine reference line. The opencircles are the observed signal, the solid squares repre-sent the theoretical expectation based on pulse-by-pulsemeasured laser beam parameters (phase and intensity)and a line-shape model [3, 6].

frequency measurement accuracy does not present anyproblem because light phase fluctuations are absent. Forthis an intense source of muons will be indispensable.

Muon Magnetic AnomalyThe spectroscopy experiments on muonium and a

measurement of the muon magnetic anomaly aµ =(gµ – 2)/2 are closely related through µµ = gµ eh- /(2mµc).This arises from the precise values of fundamental con-stants and the high accuracy tests of the validity and re-liability of QED for leptons, which both form an indis-pensable basic input for the analysis of the measureddata and the calculations of a theoretical value. Themeasurements in muonium spectroscopy and of aµ to-gether put a stringent test on the internal consistency oftheory and the values of the involved constants aµ, mµ,µµ, and α.

The muon magnetic anomaly has been measured inthree past experiments at CERN to 7 ppm. The anomalyarises from interactions with virtual particles created bythe muons own radiation field. It is dominated, like incase of the electron, mostly by virtual electron, positronand photon fields. However, the effects of heavier parti-cles are enhanced in comparison to the electron case bythe square of the mass ratio mµ/me ≈ 4 × 104. Whereasfor the electron such contributions altogether amount toabout the present experimental uncertainty at 4 ppb,they have been experimentally demonstrated for muonsalready clearly in the last CERN experiment. The influ-ence of the strong interaction can be determined in itsdominating first order vacuum polarization part from adispersion relation with the input from experimentaldata on e+ – e- annihilation into hadrons and hadronicτ-decays. It amounts to 58 ppm. Part of the hadroniccontributions is hadronic light-by-light scattering. Thiscan only be determined from calculations and is the sub-ject of ongoing highly actual research [7]. Even the signof the effect has frequently changed in calculationswithin the past decade. The weak interaction adds 1.3ppm. Accounting for all known effects, present standardtheory yields aµ to 0.57 ppm. Possible influence fromphysics beyond the SM may be as large as a few ppm.Such could arise, for example, from supersymmetry,compositeness of fundamental fermions and bosons,CPT violation, and from many others.

There is a twofold high value for a precision meas-urement of aµ. Firstly, a discrepancy with finally agreedand confirmed standard theory calculations would givehints to yet undiscovered interactions and particles andit would stimulate more direct searches. Secondly, agood agreement at a high level of accuracy would setstringent limits on parameters in a large number of spec-ulative models.

A new determination of aµ is presently carried out ina superferric magnetic storage Ring at the BrookhavenNational Laboratory (BNL) in Upton, USA (Figure 5)[8]. The difference between the spin precession and thecyclotron frequencies of the stored muons is determined.The detailed analysis of data obtained in 1999 with 2billion µ+ has given an experimental value of aµ(exp) =11 659 202(14)(6) × 10-10. The accuracy of 1.3 ppm isexpected to be significantly improved with the analysisof the already recorded data sets with four times as muchpositive particles and twice as much negative muons.The plans foresee to obtain statistically equivalentdatasets for both signs of charge.

The most recent and most accurate theory value inthe framework of the SM aµ(SM) = 11 659 276.8(6.5) ×10-11 (0.56 ppm) [7] appears to differ from the experi-mental value by some 1.6 times the combined experi-mental and theoretical uncertainties. An earlier largerdifference had led to a careful review of all standard the-ory contributions. In this process a calculational errorwas found in hadronic light-by-light scattering, showingthe sensitivity to the precision of calculations and uncer-tainty assignments for theoretical values. This is work inprogress and the future will show whether the final re-sult will be a hint to new physics beyond the SM.

It should be noted that there is a severe limitation tothe interpretation of a perhaps future muon gµ – 2 meas-urement, in connection with extracting or limiting pa-rameters of speculative models, which arises from thehadronic vacuum polarization and owes to the fact thatmeasurements of e+ – e- annihilation into hadrons andhadronic τ decays have reached a statistical limitation.Hadronic light-by-light scattering, which can only betaken from calculations, sets a principal limit as long asthe associated conceptual problems remain unsolved.

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Figure 5. The muon g-2 storage ring experiment at BNL.

In order to find new physics in precision measure-ments it may therefore be advantageous to use systems,where the standard theory predictions are simpler.Searches for a permanent electric dipole moment (edm)of any fundamental particle are here good examples.Electric dipole moments are forbidden by P, T, and CPinvariance, and the SM predictions are several orders ofmagnitude below present search limits. Furthermore,such research gains additional motivation, because theidentification of new sources of CP violation could be acrucial ingredient for explaining the dominance of mat-ter over antimatter in the universe. Driven by these ar-guments a novel idea has been brought forward [9]. It isto search for a muon edm by exploiting the motionalelectric field a highly relativistic muon experiences in amagnetic field. This motional field can be orders of mag-nitude stronger than technically achievable fields. A sixorders of magnitude improvement over the present limitis aimed for by a collaboration at BNL. At this level amuon edm experiment will be competitive with electronor neutron edm experiments and has the further benefitof probing a new particle generation.

Muonium to Antimuonium ConversionIn addition to the indirect searches for signatures of

new physics in the muon magnetic anomaly and in elec-tromagnetic interactions within the muonium atom thebound state also offers the possibility to search more di-rectly for predictions of speculative models. The processof muonium to antimuonium-conversion violates addi-tive lepton family number conservation. It would be ananalogy in the lepton sector to K0K

_0 oscillations. MM

_-

conversion appears naturally in many theories beyondthe SM. The interaction could be mediated, e.g., by adoubly charged Higgs boson ∆++, Majorana neutrinos, aneutral scalar, a supersymmetric τ-sneutrino ν∼τ, or adoubly charged bileptonic gauge boson X±±.

At PSI an experiment was designed to exploit a pow-erful new signature, which requires the coincident iden-tification of both particles forming the anti-atom in itsdecay [4]. Thermal muonium atoms in vacuum from aSiO2 powder target, are observed for M

_decays. Ener-

getic electrons from the decay of the µ- in the M_

atomcan be identified in a magnetic spectrometer (Figure 6).The positron in the atomic shell of M

_is left behind after

the decay with 13.5 eV average kinetic energy. It hasbeen post-accelerated and guided in a magnetic transportsystem onto a position sensitive microchannel plate de-tector (MCP). Annihilation radiation can be observed ina segmented pure CsI calorimeter around it. The decayvertex can be reconstructed.

The measurements were performed during a periodof 6 months in total over 4 years during which 5.7 × 1010

M atoms were in the interaction region. One event fellwithin a 99% confidence interval of all relevant distri-butions. The expected background due to accidental co-incidences is 1.7(2) events. Depending on the interactiondetails one has to account for a suppression of the con-version in the 0.1 T magnetic field. This amounts maxi-mally to a factor of about 3 for V ± A type interactions.Thus, the upper limit on the conversion probability is8.2 × 10-11 (90% C.L.). The coupling constant is boundto below 3.0 × 10-3 GF.

This new result, which exceeds limits from previousexperiments by a factor of 2500 and one from an earlystage of the experiment by 35, has some impact on spec-ulative models. For example, a certain Z8 model is ruledout which has more than 4 generations of particles andwhere masses could be generated radiatively with heavylepton seeding. A new lower limit of mX ±± ≤2.6TeV/c2*g3l (95% C.L.) on the masses of flavour diagonalbileptonic gauge bosons in GUT models is extracted,which lies well beyond the value derived from directsearches, measurements of the muon magnetic anomalyor high energy Bhabha scattering. Here, g3l is of orderunity and depends on the details of the underlying sym-metry. For 331 models the experimental result can betranslated into mX ±± ≤850 GeV/c2*g3l which excludessome of their minimal Higgs versions, where an upperbound of 600 GeV/c2 has been extracted from an analy-sis of electro-weak parameters. The 331 models neednow to refer to a less attractive and more complicatedextensions. In the framework of R-parity violating su-

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Figure 6. Muonium-Antimuonium Conversion Spectrom-eter at PSI.

persymmetry the bound on the relevant coupling param-eters could be lowered by a factor of 15 to λ132

. λ231* 3 ×10-4 for assumed superpartner masses of 100 GeV/c2.

A future MM_

-experiment could particularly take ad-vantage of high intensity pulsed beams. In contrast toother lepton number violating muon decays, the conver-sion through its nature as particle-antiparticle oscillationhas a time evolution in which the probability for findinga system formed as M decaying as M

_increases quadrat-

ically in time. This gives the signal an advantage, whichgrows in time over exponentially decaying background.For example, with a twofold coincidence as part of a sig-nature after ∆T = 2τµ beam related accidental back-ground has dropped by almost two orders of magnitude,whereas a MM

_-signal would not have suffered signifi-

cantly at all.

Future PossibilitiesAll precision muonium experiments are now limited

by statistics. For this reason significant improvementscan be expected from more efficient M atom formation.There are some encouraging developments at RIKEN-RAL where hot metal targets are used [10]. However, byfar the most promising approaches are muon sourceswith higher intensities. Such may become available, inprinciple, at any high power proton facility with particleenergies above the pion production threshold. The dom-inating figure of merit is the beam power on the produc-tion target.

At JAERI in Japan the construction of the JapaneseHadron Project (JHF) has been started which has a 1MW proton beam. Further, novel muon beam line con-cepts use compared to present facilities much larger par-ticle collection solid angles at the production target andaim for significant phase space cooling of the beam. Ex-amples are the DIOMEGA and PRISM projects [10].

In Europe a spallation source and a neutrino factoryare being discussed. Also, the planned new GSI machinecould provide such beams, if rapid cycling would beforeseen. In a similar way the Brookhaven AGS could beupgraded. The success of such high power facilities willcrucially depend on the capability of the possible targetsto withstand high beam powers. Therefore, strong re-search activities should be focussed on this aspect soon.

In addition to more precise measurements in muo-nium a rich variety of experiments could be served at

such expanded facilities. In Table 1 some possibilities aregiven, which include spectroscopy of artificial atoms andions like muonic hydrogen and muonic helium whereimportant parameters describing the hadronic particleswithin these systems can be determined. At such new fa-cilities in particular several novel experimental tech-niques will become feasible and can be expected to pro-vide most sensitive tests of fundamental interactions inan area with a high potential to discover new physics.

ConclusionsProfessor I. I. Rabi’s question after he learned about

the muon being a heavy lepton, “Who ordered that?”,has not been answered yet. The nature of the muon—thereason for its existence—still remains an intriguing mys-tery to be solved. On the way to finding an answer, the-orists and experimentalists have contributed throughtheir complementary work in fundamental muon physicsto an improved understanding of basic particle interac-tions and fundamental symmetries in physics. In partic-ular, muonium spectroscopy has verified the nature ofthe muon as a point-like heavy lepton, which differs onlyin mass, related parameters from the electron (and thetau). In addition, these measurements have provided ac-curate values of fundamental constants. With new highflux machines a fruitful future must be expected.

References1. J. Äystö et al., hep-ph/0109217 and references therein.2. W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).3. V. Meyer et al., Phys. Rev. Lett. 84, 1136 (2000); see also:

S. Chu et al., Phys. Rev. Lett. 60, 801 (1988).4. L. Willmann et al., Phys. Rev. Lett. 82, 49 (1999).5. V. W. Hughes et al., Phys. Rev. Lett. 87, 111804 (2001);

see also: R. Bluhm et al., Phys. Rev. Lett. 84, 1098 (2000).6. V. Yakhontov, K. Jungmann and R. Santra, J. Phys. B 32,

1615 (1999).7. M. Knecht and A. Nyffeler, Phys. Rev. D 65, 073034

(2002); see also: M. Knecht et al., Phys. Rev. Lett. 88,071802 (2002); M. Hayakawa and T. Kinoshita, hep-ph/0112102 (2001); J. Bijnens et al., Nucl. Phys. B 626, 410(2002).

8. H. N. Brown et al., Phys. Rev. Lett. 86, 2227 (2001).9. Y. Semertzidis et al., J. Mod. Phys. A 16, 287 Suppl 1B

(2001).10. “High Intensity Muon Sources,” Y. Kuno and T. Yokoi

(eds.) (World Scientific, Singapore, 2000).

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New technologies for producingsizable quantities of helium-3 withits nuclear spins aligned have trans-formed this substance from a labora-tory curiosity into a promising prac-tical commodity.

Helium-3 (3He) is extremely rarein nature; its abundance is only 1.4 ×10-4 percent of helium-4, the onlyother stable isotope of the noble gashelium. Since 3He is produced by theβ-decay of tritium, it became avail-able in considerable quantities in themid-1950s as a by-product of thelarge-scale production of tritium fornuclear fusion weapons. With suffi-cient 3He available one of the mostfascinating discoveries of condensedmatter physics was made in the early1970s: 3He becomes superfluid whencondensed and further cooled downto temperatures close to absolutezero. Superfluidity is a quantum me-chanical phenomenon which turnedout to be an ideal testing ground forfundamental concepts of moderntheoretical physics.

In recent years, the interest inand the use of 3He has undergone asecond blooming, based on anotherquantum mechanical property, itsnuclear spin of 1/2. As often pictured,atoms and their nuclei behave likerotating tops. Normally, the “tops”are statistically directed in space,their rotation axes pointing in all di-rections. If, however, the individualtops can be made to point collec-tively in the same direction, the spindistribution is said to be polarized,and such polarization opens the wayto the new phenomena.

We report here on a technique topolarize 3He nuclei on a large scale.Originally developed for studies ofthe neutron’s structure, polarized

3He soon found applications in theproduction of polarized neutronbeams for condensed-matter re-search and in lung diagnostics inmedicine—another story of basic re-search having spin-offs benefittingother fields.

A key problem is the productionof spin-polarized 3He in large vol-umes and with high yield. An elegantmethod to polarize 3He is opticalpumping, a method which tracesback to the early 1960s [1, 2]. Inorder to force 3He nuclei to undergoa synchronized rotation, the gas isexposed to a laser beam directedalong the axis of an external mag-netic field. The laser light is circu-larly polarized, its plane of polariza-tion rotating around the direction ofpropagation. Energy and uniformspin of the light quanta can be trans-ferred to the atomic electrons of 3He,which in turn transmit their spin di-rection to the nucleus via magneticcoupling between electrons and nu-cleus.

For 3He, optical pumping fromthe atomic ground state is not possi-ble because no excited states of suf-ficiently low energy exist. Pumping,however, can occur from themetastable 2 3S1 state (3He*). Thismetastable state can be produced inconcentrations of about 1 ppm in alow-pressure (≈1 mbar ) dischargecell that works like a fluorescencetube. The metastable state can beoptically pumped using a transition[from 2 3S1 (F = 1/2) to 2 3Po (F = 1/2)]that can be induced by laser lightwith a wavelength of 1083 nm. Theorientation of the metastable atomsbuilds up in microseconds. Withinthe same time scale the orientationof the metastable state is transferred

to the nuclear spin of the groundstate atom by so-called metastabilityexchange collisions. During such acollision, metastable and groundstate atoms form a short-lived mole-cule that allows the exchange of en-ergy and polarization and thus leadsto the nuclear polarization of the3He ground state atom.

The main obstacles which, untilrecently, made it impossible to polar-ize large quantities of 3He gas werethe lack of efficient light sources atthe required wavelengths and thedifficulty of compressing the polar-ized gas. The optical pumping ofmetastable 3He provides a spintransfer rate of one per second perground state atom; with commerciallasers of several watts, productionrates of >1019 nuclear spin-polarized3He atoms per second can beachieved. Expressed in more conven-ient units, about 3 to 4 liters perhour at one bar pressure can be pro-duced with 50 percent of the 3He inthe polarized form. This is roughlywhat is required for recent applica-tions.

For many applications, densesamples of polarized 3He gas aremandatory. Compression of the gasto several bar pressure proved to beextremely difficult because frequentinteractions with the compressorwalls, in particular with magneticmaterial, destroy the spin orienta-tion [3]. Using an innovative com-pression technique, our group of theUniversity of Mainz has been able tocompress polarized 3He gas and tostore it in glass cells whose inner sur-faces are coated with a fewmonoatomic layers of cesium. Thisthin coating prevents the interferingmagnetic interaction between para-

impact and applications


From Nuclear Physics to NMR Tomography

magnetic centers of the cell wallsand 3He nuclei [4]. We are able tocompress polarized 3He gas up to 10bar pressure without loss of polar-ization and to store it in detachableand transportable containers formore than 200 hours. The wholeprocedure can be carried out atroom temperature, and only a weakhomogeneous magnetic field acrossthe sample is sufficient to guide thespins. The practical advantages areevident.

Polarized Neutron TargetScattering experiments have

played a crucial role in the explo-ration of nuclei and their con-stituents, protons and neutrons, aswell as of the forces acting betweenthem. It was found that such interac-tions are spin dependent. To under-stand the fundamental question ofwhether the spins of neutrons andprotons are entirely due to the spinsof the three quarks constituting eachnucleon or whether there are othercontributions, one uses scatteringexperiments with spin degrees offreedom.

Experiments involving the neu-tron’s spin are hampered by the factthat a target of free, polarized neu-trons is not available. Neutronswould quickly disappear by radioac-tive decay (with half-life of 10 min-utes) and by capture in surroundingmaterial. But polarized 3He is a goodapproximation to a target of polar-ized neutrons, because the spins ofthe two protons are paired off andit’s the neutron which carries thespin of the nucleus. Plans for such anexperiment were indeed the drivingforce for the development of the new3He polarization technique.

Since quarks, the constituents ofneutrons and protons, are believedto carry fractional electric charges, atouchstone for specific quark models

is the charge distribution within pro-ton and neutron, often expressed asso-called form factor. Precise meas-urements were available for protons,but not for neutrons, while carryingno net charge, are nevertheless be-lieved to have internal structurecharacterized by some charge distri-bution. Also, there exists a magneticform factor of the neutrons whichentirely dominates the unpolarizedcross-section measurements. Using,however, the scattering of polarizedelectrons on the neutron of polarized3He an interference term betweenelectric and magnetic form factor oc-curs in contrast to the unpolarizedcase which allows to separate off andeven enhance the looked-for effect.

At the Mainz Microtron (MAMI)the electric form factor Gen wasmeasured using the quasielastic reac-tion 3He (e,e’n) in the four momen-tum transfer range Q2 = 0.2–0.7(GeV/c)2. In Figure 1 an overview ofrecent Gen measurements using dif-ferent reaction channels is given [5].The dashed line is a fit to these data

using the so-called Gaster-parame-trization. Due to medium effects themeasured data points on Gen had tobe corrected afterwards, which is in-dicated by the arrows shown in Fig-ure 1. It it obvious that a thoroughtheoretical understanding of theunderlying reaction mechanismn isessential both for deuterium andHelium-3 in order to make a safe ex-trapolation of Gen to the free neutroncase.

Neutron Spin FilterNeutron scattering is one of the

most powerful techniques used to in-vestigate the microscopic propertiesof condensed matter, especially mag-netic phenomena. The main limita-tions which, up to now, have pre-vented broad application of neutronpolarization analysis studies are thelow counting rates involved and the severe restrictions regarding therange of energy transfer and scatter-ing angle available, in other wordsthe phase space which can be cov-ered by existing polarizer and/or



Figure 1. Recent Gen neutron electric form factor measurements using thequasielastic reactions 3He (e,e’n) and D (e,e’n). The slope of Gen at Q2 ≈ 0was extracted from thermal neutron scattering on heavy atoms.

analyzer devices. It has thereforelong been recognized that a spin-de-pendent broad-band neutron filterwould have enormous potential, inanalogy to the polarizer foils in lightoptics, which operate efficiently forpolarizing and analyzing light overthe whole visible spectrum.

A very promising material forneutron-spin filters is gaseous, spin-polarized 3He functioning as an ab-sorption filter. Neutrons impingingwith spin opposite to that of the 3Henucleus are absorbed with very largeprobability (the cross-section is 6000barn at a neutron de Broglie- wave-length of 1 Å and decreases in pro-portion to the wavelength). The par-allel-spin component, on the otherhand, is hardly attenuated and thuspasses through the filter, so that theresult is a highly polarized neutronbeam. The contrast (or effectiveness)of the filter rises, of course, with the3He polarization. With PHe ≈ 70%presently being achieved, 3He neu-tron spin filters meet the numbers oftransmission (Tn ≈ 30%) and polar-izing power (Pn ≈ 94%) of classicalpolarizer devices, e.g., supermirrors.Unlike supermirrors, however, theyprovide their performances over thefull energy range of cold, thermal,and hot neutrons from reactors andspallation sources.

It did not take long for the neu-tron physics community to becomeinterested. The Institut Laue-Langevin (ILL) at Grenoble, operat-ing the powerful European high-fluxresearch reactor, initiated a develop-ment program in this direction. Acopy of the Mainz 3He polarizer andcompressor is being installed in adedicated laboratory at ILL. Theshort filling time of such a neutron-spin filter cell makes it possible toprovide several cells nearly simulta-neously for different experimentalapplications at the multipurpose ILL

reactor. The cells are used in a re-mote type of operation. In order tokeep the 3He polarization close tothe initial polarization value, thecells are refilled with freshly polar-ized gas every day.

In a first round of experiments,several possible applications wereexplored, including polarizationanalysis in fundamental physics ex-periments. In solid state physics asearch for magnetic correlations inhigh temperature superconductingmaterials like the famous yttrium-barium-copper oxides was under-taken, since a possible explanationfor the still mysterious phenomenonof high temperature superconductiv-ity could be magnetic fluctuationssurviving in the superconductingphase.

Also, first steps were undertakentowards a highly efficient polariza-tion analysis of scattered neutrons

[6]. The idea is simple: close to thesample under study a banana-shaped3He neutron-spin filter cell, is posi-tioned, surrounded by a large multi-detector array. With the cell tailoredto the detector arrangement of a dif-fuse-scattering instrument at ILL, anangle of 90 degrees in the horizontalplane and ±15 degrees in the verticaldirection was covered. From themeasured non-spin-flip and spin-flipdifferential cross-sections, the nu-clear and magnetic cross-sectionscould be extracted over the kinemat-ically accepted range of scatteringvector Q which are shown in Fig-ure 2.

The full potential of 3He neu-tron-spin filters will become avail-able with accelerator-based neutronsources. In these sources neutrons ofa wide range of energies are pro-duced, by a process known as spalla-tion, when heavy-metal target is



Figure 2. Extracted nuclear and magnetic cross-sections (a.u.) from uniaxialpolarization analysis on amorphous ErY6 Ni3 as a function of the scatteringvector Q.

bombarded with very energetic pro-tons from a high power accelerator.Due to the pulsed structure of theproton beam, the neutrons also ap-pear as pulses. This allows the si-multaneous use of the whole rangeof neutron energies provided in theneutron pulse, the different energiesbeing distinguished by time-of-flighttechniques. Needless to say, thatbroad-band polarizers had to beused in order to make use of thesebenefits for an efficient polarizationanalysis measurement, too.

Tomography of Human LungsIn a seminal 1994 paper, W.

Happer’s group at Princeton Univer-sity in cooperation with the mag-netic resonance imaging group atDuke University demonstrated thepossibility of imaging lung tissuefilled with a “hyperpolarized” noblegas. The term hyperpolarized is usedto convey the fact that the noble gasis polarized by optical pumping to adegree far beyond the so-calledBoltzmann-polarization achieved inthe magnetic field of a magnetic res-onance imaging (MRI) device as aresult of the Zeeman-splitting of themagnetic sublevels.

The medical community becameinterested in this method becauseporous tissues like the lungs are dif-ficult to image by conventional MRItechniques. Also X-rays and γ-raysdo not give satisfactory results. X-ray imaging suffers from poor con-trast and γ-ray scintigraphy frommarginal resolution. With our tech-nique of compressing hyperpolarized3He into detachable and trans-portable cells, we found ourselveswell prepared for entering this newfield. In collaboration with the Radi-ological department of the Univer-sity of Mainz and the German Re-search Center in Heidelberg wemade a first attempt to image human

lungs in vivo by having the subjectinhale 0 .5 bar . liter of 3He polar-ized to 46%.

A series of morphological im-ages during apnea were performed.The purpose of this study was todescribe the 3He findings of normalpulmonary ventilation in healthyvolunteers and to evaluate abnor-malities in patents with differentlung deseases. Figure 3 shows im-ages of lungs from a healthy volun-teer and a smoker. The lung paren-chyma of volunteers with normalventilatory function exhibited arather homogeneous intermediate tohigh signal, whereas patients (here asmoker) presented with severe signalinhomogeneities with patchy ofwedge-shaped defects, a diagnosis ofhigh relevance. Tumors and tubercu-losis have also been identified in afirst survey of patients.

For transport to the MR-scan-ner, cells filled with hyperpolarized3He gas are stored inside cylindricaltransport boxes made out of soft-iron and µ-metal with permanentmagnets, providing a homogeneousmagnetic guiding field. Cell trans-port by car, train, and airplane weredone within Europe without notice-

able loss of 3He polarisation. Insidethe MR-scanner, the 3He samples areconnected to a gas administrationunit developed in our group. Thisdevice permits administration of 3Heboli of fixed volume (20 . . . 500 mlat atmospheric pressure) into the in-spiratory tidal volume at any prede-fined time with high reproducibilityand negligible loss of hyperpolariza-tion. Volunteers or patients can ei-ther breathe spontaneously throughthe application unit, or ventilationcan be supported by commercial res-pirator units. Finally, the exhaledair-3He gas mixture is collected intoa helium-tight bag and, by means ofcryogenic traps, the rare helium iso-tope can be recycled to a high degree(≈95%) and be reused as contrastagent for a next 3He-MRI cycle.

Besides morphological MRI,studies of the dynamics of lung func-tioning have become an integral partof a routine examination protocolnow, i.e., ultra-fast imaging, diffu-sion weighted imaging, and 3He-MRIbased measurements of the intrapul-monary oxygen partial pressure.

Looking more closely on the lat-ter example: the longitudinal relax-ation time T1 of 3He administered to



Figure 3. 3He MRI images of a non-smoker’s (left) and a smoker’s lung(right).

the airspaces is limited to 10–20 s.The key factor is paramagnetic oxy-gen, which, via dipolar coupling tothe 3He nuclei, causes rapid depolar-ization and hence irreversible signalloss. Making use of this relaxationeffect the local oyxgen partial pres-sure and its evolution during apneacan be measured which is shown inFigure 4. Since intrapulmonary dis-tribution of (pO2

) is governed byboth regional ventilation, regionalperfusion, and oxygen uptake intothe blood, the method constitutes anew approach to lung functionanalysis [7].

Judging by these encouraging re-sults, 3He tomography appears tohave a bright future for visualizingand assessing pulmonary ventilation.It will help provide further insightsinto the pathophysiology of breath-ing, and it may challenge ventilationscintigraphy in the preoperativetreatment of patients with pul-monary diseases. Since only a fewaccessory tools are needed to per-form 3He imaging with standardMRI equipment, the technique couldbecome widely available within arelatively short time.

References1. Bouchiat M. A., Carver T. R., Var-

nurn C. M. (1960). Nuclear polariza-tion in 3He gas induced by opticalpumping and dipolar exchange. PhysRev Lett 5: 373–375.

2. Colegrove F. D., Schearer L. D., Wal-ters K. (1963). Polarization of 3He gasby optically pumped gas. Nucl InstrMeth Phys Res A 320: 53–65.

3. Becker J. et al. (1994). Study of me-chanical compression of spin-polar-ized 3He gas. Nucl. Instr. and Meth. A346: 45–51.

4. Heil W. et al. (1995). Very long nu-clear relaxation times of spin polar-ized 3He in metal coated cells. Phys.Lett. A 201: 337–343.

5. Rohe D. et al. (1999). Measurementof the neutron electric form factorGen at 0.67 (GeV/c)2 via 3He(e,e’n).Phys. Rev. Lett 83: 4257–4260.

6. Heil W. et al. (2002). Large solid-angle polarization analysis with ther-mal neutrons using a 3He spin filter.Nucl. Instr. and Meth., in press.

7. Deninger A. et al. (1999). Quantifica-tion of regional intrapulmonary oxy-gen partial pressure evolution duringapnea by 3He MRI. Journal of Mag-netic resonance 141: 207–216.



Figure 4. Lung image of a pig (left) with ROI (region of interest) and plot ofthe local intrapulmonary oxygen partial pressure evolution (right).

FILLER -

In April 2002 a beam of protons,accelerated up to 62 MeV by the CSSuperconducting Cyclotron, wasused at Laboratori Nazionali delSud, Catania, to irradiate uvealmelanoma of the eye of three pa-tients. Five more patients weretreated in May. This is the first timethat hadrontherapy was used inItaly. The irradiation of patients af-fected by tumours with hadrons, andin particular protons, is nowadaysan established technique [1], whichis, however, used in only a few cen-tres in the world, located in sevenEuropean nations and in four non-European nations.

The dose released in tissues bycharged particles is mostly concen-trated at the end of their path (Braggpeak). The path itself is essentiallystraight. Taking advantage of thesegeometrical properties, and of thehigher RBE with respect to gamma-ray, X-ray, and electron irradiation,hadrontherapy is especially suitedfor the treatment of well-localizedtumours, particularly when the ir-radiation can damage nearby vitalorgans.

The maximum energy of theprotons accelerated by the Supercon-ducting Cyclotron operational atLNS, 62 MeV, is such that a depth ofabout 3 cm at most can be reachedin tissues. The use of heavier projec-tiles would imply a shorter range. Soit was decided to apply protonther-apy to pathologies of the eye, in par-ticular the uveal melanoma of thechoroids and the macular degeneracy.

The project has involved the ef-forts of physicists of LNS, of theUniversity of Catania and of otherlocal and national institutions, to-gether with the competences of oph-talmologists, radiotherapists, andradiologists. It was necessary tolearn how to characterize the protonbeam (shape, current, and energymodulation), define the treatmentplans, and accurately control thedose released during the treatment.

It is worth noting that, due toSicily’s geographical centrality withrespect to the Mediterranean, whereCatania stands, the activity of thetherapeutical facility installed at

LNS is of interest not only for Italybut also for other European andAfrican countries.

Reference1. NuPECC Report on Impact, Appli-

cations, Interactions of Nuclear Sci-ences, Chapter on Medical Therapy(2001).

DOMENICO VINCIGUERRA

Dept. of Physics and Astronomy and LNS,

Catania, Italy

news and views


Hadrontherapy Used for First Time in Italy

View of the protontherapy installation at LNS.

AU: TitleOK? Ifnot,pleaseprovide anew title.

The Workshop on Future Instru-ments for Nuclear and ParticlePhysics and Methods at the FRM-IItook place on April 12th, 2002 inGarching. The scope of the work-shop was to bring together differentgroups of interest in the field of nu-clear and particle physics as well asnuclear methods in view of thefuture experimental facilities at thenew German neutron source FRM-II. Actually, two large projects inthese areas are under development atthe FRM-II, namely the Munich Fis-sion Fragment Accelerator MAFFand the Ultra Cold Neutron Source.The motivation to organise theworkshop was to discuss new instru-ments beyond these large projectsand possible applications of thesesources, respectively.

Besides the conventional neutronsources, the FRM-II will providenew sources for neutron-rich fissionfragments, positrons, and ultra coldneutrons. They will extend intensi-ties from existing sources by ordersof magnitude. Throughout theworkshop the speakers pointed outthe urgent need to start the opera-tion of the FRM-II immediately inorder not to lose this unique advan-tage.

J. Neuhaus introduced the work-shop by a short overview of the plan-ned installations and instruments atthe FRM-II. The workshop was di-vided into three sessions, namelyNuclear Physics, Particle Physics,

and Nuclear Methods. D. Habs gavean overview of the possibilities andthe status of the MAFF project. Ac-tually a large number of componentsdeveloped for MAFF are tested atother facilities like REX-ISOLDE.Concerning reactor installations, thethrough-going beam tube has beencompleted, while further installa-tions are desperately waiting for thenuclear startup of the FRM-II. Onlythen can the MAFF project movefurther in the commissioning phase.Possible applications for the MAFFbeam were pointed out by G. See-wald (nuclear orientation studiesNMR-ON).

R. Casten and J. Jolie presentedapplications for a multipurpose beaminstrument (neutron capture) for nu-clear spectroscopy. With modern Ge-array detectors or high resolutioncrystal spectrometers together with aneutron lens a versatile instrumentcould be installed in the neutronguide hall, which also might servefor prompt g-ray neutron activationanalysis, as pointed out by A. Türler.

The session on Particle Physicswas introduced by H. Abele. Heshowed the large variety of applica-tions of neutron physics rangingfrom astro physics to particlephysics. O. Zimmer presented appli-cations of polarised nuclei for neu-tron scattering. They can be used asspin filters (polarisers and analysers)and for stroboscopic spin contrastvariation in the sample. Finally F.

Hartmann presented the ultra coldneutron source and first applicationsfor the ongoing research for theEDM and lifetime of the neutron.The expected large increase in neu-tron density by a factor of 100 to1,000 from the UCN source, whencompared to existing sources, willallow a significant decrease in statis-tical errors for neutron particle ex-periments.

In the last session on NuclearMethods, C. Hugenschmidt pre-sented the high intense positronsource at the FRM-II. Here again asubstantial increase in intensity upto 1010 positrons/s will allow newand exciting experiments rangingfrom fundamental physics to surfacescience and solid state physics. D.Schwalm showed experiments onpositronium which will substantiallyprofit from the increase in positronflux compared to conventionalsources.

The workshop concluded that,with the tremendous increase in in-tensity for fission fragments, ultracold neutrons, as well as positrons,new and exciting experiments will bepossible. This underlines the urgentneed for the startup of the FRM-II.The organiser welcomed the interestof user groups from nuclear and par-ticle physics to build up new experi-ments at the FRM-II, which demon-strates the possibilities of the FRM-IIas a multipurpose source.

meeting reports


Workshop on Future Instruments for Nuclear andParticle Physics and Methods at the FRM-IIJÜRGEN NEUHAUS

ZWE FRM-IITechnische Universität München

The 25th edition of the “Sympo-sium on Nuclear Physics” was heldin the town of Taxco, Mexico, fromJanuary 7th to 10th, 2002. This con-ference has been taking place everyyear for the last 25 and has becomean important international venue forthe nuclear physics community. Thismeeting was held for the second timein the beautiful mountain town ofTaxco, renowned for its silver artand crafts. Previous symposia weretraditionally held in the town ofOaxtepec, Mexico, for which reasonthe conference became known as“The Oaxtepec Meeting.”

The Symposium on NuclearPhysics was conceived from the be-ginning as a small meeting designedto bring together some of the leadingscientists in the field. During these25 years, the conference has becomeone of the best known internationalconferences on Nuclear Physics. Itsmost distinctive feature is its abilityto gather a wide range of specialistsin different nuclear physics subjects,both theoretical and experimental,in a relaxed and informal environ-ment, providing them with a uniqueopportunity to exchange ideas.

This year, 40 colleagues attendedour symposium, of which about halfcame from abroad. In addition, adozen graduate students participatedin the meeting, where 23 invitedtalks and 10 posters were presented.The subjects discussed covered dif-ferent aspects of nuclear and sub-nuclear structure, radioactive beams,nuclear astrophysics, relativisticheavy-ion collisions, and severalother related subjects. There werethree main themes of the conference,namely nuclear structure, exotic nu-clei, and relativistic heavy ion colli-

sions, plus a small number of talkson special topics.

Nuclear structure talks rangedover a large gamut of topics includ-ing random interactions, criticalpoint symmetries, the effects of re-pulsive interactions between com-posite bosons, level crossings, thedescription of spurious states, reso-nances, and quasimolecular states.

The field of exotic nuclei is amajor growth area in nuclearphysics these days, and several talksat the conference dealt with aspectsof this such as symmetries in N = Znuclei, exotic decay modes, produc-tion of superheavy and radioactivenuclei, and coupling to the contin-uum.

Collisions of relativistic heavyions and the formation and possibledetection of the quark-gluon plasma,as well as the structure of QCD athigh densities and temperatures,formed another important themethat is very current these days nowthat RHIC has come on line.

The posters complemented thetopics discussed and represented anopportunity for graduate students toshow the progress of their researchwork.

During the welcoming dinner,the distinguished Mexican nuclearphysicist, Prof. Marcos Moshinsky,addressed the attendants to recall thehistory of the Oaxtepec Symposiaand to emphasize the importance ofthese meetings to strengthen the tiesbetween the Mexican and interna-tional nuclear physics communities.After his words, we enjoyed themusic of a mariachi band.

As is customary, many of the for-eign participants stayed for a whilelonger in Mexico after the end of the

conference to initiate or continuecollaborations with their Mexicancolleagues.

The level of maturity reached bythe small but very active Mexicannuclear physics community leads usto believe that this 25th jubilee ofthe Nuclear Physics Symposium con-stitutes only a first stage in a longand exciting series of meetings tocome. Congratulations and thanksto all our colleagues who have en-thusiastically taken part in thesemeetings throughout the years.

ALEJANDRO AYALA

ROELOF BIJKER

ALEJANDRO FRANK

JORGE G. HIRSCH

Instituto de Ciencias NuclearesUniversidad nacional Autónoma de México

meeting reports


XXV Symposium on Nuclear Physics

The international symposiumPOSTYK01 was held at the YukawaInstitute for Theoretical Physics,Kyoto, Japan, from November 12 to14, 2001. It was organized as a postsymposium of the Yukawa Interna-tional Seminar (YKIS 2001) on thePhysics of Unstable Nuclei held inKyoto from November 5 to 10,2001. There were about 86 partici-pants from 13 countries. Most ofthem had also attended the YKIS2001 conference, which prominentlycovered clustering in unstable nuclei.At the post-YKIS symposium unsta-ble nuclei were further discussed indepth, but the scope was extended toclustering aspects of other quantummany-body systems as well.

At the last international clusterconference at Rab, Croatia, it wasdecided that the next number of thatconference series will be held atNara, Japan, in 2003. It was also de-cided that we would have a sympo-sium in England in 2001. Unfortu-nately, organizational difficultiesarose in England. The symposium inKyoto following the YKIS confer-ence was meant to substitute forthat meeting. Our aim was to bridgethe time gap between Rab and Naraand to encourage studies in this fieldas a preparation for the Nara con-ference.

The first topic discussed was“Clustering in Unstable Nuclei.” Awhole morning was devoted to thismain subject. Four talks were aboutcluster structure in He and Li iso-topes and four other talks aboutmolecular structure, especially in Beisotopes. The 6He + 6He structure in 12Be may be as fundamental for

cluster studies on unstable nuclei asα + α has been for stable nuclei.

The cluster studies which beganwith α-clusters, later embraced vari-ous other clusters, e.g., d, t, 3He andheavier clusters, such as 12C and 16O.Further recent developments werefocussed on cluster problems of un-stable nuclei and on the study of hy-pernuclei. The cluster models for hy-pernuclei have been used widely andsuccessfully in the last two decades.The subject “Cluster Structure inHypernuclei’’ was discussed in thesecond session.

In the next session “ClusterStructure in Light to Medium-HeavyStable Nuclei” was discussed. Thissession covered molecular reso-nances and the problem of internu-clear potentials related to clustering.We learned of new developments inexperimental techniques and instru-ments and in theoretical approachesand interpretation of resonances andinternuclear potentials in heavy ioncollisions.

In the session on “Alpha andDineutron Condensation,” a veryintriguing study on Bose-Einsteincondensation of clusters in nucleiwas reported by Dr. Schuck. Thecalculations of Schuck, Tohsaki-Suzuki, and their collaborators for12C and 16O result in some states,around the 3α and 4α thresholds,respectively, which are interpreted asshowing Bose-Einstein condensationof clusters.

We had a session on “NuclearCluster Physics in Astrophysics.”Cluster models were used success-fully in the description of energy lev-els and widths for many light nuclei

which appear in astrophysics. Sev-eral clustered nuclear states havebeen shown to play important rolesin nucleosynthesis.

The session on “Fragment For-mation in Nuclear Reactions andProperties of Nuclear Matter” com-prised two experimental and fourtheoretical talks. Cluster dynamicshas been shown to play an impor-tant role in fragment formation.

The session on “Clustering,Large Deformation and Formationof Heavy Nuclei” has contributed tothe clarification of the relation be-tween large deformation and cluster-ization.

The next topic was “ClusteringFeatures of Few-Body Systems.” Dr.Lovas reported on ab initio calcula-tions for light nuclei in the frame-work of a stochastic variationalmethod based on correlated Gauss-ian bases. Furthermore, we learnedof recent theoretical developments ina more sophisticated RGM (resonat-ing group method) and algebraic ap-proaches of the RGM based onSU(3) cluster wave functions.

Applications of the algebraic ap-proach to many-channel s-clustersystems were discussed also in thenext session, on “Theoretical Devel-opments in Nuclear Cluster Physics.”Three talks discussed the applicationof the complex scaling of the Fa-ddeev equations and the Jost func-tion method to unstable nuclei. Onetalk was on the cluster effects innuclear binding energies.

The subject of the last sessionwas “Cluster Effects on Photon Pro-duction and Atomic Physics.” Aninteresting report was presented by

meeting reports


International Symposium on Clustering Aspects ofQuantum Many-Body Systems

Dr. Löhner on bremsstrahlung phe-nomena in proton and α-particlecollisions with nuclei. A topic relatedto atomic physics, atomic spectra ina bubble of liquid helium, was dis-cussed by Nakatsukasa.

Finally, a beautiful summary wasgiven by Dr. Brink. He emphasizedthe coexistence of many differentstructures in the same nucleus.

The proceedings of the sympo-sium will be published by World Sci-entific.

This symposium was hosted bythe Yukawa Institute for TheoreticalPhysics, Kyoto University, the Re-search Center for Nuclear Physics,Osaka University, and the Hadronand Nuclear Theory Group in KEK,the High Energy Accelerator Re-search Organization. It should bestressed that the Yukawa Institute,where the symposium actually tookplace, has made a significant impacton the progress of cluster studies inJapan. The symposium was organ-

ized and attended mostly by youngresearchers. It was in fact a début fora new generation of devoted clusterphysicists. We can thus look forwardto the development of experimentaland theoretical research on nuclearcluster physics with great expecta-tions.

K. KATO

meeting reports


Report on the Symposium EMI2001 (Electromagnetic Interactions in Nuclear and Hadron Physics)

The International Symposium onElectromagnetic Interactions in Nu-clear and Hadron Physics (EMI2001)was held at Osaka University, Japanfrom December 4th to 7th, 2001.The symposium is organized withthe aim to discuss the fundamentalcurrent problems in nuclear andhadron physics developed with“electromagnetic probes.” The inter-national forum brought together128 physicists from 16 countries in-cluding 48 participants from Japan.There were lively discussions on thelatest advances in the following sub-jects;

1. Meson and hadron productionsby real and virtual photon inter-action with nucleons and nuclei

2. Astrophysics studies via photo-reactions and hadron reactions

3. New technologies for the electro-magnetic (E.M.) probes and thedetector development

4. Nuclear structure studied withE.M. probes

5. Fundamental symmetries withE.M. probes and related prob-lems

When a decision was made in 2000to organize this symposium, severalmovements towards new develop-ments of physics with electromag-netic probes were expected to be

a fashion in the world. Actually,interesting and hot results frommany laboratories in the world havebeen presented discussed in theEMI2001 symposium.

This symposium is supported byMinistry of Education, Culture,Sport, Science and Technology(Monbu-Kagaku-shou) under COE(Center of Excellence) Program, andis hosted by the Research Center forNuclear Physics (RCNP). The sym-posium belongs to a series of inter-national meetings at RCNP. It wastimely to discuss the subjects men-tioned above since we expect to havesome interesting results from thenew facilities like the LEPS (Laser-

Electron-Photon Spectrometer) facil-ity at SPring-8 using the photonbeam with an energy of 1.5–2.4GeV, and the Jefferson Laboratoryusing a high intensity electron beamsince noble technical developmentshave been delivered for future exper-iments. The symposium is also in-tended for celebrating the 30-yearanniversary of RCNP, Osaka Uni-versity. The ceremony and receptionof the 30-year RCNP anniversary isheld on December 3rd, 2001, beforethe symposium.

In addition to invited talks, wearranged a poster session and a spe-cial session where the studentsworking at RCNP presented theirlatest results for the attendant ex-perienced scientists. This special ses-sion seems to work very well tostimulate the young students. Theproceedings of the EMI2001 sympo-sium will be published from theWorld Scientific.

MAMORU FUJIWARA

AU:Pleaseprovideaffiliation.

AU:Pleaseprovideaffiliation.

The study of multifragmentationand its possible link to a nuclear liq-uid-gas phase transition has beenmotivated by the desire to under-stand the nuclear equation of state,with its broad applications to nu-clear physics and astrophysics. Nu-clear fragmentation reactions firstbecame of interest in the 1950s as aresult of radiochemical and emulsionmeasurements conducted withhadron beams [1–3]. However, de-tector technology and data-acquisi-tion capabilities permitted only in-clusive investigations of thesecomplex reactions until the late1970s. In a set of key experiments atFermilab and the Brookhaven AGS,the Purdue group measured com-plete spectra and isotope yields frombombardments of heavy nuclei with1–300 GeV protons [4]. While theseexperiments lacked the multiparticledetection capability needed to con-firm the existence of a phase transi-tion, they stimulated extensive scien-tific discourse about this possibility.Further, the results spurred construc-tion of several large 4π detector ar-rays dedicated to the search for thenuclear liquid-gas phase transition inboth hadron- and heavy-ion-inducedreactions [5].

The Indiana Silicon Sphere (ISiS)project was initiated in the late1980s in order to focus on light-ioninduced reactions. Light ions, espe-cially hadrons, are particularly ad-vantageous for multifragmentationstudies since they emphasize thethermal properties of the disintegrat-ing residue, with minimal rotationaland compressional effects. Experi-mentally, one also has the advantage

of producing a broad, continuousdistribution of excitation energies ina single reaction and observing thebreakup in a reference frame veryclose to the center-of-mass system.To search for evidence of a phasetransition, a 4π detector was requiredin order to provide fragment multi-plicity information, event topologyand calorimetry.

Because the previous studies [4,6] had shown a broadening to lowenergies in the kinetic energy spectraof the clusters (IMFs: 3 � Z � 20)emitted in reactions above severalGeV bombarding energy), the detec-tor design also demanded very lowthresholds and good energy reso-lution. Thus, it was decided toconstruct a silicon-based array aug-mented by low pressure gas-ioniza-tion chambers for Z-identification ofthe lowest energy fragments and aCsI scintillator with photodiodereadout for Z and A identification ofthe energetic lighter fragments,shown in Figure 1 and described in[7]. Consistent with light-ion kine-matics, a spherical geometry waschosen for the 162 close-packedtriple telescopes in the array, ar-ranged in nine concentric rings, eachcontaining 18 detector modules. Aschematic of the ISiS array is shownin Figure 2. The detector configura-tion yielded a kinetic energy accept-ance of 1 MeV � E/A � 92 MeV forcharge-identified fragments up to Z= 16; Z and A identification for 8MeV � E/A � 92 MeV products,and “grey particle” detection for fastparticles (primarily protons andpions) up to 350 MeV. Some devel-opment of the detector modules pro-

ceeded in parallel with our Saclaycolleagues, who were also involvedin the development of the siliconmodules for the INDRA array forheavy-ion measurements.

Four campaigns were carried outwith the ISiS array: E228 at LNSSaclay with 1.8–4.8 GeV 3He ions;E375 at IUCF with 130–260 MeVproton and 3He beams; E900 at AGSwith 5.0–14.6 GeV/c proton and π-

beams, and E900a at AGS with 8.0GeV/c tagged antiproton and π-

beams. Principal experimentalists in-volved in the collaboration includedscientists from Simon Fraser Univer-sity (R. G. Korteling), CEA Saclay(C. Volant, R. Legrain, and E. C.Pollacco), Texas A&M University

facilities and methods


The Nuclear Liquid-Gas Phase Transition:Studies with the ISiS Array

Figure 1. Drawing of an ISiS arc barfor the forward hemisphere, with theangular coverage of each telescopelabeled. Each unit is a part of an 18-member ring; the forward-most ele-ment is divided into two segments.Rings are identified as follows:14–22° (1A); 22–33° (1B); 33–52°(2); 52–69° (3); 69–86.4° (4);93.6–111° (5); 111–128° (6);128–147° (7); 147–166° (8).

AU:Pleasecheckmathclosely.Thanks.

Figure 2. Assembly drawing of the ISiS system. Components are as follows:(1) center ring, (2) window, (3) arc bars, (4) center disks, (5) support cones,(6) target ladder assembly, (7) steel rails, and (8) vacuum chamber.

(S. J. Yennello), Jagiellonian Univer-sity (J. Brzychczyk), the University ofMaryland (H. Breuer), and WarsawUniversity (L. Pienkowski), as wellas former members of the IU group,T. Lefort, L. Beaulieu, K. B. Morley,E. Foxford, and D. S. Bracken.

The clearest signatures of a phasetransition are found in the AGS data,in particular the 8.0 GeV/c π- + 197Aureaction, where 2.5 × 106 events withmultiplicity M ≥ 3 for thermal-likecharged particles were recorded.These data exhibit several experi-mental criteria characteristic of anequilibrium system undergoing aphase transition. First, the fragmentsare emitted nearly isotropically andexhibit Maxwellian-like kinetic en-ergy spectra. This behavior is illus-trated in the differential cross sectionplots for carbon fragments in Figure3 as a function of the heat content,

excitation energy per residue nu-cleon E*/A, of the hot target residue[8]. One observes that as E*/A in-creases, the spectra are broadenedtoward lower and lower energies,consistent with the breakup of a sys-tem with lower than normal nucleardensity.

The fragment multiplicities andsize distributions are also importantcriteria. Figure 4 shows the evolu-tion of the emitting source chargeand the charges of the three largestfragments as E*/A increases. ForE*/A � 4–5 MeV, which comprises~95% of the total reaction cross sec-tion, Figure 4 indicates that theevents are associated with a heavyresidue, consistent with evaporativeemission. At higher excitation ener-gies the tendency is for each eventto produce fragments of increasinglysimilar sizes, so that above E*/A � 6 MeV, multifragmentation into



Figure 3. Kinetic-energy spectra of oxygen nuclei at four angles in the labo-ratory system for three bins of excitation energy for 8 GeV/c π - + 197Au re-action; open circles are for E*/A = 2–4 MeV; closed triangles for E/A = 4.6MeV; open triangles for E*/A = 6–9 MeV. The lines correspond to SMM cal-culations for breakup volume V = 3V0 with extra expansion energy, equal tozero (solid line) and 0.5A MeV (dashed line) [10]. For each bin in excitationenergy the simulated spectrum is normalized to the maximum of the experi-mental one.

IMFs and light-charged particles isthe dominant process. The upperpanel of Figure 5 shows how theprobability for a given IMF multi-plicity depends on E*/A (the unde-tected largest residue is not in-cluded). In the second frame thecorresponding charge distributionshave been fit with a power law;σ(Z)αZ-τ . A minimum in the power-law exponent τ is observed nearE*/A ~ 6 MeV, indicating a tendencyto form increasingly large clusters upto this point. This minimum signalsthe possible onset of a phase transi-tion, as discussed in [9] and [10]. Athigher excitation energies, the clus-ter sizes begin to decrease, in partdue to secondary decay of the hotfragments.

The breakup time scale is centralto distinguishing between the “in-

stantaneous” breakup associatedwith a phase transition and a slowersequential evaporative process. Inthe bottom frame of Figure 5, theevolution of the relative emissiontime for IMFs is shown as a functionof E*/A [11]. At low excitation en-ergy, the time scales are relativelylong, typical of evaporative emis-sion. However, with increasing E*/Athe time scale decreases rapidly,reaching values of ∆τ ~ 20–50 fm/cfor E*/A � 4 MeV; i.e., the breakupis nearly instantaneous. In this sameexcitation energy range, the thirdpanel shows evidence for a slightextra thermal expansion energy [12],much smaller than the compression-induced values found in collisionsbetween mass-symmetric heavy-ionstudies. All of the above observ-ables—multiplicity and charge dis-

tributions, time scale, and extra ther-mal expansion energy—indicate amechanism change near E*/A ~ 4–6MeV, corresponding to the predictedthreshold from multifragmentationmodels [13–15].

When temperatures derivedfrom double isotope ratios are plot-ted versus the heat content of thesystem (the caloric curve), the ISiSdata exhibit behavior similar to theheating of a liquid to the boilingpoint, as originally shown byPochodzalla et al. [16] for the AL-ADIN results. Further analysis sug-gests evidence for a negative heat ca-pacity at the liquid-gas transitionpoint, consistent with the recent re-sults of D’Agostino et al. [17]. Inboth cases a first-order phase transi-tion is indicated. Beaulieu et al. [18]showed that the ISiS data exhibit bi-nomial reducibility and thermal scal-



Figure 4. Dependence of fractional source charge and IMF charges as a func-tion of E*/A for the 8 GeV/c π - + 197Au reaction [16]. Top: Fractional sourcecharge of residue. Middle: Missing charge in ISiS, assumed be the largestfragment; and SSM prediction for missing charge (solid line) and for largestfragment (dashed line), both passed through the ISiS filter. Bottom: Chargeof two largest observed fragments; solid line is the SMM prediction for sec-ond largest fragment (Zmax2), and dashed line, for third largest fragment(Zmax3).

Figure 5. Dependence on E*/A forthe following qualities, from bottomup: relative IMF emission time t,extra radial expansion energyEexp/AIMF, charge distribution powerlaw exponent τ and probability for agiven IMF multiplicity [16].

ing, adding support for the case ofstatistical concepts in evaluating thedata. General agreement with nu-clear multifragmentation models hasalso been obtained using the calcula-tions of Botvina et al. [13] and Fried-man [14].

However, perhaps the most com-pelling evidence for a nuclear liquid-gas phase transition may lie in theability to describe the distributionswith more general statistical theoriesof liquid-gas properties. Using a per-colation model, Berkenbusch et al.[9] have shown evidence for a con-tinuous phase transition, with theexpected critical parameters, for themass distribution of 10.2 GeV/c pro-tons incident on 197Au. At the sametime, Elliott et al. [10] applied a

Fisher scaling model analysis to thedata and found an equivalent result,i.e., evidence for a phase transitionand critical behavior. The collapse ofthe IMF data for the 8.0 GeV/c π- +197Au reactions onto a single locusextending over six decades, when re-duced to a single set of Fisher-scalingexponents, is shown in Figure 6.

Thus, given the ISiS results, com-bined with heavy-ion results ob-tained at GANIL (INDRA), GSI(ALADIN), NSCL (Miniball/Wall),Texas A&M (NIMROD), and theformer LBNL Bevalac (EOS/Pur-due), it appears that the questionfacing the nuclear dynamics commu-nity today is no longer, “Does thephase transition exist?”, but rather,“What is the nature of the phasetransition and what are the criticalparameters?”

References1. N. A. Perfilov, O. V. Lozhkin, and

V. P. Shamov, Sov. Phys. Usp. 3, 1(1960).

2. J. Hudis, in Nuclear Chemistry, ed-ited by L. Yaffe (Academic Press,New York, 1968).

3. W. G. Lynch, Ann Rev. Nucl. Part.Sci. 37, 493 (1987).

4. N. T. Porile et al., Phys. Rev. C 39,1914 (1989).

5. See, for example, Nucl. Phys. A681,267c (2001) and Proc. of Int. Work-shop XXVII on Gross Properties ofNuclei and Nuclear Excitations:Multifragmentation, Jan. 1999 (GSIDarmstadt, DE, edited by H. Feld-meier, J. Knoll, W. Norenberg and J. Wambach).

6. S. J. Yennello et al., Phys. Rev. Lett.67, 671 (1991).

7. K. Kwiatkowski et al., Nucl. Instr.Meth. A 360, 571 (1995); A. Ru-angma et al. submitted to Phys. Rev.C.

8. T. Lefort et al., Phys. Rev. C 64,064603 (2001); L. Beaulieu et al.,Phys. Rev. C 64, 064604 (2001).

9. M. Berkenbusch et al., Phys. Rev.Lett. 88, 022701 (2002).

10. J.B. Elliott et al., Phys. Rev. Lett. 88,042701 (2002).

11. L. Beaulieu et al., Phys. Rev. Lett.84, 5971 (2000).

12. T. Lefort et al., Phys. Rev. C 62,0316(R) (2000).

13. A. Botvina, A. S. Iljinov and I. N.Mishustin, Nucl. Phys. A 507, 649(1990).

14. W. Friedman, Phys. Rev. C 42, 667(1990).

15. D. H. E. Gross, Rep. Prog. Phys. 53,605 (1990).

16. J. Pochodzalla et al., Phys. Rev. Lett.75, 1040 (1995).

17. M. D’Agostino et al., Phys. Lett. B473, 219 (2000).

18. L. Beaulieu et al., Phys. Rev. C 63,031302 (2001).

V. E. VIOLA

K. KWIATKOWSKI



Figure 6. The scaled yield distribu-tion versus the scaled temperaturefor the ISiS data (upper) and d = 3Ising model calculation (lower) from[10]. For the Ising model the quan-tity (nA/q0A

-τ)/10 is plotted againstthe quantity Aσε/1.435T. Data for T > Tc is scaled only as nA/q0A

-τ.

AU: Thisis a B&Wpublica-tion. Thecolor inthis art willnot be dis-cernibleas shadesof greys.Providenew art?

AU:Pleaseprovideaffiliations.

IntroductionJESSICA (Juelich Experimental

Spallation Target Set-up In COSYArea) is an experiment at the COSYcooler synchrotron at the Forsch-ungszentrum Jülich. The aim of theexperiment is the investigation ofadvanced cold moderators for up-coming next generation neutronsources like ESS (European Spal-lation Source) [1, 2], SNS (SpallationNeutron Source, under constructionin Oak Ridge, USA) [3], or JSNS(J–apanese Spallation NeutronSource). In order to design and con-struct intensive pulsed spallationneutron sources experimental inves-tigations of the crucial technicalcomponents are required. JESSICAis a 1:1 mock-up of the target-moderator-reflector assembly of one5 MW target station of the planned10 MW source ESS. The data ob-tained at JESSICA will be used tofind the best-suited moderator fornext generation neutron sources. Onthe one hand, the experimental in-vestigation of the neutronic behav-iour of advanced cold moderators isa main topic of the experiment. Onthe other hand Monte-Carlo simula-tion codes can be validated as well.Especially new neutron scatteringkernels—which are still under de-velopment—can be validated andchecked against measured data. Thetarget containing 35 l of mercury islocated in the centre of the reflector.A lead reflector with a diameter of1.3 m and a height of 1.3 m sur-rounds the target. The moderatorsare placed in the so-called winggeometry. This means two modera-tors are mounted above and belowthe target to prevent fast neutronsfrom the target directly leaking out

of the system. This reduces the fastneutron background considerably.Whereas three moderators are filledwith water, the lower upstream mod-erator position is used to study vari-ous cold moderator materials, as canbe seen in Figure 1(a). Figure 1(b)gives an impression of the facility in-stalled at COSY. But why is JESSICAinstalled at COSY? Due to the lowproton beam intensity radiolysis, en-ergy deposition and activation arenegligible. This enables easy modifi-cations of the experiment afterswitching off the proton beam andomitting a cooling loop for the mer-cury target.

Experimental Set-UpJESSICA is operated with a

beam intensity of 4 . 108–4 . 109

protons per pulse. The repetitionrate is 1/30 Hz with a pulse length ofapproximately 0.5 µs. To determine

the number of protons per pulse,two proton beam monitors with dif-ferent working principles are in-stalled in the proton beam line. Onthe one hand a wall current monitor(WCM) measuring the mirror cur-



Investigation of the Neutronic Performance ofCold Moderators with JESSICA

Figure 1(a). 3D view of the target,moderator, and reflector assembly.

Figure 1(b). The JESSICA Experiment at the COSY proton synchrotron inJülich.

rent in the wall of the beam tube andon the other hand an integrating cur-rent transformer (ICT) measuringthe current induced in a coil whenthe proton beam passes through areused. The number of protons perpulse is indispensable to determinethe neutron to proton ratio in orderto compare the experimental datawith Monte Carlo simulations on anabsolute scale. The characteristics ofthe moderators to be investigated arestudied by time of flight measure-ments of the neutrons coming out ofthe moderator surface. Therefore, a5.37 m long neutron flight path wasconstructed. At the end a neutrondetector is placed to measure thetime of flight spectra, from whichthe energy spectra can be deduced.To obtain detailed information ofthe time structure and wavelengthdependency of the neutron pulses, agraphite crystal can be moved intothe neutron flight path. Neutronsfulfilling the Bragg condition are re-flected by the crystal and can be de-tected with a second neutron detec-tor viewing the crystal.

Figure 2 illustrates the set-up ofthe experiment. In order to achieve a

better time resolution, the surfacesof the moderator, crystal, and detec-tor can be aligned in parallel.

Advanced Cold ModeratorsTo improve the performance of

next generation neutron sourcesJESSICA is looking for the mostadvantageous candidate moderator

materials. Most promising modera-tors are

• ice at 20 K,• solid methane at 20 K,• methane pellets in liquid

hydrogen, and• methane hydrate at 20 K.

As a reference, water at ambienttemperature and liquid hydrogen at20 K will also be measured. Basedon measurements performed byInoue et al. [4] ice and solid methaneas moderator materials are expectedto be superior to liquid hydrogenmoderators as can be seen in Figure3. When comparing solid methanewith liquid hydrogen the advantageis dominating for kinetic energiesbelow 0.01 eV. Ice at 20 K is ex-pected to yield higher neutron fluxesin an energy regime between 0.001eV and 0.1 eV. To benefit fromadvantages of both ice and methanethe idea is to combine both materi-als. One possibility is using methanehydrate because here a methane mol-ecule is encapsulated in an ice cage.JESSICA will investigate whether anincrease of the neutron flux can be



Figure 2. Set-up of the JESSICA experiment with proton monitors, neutrondetectors, scattering crystal, and target-moderator-reflector assembly.

Figure 3. Measured neutron energy spectra for various cold moderators car-ried out at an electron accelerator [4].

observed in the energy regime be-tween 0.001 eV and 0.1 eV whenusing a methane hydrate moderator.

The data described above wereobtained with an electron accelera-tor driven experiment [5]. A 45 MeVelectron beam hits a heavy metal tar-get (tungsten or lead). The decelera-tion of the electrons causes brems-strahlung in an energy range of theresonance for (γ, n)-reactions withthe heavy target nuclei. The gener-ated fast neutrons are moderated inthe adjoining moderator. In contrastto JESSICA no reflector was in-stalled and another moderatorgeometry was used. Because of theabove-mentioned differences it is upto JESSICA to prove if the samegains can be found in a spallationsource driven by a 1.334 GeV pro-ton beam.

First Results from JESSICAUp to now the neutronic per-

formance of two moderators was

investigated. During the first meas-uring campaign water at ambienttemperature was studied. From thetime of flight spectra not only the en-ergy spectra can be deduced but alsothe moderator temperature can bedetermined. This is possible becausethe kinetic energy of the neutrons isMaxwellian distributed. The deter-mined temperature of 307 K is in agood accordance with the measuredtemperature of the moderator of294 K. Furthermore, the shape of themeasured time-of-flight spectrum isin line with the spectrum from aMonte-Carlo simulation performedwith MCNPX [6], as can be seen inFigure 4. In this case the peak valuesare normalised to one. This spec-trum is obtained in two steps. Thefirst measurement counts all neu-trons leaving the moderator includ-ing background. To eliminate thebackground a further measurementis performed. In this second meas-urement only those neutrons are de-tected, which are not absorbed in an



Figure 4. Comparison of the time of flight spectrum between experimentaldata (solid line) and Monte Carlo simulation (open circles) for an ambienttemperature water moderator.

Figure 5. Energy spectra for 20 K and 70 K ice and water at room tempera-ture (300 K).

additionally inserted Cadmium layerin front of the neutron flight path.The high neutron absorption crosssection of Cadmium for thermalneutrons prevents them from reach-ing the detector. The difference ofboth spectra results in the time offlight spectrum for the thermal neu-trons. At this time a comparison be-tween experimental data and simu-lated ones is only possible for anambient temperature water modera-tor due to missing neutron scatteringkernels for cold moderator materi-als. But with JESSICA also an icemoderator at 20 K and 70 K was in-vestigated. Transforming the time-of-flight spectrum into an energyspectrum shows a similar behaviouras observed by Inoue et al. In Figure5 the energy spectra of ambient tem-perature water, ice at 70 K, and iceat 20 K are plotted. The shown dataare normalised relative to the inci-dent number of protons. In contrastto the slowing down regime (>0.2eV) where all three moderators showthe same behaviour, large differencescan be observed in the lower energyregime. Water is superior in the en-ergy regime between 3 . 10-2 eV and0.2 eV compared to the ice modera-tors. But for low energetic neutronsthe intensity drops down and the icemoderators seem to be more advan-tageous. It can be seen that thecolder the moderator is, the moreshifted is the peak position towardslower neutron energies. The positionof the peak for 20 K is at 6 . 10-3 eV,for 70 K at 1 . 10-2 eV, and for 300K at 3 . 10-2 eV, respectively. To ob-tain more information about themoderation process inside the mod-erator, the wavelength-dependenttime structure of the neutron pulsehas to be investigated. For that rea-son the graphite crystal is installed inthe neutron flight path. Only neu-trons fulfilling the Bragg conditionare reflected in the crystal and can becounted in a second detector. Theobserved spectra for an ambient

temperature water moderator andan ice moderator at 20 K are plottedin Figure 6. The spectra show thetime structure of the neutron pulsesfor five specific wavelengths (ener-gies): 0.95 Å, 1.19 Å, 1.57 Å, 2.37Å, and 4.74 Å. As expected, the peakintensity for the longer wavelengths(lower energies and longer flighttimes) increases (2.37 Å and 4.74 Å)in case of the 20 K cold ice modera-tor compared to the 300 K watermoderator. These experiments con-firm the results presented in Figure 5that an ice moderator will be supe-rior compared to a water moderatordue to increasing intensity for lowerenergetic neutrons.

OutlookAfter first experiments of JES-

SICA are finished successfully withwater and ice moderators, we willnow study advanced moderators likemethane hydrate or methane pellets.As a reference moderator for coldmoderators, liquid hydrogen willalso be measured, because it is oneof the standard cold moderatorsused at several neutron sourcesaround the world. With the set ofdata obtained from the JESSICA ex-periments new developed neutronscattering kernels for neutron trans-

port codes will be checked and opti-mised.

If the advanced moderators,mainly methane-hydrate, will deliverthe expected gain in the neutron out-put, the JESSICA experiment canhelp to improve the neutronic per-formance of moderator systems.

K. NÜNIGHOFF FOR THE

JESSICA COLLABORATION1

1H. Conrad, D. Filges, F. Goldenbaum, R.-D.Neef, K. Nünighoff, N. Paul, Ch. Pohl, H.Schaal, H. Stelzer, H. Tietze-Jaensch, M. Wohl-muther (Forschungzentrum Jülich, Germany);A. Smirnov (JINR Dubna, Russia); W. Ninaus(Technische Universtität Graz, Austria).

References1. ESS Volume III. The ESS Technical

Study. ISBN 090-237-6-659, Novem-ber 1996.

2. National Spallation Neutron Source,Executive Summary, Oak Ridge Na-tional Laboratory, May 1997.

3. K. Inoue et al., Atomic Energy SocietyJapan, 21 (1979) 865.

4. K. Inoue and N. Otomo, Pulsed ColdNeutron Source, Journal of NuclearScience and Technology 13(389) 1976.

5. H. G. Hughes et al., MCNPX—TheLAHET/MCNPX Code Merger. LosAlamos National Laboratory, X-Divi-sion Research Note XTM-RN(U)97-012, LA-UR-97-4891, 1997.



Figure 6. Comparison of the time structure of the neutron pulses for 20 K(solid line) and 300 K (shaded area) and different wavelengths.

September 12–20Geneva, Switzerland and Les

Houches, France. EURO SUMMERSCHOOL ON EXOTIC BEAMS2002. Contact: F. Herfurth, CERN-EP/ISOLDE, 1211-Geneva 23. E-mail:[email protected]. Tel: +4122 767 2780.

Web: http://cern.ch/euroschool2002

September 16–24Erice, Sicily, Italy. Quarks in Had-

rons and Nuclei. Contact: [email protected], or [email protected].

September 17–21Warsaw and Krakow, Poland.

XXXIII European Cyclotron ProgressMeeting. Heavy Ion Laboratory of theWarsaw University and Institute ofNuclear Physics. Contact: [email protected].

Web: http://www.slcj.uw.edu.pl/conf

September 23–27Legnaro–Padova, Italy. Nuclear

Structure with Large Gamma-Arrays:Status and Perspectives (NS2002).Contact: NS2002 c/o Dr. BarbaraTonello, INFN—Laboratori Nazionalidi Legnaro, Via Romea 4, I-35020Legnaro Padova, Italy. E-mail:[email protected]. Tel: +390498068521. Fax: +390498068514.

Web: http://ns2002.lnl.infn.it

September 30–October 3ATOMKI, Debrecen, Hungary.

Nuclear Physics in Astrophysics’ 17thInternational Nuclear Physics Divi-sional Conference of the EuropeanPhysical Society. Contact: As. Fulop,ATOMKI, H-4001 Debrecen, Hun-gary, POB. 51. E-mail: [email protected]. Fax: +36-52-416-181.

Web: www.atomki.hu/inpdc17

September 30–October 4Osaka, Japan. 16th International

Conference on Particles and Nuclei(PaNic02). Contact: [email protected].

Web: http://www.rcnp.osaka-u.ac.jp/~panic02/

October 23–25Gent, Belgium. International Sym-

posium on “The Nuclear Many-BodySystem: Exploring the Limits.” Sympo-sium organized on the occasion of KrisHeyde’s 60th birthday.

Web: http://ssf.rug.ac.be/kris60

November 12–16CAARI 2002: 17th International

Conference on the Application of Ac-celerators in Research and Industry.Contact: Jerome L Duggan, E-mail:[email protected]. Tel: +940-565-3252.

Web: http://orgs.unt.edu/CAARI

NovemberHalong Bay, Vietnam. The Inter-

national Symposium on Physics ofUnstable Nuclei (ISPUN02).

Web: http://www.vaec.gov.vn/instispun02

2003January 26–February 2

Bormio, Italy. XLI InternationalWinter Meeting on Nuclear Physics.Contact: Iori Ileana. E-mail: [email protected].

June 17–21Moscow, Russia. VIII Interna-

tional Conference on Nucleus-NucleusCollisions. Contact: Yu. Ts. Organess-ian or R. Kalpakchieva, Flerov Labo-ratory of Nuclear Reactions, JINR,141980 Dubna, Moscow region, Rus-sia. E-mail: [email protected]. Tel: 7-09621-62151. Fax: 7-09621-65083.

Web: http://www.nn2003.ru/

March 23–30Erice, Sicily, Italy. Symmetries in

Nuclear Structure. Contact: AnnarosaSpalla, Department of Physics andINFN, Padova. E-mail: [email protected].

NuPECC is preparing a newLong Range Plan of Nuclear Physicsin Europe. In this exercise NuclearPhysics is assessed as a unified andcoherent science of strongly inter-acting many-body system enrichedby impacts on astrophysics, funda-mental interactions, and symmetriesas well as applications derived fromnuclear physics research. In order

to achieve the goal, NuPECC hasestablished six working groups,whose compositions can be foundon the NuPECC web page underhttp://www.nupecc.org.

The draft reports of these work-ing groups will be presented and dis-cussed in the open Town Meeting atGSI on January 30–February 1,2002. The meeting will also provide

a possibility for other contributionsand will discuss the priorities andrecommendations.

The programme committee ofthe Town Meeting consists of theNuPECC chairperson and the Nu-PECC liaison members of the work-ing groups.

J. ÄYSTÖ

NuPECC Chairman

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