Identifying key studies in nuclear astrophysics through the CARINA network
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Identifying key studies in nuclear astrophysics through the CARINA networkCarmen Angulo [email protected] CARINA network andCRC Louvain-la-Neuve, BelgiumEURISOL workshop ECT* TrentoJanuary 16-20, 2006The CARINA network in the I3 EURONSCARINA = Challenges and Advance Research In Nuclear AstrophysicsI3 = Integrated Infrastructure Initiative (FP6)EURONS = EURopean Nuclear Structure
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Main goals of the CARINA network To carry out mapping studies of the European situation in terms of projects, facilities and teams in order to identify the available instrumentation and human potential. To develop the research capabilities of existing Large Scale Facilities (LSF) and of smaller laboratories and enhance involvement in the future RIB facilities. To record the needs for new instrumentation and techniques; look for existing solutions in other fields. To coordinate research efforts by defining and proposing common research goals and by encouraging new collaborations and new R&D projects.
Date of beginning: 1 January 2005Date of end: 31 December 2008Budget: 35 k
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Which are the EURONS LSF ?The world-class facilities, agreed by the EC, that constitute the backbones of EURONS are:CRC/UCL (B) ECT* (EUR)CERN-ISOLDE (EUR)GSI (D)GANIL (F)JYU-JYFL (FIN)INFN-LNL (I) RUG-KVI (NL)
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What is the role of CARINA?Who is involved in CARINA? To provide coherence to the research activities in nuclear astrophysics in Europe by: Identifying the key forefront studies Providing guidance to laboratories Assuring best development and usage of the facilities Representatives of the EURONS experimental LSF. Representatives of other European laboratories involved in nuclear astrophysics that answered to the call. CARINA is also (and mainly) intended as a forum of discussion.
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CARINA Tasks (I)Task 1: Setup activity
1.1 Four working groups have been established (January 2005):
"Theory" - nuclear and astrophysical models Conveners: Alain Coc (CSNSM)/ Jordi Jos (Barcelona)
"Instrumentation" Conveners : Tom Davinson (Edinburgh)/ Giacomo de Angelis (INFN LNL)
Link to the EURONS LSF Conveners : Alberto Mengoni (CERN) / Klaus Smmerer (GSI)
Link to non-EURONS LSF labs working on nuclear astrophysics Conveners : Michael Heil (KFZ Karlsruhe) / Endre Somorjai (ATOMKI)
1.2 The CARINA webpage is launched on January 2005
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CARINA Tasks (II)Task 2: Actions
2.1 Workshops
The first CARINA workshop held on June 8-10, 2005.Co-organized by the IEEC/UPC Barcelona and the CARINA coordinator.Announced in the CARINA webpage at end of January 2005.Announced in the NuPECC website: www.nupecc.org/calendar
Information sent to the coordinators of all EURONS activities.First Circular sent in February 3rd, 2005.
2.2 Report on the First workshop: November 2005.
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CARINA: milestones and deliverables
Milestones
Date due
Date accompl.
Working groups set
01/05
Webpage available
01/05
Organization & announcement of 1st workshop
02/05
First workshop held
06/05
Working groups meeting / visits
06/06
Organization and announcement of 2nd workshop
05/07
Second workshop held
09/07
Working groups meeting / visits
08/08
Deliverables
Date due
Date
delivered
Dissemination level
Report
04/05
07/05
public
First report on workshop
10/05
11/05
public
First report on WG meetings
10/06
public
Second report on workshop
01/08
public
Second report on WG meetings
12/08
public
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The goal of the first workshopQuestions to be answered:What is the European situation in terms of projects, facilities and teams? What is the present available instrumentation and human potential?What are the research capabilities of the existing LSF and of the other laboratories ? How to enhance involvement in the future RIB facilities?What are the needs for new instrumentation and techniques; for existing solutions in other fields?Does this network sound meaningful to European research ?Perspectives in European nuclear astrophysics
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Program of the first workshopPerspectives in European nuclear astrophysics(39 registered) 37 participants from 10 EC countries and Associated statesProgram: review talks, working group sessions (all plenary) 5 review talks: Astrophysical models explosive burning (M. Hernnz, Barcelona) Astrophysical models quiescent burning/AGB (M. Busso, Perugia) Nuclear models for astrophysics (P. Descouvemont, Brussels) Experiments using RIB at European LSF (K. Smmerer, Darmstadt) Experiments at European non-EURONS facilities (M. Heil, Karlsruhe)
Working group sessions: short talks + round table discussions Summary Election of the Steering Committee
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Quests in Nuclear AstrophysicsLarge variety of problems large variety of methodsBeams of electrons, neutrons, light and heavy ions (stable and unstable).Energies: from ten of keV to multi-GeV.Facilities: university and small labs accelerators, table-top underground labs, large-scale facilities
Specific tools: Big Bang nucleosynthesis, pp-chain, CNO cycleRecoil separators, forward magnetic spectrometers, high-efficiency gamma detectorsExplosive scenarios (hot CNO, rp process, etc)Low-energy, intense & pure radioactive beams (ISOL-type)High beam energies, purity and speed of separation (fragmentation + in-flight)
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Facilities for Nuclear AstrophysicsLarge number of small- and medium-scale facilities which are beneficial to the field (attract students, act as feeders to large-scale facilities).A few important reactions in quiescent burning: still to be investigated. But the scientific interest will move towards astrophysical sites involving radioactive species.In the future, two large-scale radioactive beam facilities: ISOL-type: EURISOL Fragmentation: Super-FRS @ FAIRBoth have nuclear astrophysics in their agenda. but:How much beam time can be devoted to nuclear astrophysics at these large and expensive facilities that cater to a very broad range of physics interest?The long time-span until they become fully operational does matter.
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How to fulfil the needs in the near future? (I)How to fulfil the needs of the European NA community, at least in the years of about 2008-2015? CARINA proposes a three-tiered intermediate step:To identify and to secure the long-term availability of: Key facilities for specific experiments Key theoretical institutes
To combine in a network these key facilities/institutes to assure the coherence of the scientific activities and to secure:Technical know-howManpower
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How to fulfil the needs in the near future? (II)To establish a flagship ISOL-type facility providing: High-intensity, high-purity light- to medium-mass radioactive beams. Equipped with a full range of experimental tools (more on that later). It could be established cost-efficiently at one of the existing European ISOL-facilities (or their upgrades): CRC at Louvain-la-Neuve (Belgium) orREX-ISOLDE (CERN) or,SPIRAL at Caen (France)The main constraint of this flagship ISOL-type facility:Sufficient financial investmentMajor commitment towards the field of nuclear astrophysics
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Instrumentation for nuclear astrophysicsA survey of instrumentation available in present-day laboratories active in experimental nuclear astrophysics suggests the following required devices:Gas targets (recirculation for rare gases; continuous luminosity monitoring)A multi-stage fusion-product recoil separator (high leak-beam suppression, high rate focal plane detectors)A high-resolution magnetic forward spectrometer (high rate focal plane detectors)Large-area, fine-granularity solid-state detectors or telescopes (on sharing basis; standard electronics and DAQ systems)A dedicated high-resolution, high-efficiency gamma-ray detection systemThe flagship ISOL type facility must have these tools available for the nuclear astrophysics community.
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Theory for nuclear astrophysicsA tentative list of theoretical models of interest to nuclear astrophysics:Shell modelHauser FeshbachMicroscopic models, Indirect methods (Trojan Horse, ANC, ..) R-matrixPlus astrophysical modelsA tentative list of stellar processes and sites
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Stellar processes and sitesBig BangMain sequence starsHelium burning3-a process, 12C(a,g)16O, other (a,g) and (a,n) reactions
Red Giants starsAsymptotic branch starsExplosive burningHot CNOrp process (rapid p capture)NovaeSupernovaeX-ray burstNucleosynthesis beyond Irons process (slow neutron-capture)r process (rapid neutron capture) p process (p capture)
AGB starsSupernovae II??Hydrogen burning pp chainsCNO cycleNe-Na chainMg-Al chain
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Nuclear reactions at extreme conditionsUnder extreme stellar conditions of T and density: any nucleus can undergo a series of light particle captures forming a nucleus far from stability (loosely bound, short b-decay lives): nuclear reactions rates b-decay intrinsic rates or photodissociation (balance)Hundreds of different reactions involving unstable nuclei may lie on the reaction pathWhat nuclear information is needed in the astrophysical models?nuclear masses,excited state properties,decay properties and lifetimes,electron capture rates,neutrino and photon interaction rates, light particle reaction rates.
But our current knowledge is very incompleteExperimental challenge !Information inaccessible for many years to come (specially on the r-process path)
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Explosive burning - astrophysical sitesIn explosive astrophysical sites such as the binary systems novae and X-ray bursters, nucleosynthesis [ up to A ~ 60 (nova) and A ~ 80 100 (X-ray burst) ] is thought to be provided by hydrogen and helium burning at high temperatures and densities. [J.Jos et al. ApJ (1999), H., Schatz et al., Phys. Rep. (1998) ]
Hydrogen and helium rich material from a companion aging main sequence star piles up onto the surface of a white dwarf (WD in nova) or neutron star (NS in X-ray burst) forming an accretion disk.The temperature and density increase in the surface of the WD (T>108 K, r>103g/cm3) or NS (T>109 K, r>106 g/cm3) generating a sudden increase of the star luminosity.Critical T and r values: reactions involving H and He on nuclei ranging from C to Ca releasing energy in a runaway thermonuclear explosion.Snapshots of a Classical Nova Outburst (cortesy of J. Jos)
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Identification of the key nuclei and reactionsThe most important reactions can be identify by studying the sensitivity of the models.For example, at very high T: capture rate photodissociation rate (equilibrium)The reaction path is insensitive to individual reaction rates.The material concentrates at the so-called waiting-point nuclei (and the most important parameters are the masses and b-decay rates). [H., Schatz et al., Phys. Rep. (1998).]However, many individual reaction rates are of critical importance:The statistical model can be used as an estimation, BUT :Q-value is low for nuclei far from stabilityLevel-density is lowerOften, only 1 or 2 states contributing: there is no alternative to the study of the resonance properties.Some innovative experimental techniques (ex. ANC and TH methods) to indirectly determine level information, but often direct measurement is needed.
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Reaction path: the hot CNO and beyondunstablestable(exact path depends on given stellar conditions)15O(a,g)19Ne14O(a,p)17F19Ne(p,g)20Na18Ne(a,p)21Na30P(p,g)31Sheavy nuclei beyond S
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Experimental ChallengeOne of the main difficulty in experiments related to explosive burning is the implications of instable nuclei.Experiments on reactions involved on explosive burning requires radioactive beam production. Methods :ISOLProjectile fragmentationIN-FLIGHThot CNO, escape to rp-process13N (10 m), 15O (122 s), 17F (65 s), 18F (110 m), 19Ne (17 s) r-process neutron-rich nuclei, far from stability
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Radioactive beam facilitiesISOL (Isotope Separation On Line): a radioactive beam is produced practically at rest in a thick target bombarded with a primary beam and post-accelerated.CYCLONE @ Louvain-la-NeuveREX-ISOLDE @ CERNSPIRAL @ Ganil, CaenHRIBF @ Oak Ridge National LabISAC @ TRIUMF, VancouverTwo major projects: RIA in the USA and EURISOL in Europe
Projectile fragmentation: typically a very high energy beam is used and fragmented in a low Z target. From the many reaction products, the desired one is selected in mass, charge and momentum via a fragment separator and transported to the experimental area without acceleration.GANIL @ CaenGSI @ DarmstadtFlerov Laboratory @ DubnaNSCL @ MSURIKEN @ SaitamaIMP @ LanzhouTwo major projects: FAIR @ GSI, RIBF @ RIKEN (under construction)
IN-FLIGHT: a heavy ion at low energy (typically just above the Coulomb barrier) induce single neutron transfer reactions.ATLAS @ Argonne Nat. Lab.CRIB @ RIKENTexas AMUNotre Dame
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Experimental quests and toolsFacilitiesAccelerators and beamsTargetsDetectorsGround-state propertiesMasses, b-decay ratesCapture reactionsResonant and non-resonant captureCoulomb dissociationTransfer reactions: type (p,a) and (a,p)Resonant propertiesElastic and inelastic scatteringTransfer reactionsFusion evaporation
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Resonant properties: the elastic scattering method in inverse kinematicsWith the acceleration of the first radioactive beam at Louvain-la-Neuve (1990), it was necessary to develop a technique to study in one step low-energy resonances using:Projectile: a RIB of a few 106 - 107 pps (should be enough)Target: a proton-rich foil of very simple handlingThe first elastic scattering experiment in inverse kinematics with a stable and a RIB and a quantitative analysis, was performed in 1991 at Louvain-la-Neuve:13C+p13N+pCross section (in barn/sr) versus c.m. energy at qlab=17One-step energy scanning of wide low lying 1- resonances in 13C+p and 13N+p scatteringTh. Delbar et al., Nucl. Phys. A542 (1992) 263.
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The methodTypical spectrum for a =0 resonant stateBeam important energy loss in the target spectacular changes in the recoil proton spectraRecoil protons negligible energy loss in the target sensitivity to presence of a resonant stateProton spectra information on the resonance energy, orbital momentum, and proton widthMain features
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The choice of the targetA very thick target, that will stop the beam, can be used to obtain a general overview of a nuclei level scheme
A thinner target must be used if precise information on energy, width and spin of one or of a few states are searched
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On-line spectra and data analysis: (i) from raw spectraThe energy resolution is limited: the resonance widths must be larger than a few keVAbove a certain large value of the width, the spectra are independent of the energy resolutionFor very thick targets, only the detection at small angles is appropriateLimitationsJ.S. Graulich et al., Phys. Rev. C63, 011302(R)(2000).An example: 1H(18F,p)18F
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to the theoretical analysisA.N. Lane and R.G. Thomas, Rev. Mod. Phys. 30 (1958) 257-353.The R-matrix formalismAn alternative parameterization to easily switch between formal and experimental parameters is presented in C. Angulo and P. Descouvemont, Phys. Rev. C61 (2000) 064611(A generalization of this procedure is in C.R. Brune, Phys. Rev. C 66 (2002) 044611)The usual procedure to related these quantities is not direct!
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Capture reactions: (p,g) and (a,g)Involved in quiescent and explosive burningMost of the important capture reactions involving stable isotopes have been studied using intense p and a beams.Main disadvantages of direct measurement: Low efficiency of gamma detectorsRadioactivity of the target materialBackground sourcesUse inverse kinematics and detect the recoiling reaction products in recoil separatorsARES @ Louvain-la-Neuve Daresbury Recoil Separator @ Oak Ridge DRAGON @ TRIUMFERNA @ Bochum FMA @ Argonne Nat. Lab.
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The ARES recoil separatorwg 15.2 eV (90% c.l.) Tough job ! First 19Ne radioactive beam from CYC44 Study of the 2.643 MeV level in 20NaM. Couder, PhD Thesis, 2004
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ARES-II (2006 - )Improvements on the ARES beam-lineCYCLONE 44 beamInstallation of a beam monitoring system and an additional analyzing magnet.ARES efficiencyNew simulations including all beam line elements; modifications of some elements along the beam line.ARES rejection powerInstallation of an additional dipole magnet.Reactions:19Ne(p,g)20Na13N(p,g)14O11C(p,g)12N15O(a,g)19Ne7Be(a,g)11C
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TargetsGas cells, windowless gas targets, polyethylene foilsNew alpha-implanted targets [F. Vanderbist et al., NIM (2004)] Requirements: Low Z substrateThick enoughSelf-supportingHigh 4He concentrationHomogeneity and uniform concentration
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Alpha-implanted targets1st campaignTest of substrate resistance during implantation (C, Al, Ni, Cu, Si, Sn): best results with AlStudy of evolution of content versus dose2nd campaignStudy of implantation profile : Analysis of homogeneity (ERDA) and content (RBS)Implantation of very thing Al foils to study (a,g) resonances: 50 & 100 g/cm2
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Use of alpha implanted targetsFirst experimental approach to 15O+a and 15N+a elastic scattering using solid alpha implanted targetsFinal goal: Study of 15O(a,g)19Ne with ARESStudy of a state Jp = 1/2+, Ex = 6.250 MeV state in 19F by 15N+a elastic scatteringGa = 8 keV [Smotrich et al., PR(1961); re-analysis (R-matrix): Bardayan et al., PRC (2005)].
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15N+a with alpha implanted targetsGa = 4.0 0.7 keVGa = 3.2 0.7 keV
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Some key reactions18F(p,a)15OThe competition between the 18F(p,a)15O and the 18F b-decay has consequences regarding a possible observation of the 511 keV g-ray from novae (ex. INTEGRAL): g-rays from novae have not been detected yet.Many experiments. (more recent works: see later)
17O(p,g)18F , 17O(p,a)14N17O (and perhaps 19F): galactic chemical evolution; it is believed that 17O on earth or in our bodies was made in novaeC, N, O elemental abundances are observed in emission spectra of nova ejecta; isotopic ratios 12C/13C and 14N/15N are observed in pre-solar grains that originated from nova explosionsRecent experiments at LENA @ NC (Iliadis, Champagne et al.); CSNSM @ Orsay (Tatischeff et al.)
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Some key reactions14O(a,p)17FThe reaction is thought to play an important role in advanced stages of hydrogen burning, either as: a way of bypassing the slow positron decay of 14O (t1/2 = 70.6 s) in the hot CNO cycle or as a starting point to break out the cycle through the subsequent 17F(p,g)18Ne(a,p)21Na reactions. Recent experiment at RIKEN; project at LLN
15O(a,g)19NeOne of the main breakout reaction from the hot CNO cycle. No direct measurement ever performed: Very low cross section: very intense 15O beam needed (< 1012 pps)Presently, 15O beam intensity is ~ 107 pps.
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Some key reactions
22Na(p,g)23MgPeak fluxes for the 1275 keV g-ray line (22Na decay) might be detectable by near future g-ray satellites (i.e. INTEGRAL) if an ONe nova explodes within a distance of less than ~ 0.5 kpc.
30P(p,g)31SiNuclear activity in the Si-Ca region is powered by a leakage from the NeNa-MgAl region, where the activity is confined during the early stages of the outburst. This is the main reaction that drives nuclear acitivity towards heavier species beyond S.Uncertainties affecting 30P(p,g)31S influence Si yields (relevant for the identification of presolar nova candidate grains) and the nuclear activity beyond S (J. Jos, 2004)
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The role of 18F(p,a)15O in the nova nucleosynthesis[J.S. Graulich et al. Phys. Rev. C63, 011302(R) (2001), and references therein.]Influence of the low-energy levels? Interferences ? 6.449 MeV (3/2+) 6.437 MeV (1/2-) 6.419 MeV (3/2+) other states below threshold ?The 18F(p,a)15O rate is largely uncertain: up to 300 on the g-ray flux due to the unknown low-energy resonance strengths (A. Coc et al. A&A 2000)Previous studies at Louvain-la-Neuve, Oak Ridge and Argonne concentrated mainly on two 19Ne states: 7.066 MeV (3/2+) 6.742 MeV (3/2-)
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The 18F(p,a)15O S-factorNeed to determine the proton widths of the 3/2+ and 1/2- states below 0.2 MeV
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18F(d,pa)15N: an indirect way to investigate 18F(p,a)15O19Ne levels of interestA 14 MeV 18F beam (2 x106 pps) on a CD2 targetCoincidences p (LAMP) and 15N or a (LEDA)Experimental set up:Study the analog levels in 19F by the transfer reaction d(18F,p)19F(a)15N
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18F(d,p)19F*(a)15Ne: resultsTwo 3/2+ astrophysical levels isolated (but not resolved: FWHM 100 keV).Coincidence spectrumDWBA analysis Spectroscopic factors: S(6.528) + S(6.497) 0.2
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N. de Srville, Ph.D Thesis, 2003.18F(d,pa)15O also investigated at Oak Ridge at higher beam energies [Kozub et al., PRC (2005)] (a bit different conclusions).
15N(a,a)15N scattering data from Smotrich et al, (1961) re-analized by Bardayan et al., PRC (2005).Uncertainty reduced by a factor of about 5 in the nova temperature range
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Interference effectsBetween the two 3/2+ resonances (at Ecm = 38 and 665 keV) can significantly alter the rate of 18F destruction in novae.Data from Bardayan et al 2002, resonance strength from de Srville et al. 2003.Remaining nuclear uncertainties: a-width for low energy resonances Interference sign between 3/2+ states Missing states ?A new experiment at the CYCLONE RIB facility
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The RIB facility at Louvain-la-NeuveProduction & acceleration of isobarically pure and intense low-energy radioactive ion beams specially suitable for nuclear astrophysicsCYCLONE44ARESLEDA beam lineCYCLONE30CYCLONE110E: 0.2 - 0.8 MeV/AM/Q: 4 to 14
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Particle detector arrays at Louvain-la-NeuveLarge area, highly segmented silicon strip detector arrays LEDA and CD-PAD: they can be used in many configurations to cover the required angular range
Developed and largely used at Louvain-la-NeuveUse at present at many laboratories worldwide (Oak Ridge, TRIUMF, REX-ISOLDE)
Solid angle: 10% of 4pLEDA type16 strips in q300 mm or500 mm16 strips x 4 DSSD50 mm or 500 mm4 x PAD 1.5 mmCD typeDavinson et al., NIM A 2000Ostrowski et al., NIM A 2002
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A new 18F(p,a) direct measurementMay 17 25, 2005 @ Louvain-la-Neuve nominal 18F beam energy: 13.8 MeV beam intensity ~ 106 pps a 70 mg/cm2 CH2 target several energies using degraders: Al foils (of different thickness) total efficiency (incl a-15O coinc.) 30%Also: a proposal at TRIUMF on 18F(p,a)15O (A. Laird, A. Murphy), standing by for 18F beam development.
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18F beam production and acceleration at LLNWe got: 17 bunches of 18F over 1.5 week and continuous 18O over the night18F (T1/2 = 110 min):
CYCLONE30: production18O(p,n)18F with a intense p beam @ 30 MeV
UCL / PET group: chemical extraction45 minutes process, CH318F
CYCLONE110: acceleration and mass separation1 bunch of 18F every 2 h (0.5 to 1 Ci) (almost) free of 18O contamination
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18F beam purity18O / 18F different energy loss18O / 18F < 1%Measurement at 0 degree (PIPS) check degrader thickness determine beam energy profile at target entrance
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Preliminary resultsObjective: sign of interference between 3/2+ states18F beam energies:13.8, 12.6, 9.1, 7.6 MeVFor c.m. energy below 0.2 MeV: beam of less than 4 MeVBut the cross section is order of magnitude lower !! Beam intensities ~ 1010 1012 pps
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14O(a,p)17FThe rate is dominated by the resonant contribution from the 1-, 6.15 MeV state in 18Ne, contributions from states in the energy range 7 8 MeV possible.
Indirect studies: By transfer reactions (Garcia et al. 1991, Hahn et al. 1996, Park et al. 1999) By the inverse reaction 17F(p,a)14O at Argonne (Harss et al. 1999, 2004) and Oak Ridge (Blackmon et al. 2002 preliminary)Contribution of the first excited state in 17F?
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14O(a,p)17F: direct measurementA recent experiment at RIKEN (Notani et al. 2004) using a 43 MeV 14O beam produced by the 14N(p,n)14O reaction and a novel 4He gas target at 30 K (ten times more density than at room temperature).Set up:
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14O(a,p)17F: direct measurement at LLNA new proposal (LEDA coll.) has been accepted to study this reaction.A low-energy 14O beam (expected intensity 5 x105 particles per second) to be produced using a new cyclotron configuration: CYCLONE110 to produce the beam by the 12C(3He,n)14O reactionCYCLONE44 to accelerate the 14O beamARES beam line with a new LEDA chamber and a 4He gas cell
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17O(p,a)14N, 17O(p,g)18FOf special interest is the branching ratio at 17O: the probability that this nucleus is destroyed during thermonuclear burning via the (p,a) reaction as opposed to the (p,g) reaction. (p,a) and (p,g) rates are uncertain by several order of magnitude.
The branching ratio (p,a)/(p.g) varies by almost 5 orders of magnitude at the novae temperatures (0.1-0.4 GK).
Consequently, 17O and 18F abundance predictions based on the current 17O+p reaction rates are highly uncertain.Coc et al. 2000; Iliadis et al. 200217O+p NACRE rates:
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17O+p: two recent results Observation of a new resonance at Elab,R= 190 keV in 17O(p,g)18F Measured resonance strength wg = (1.2 0.2) meVImportant consequences in final abundances of CNOF isotopes1) Experiment at LENA facility at TUNL, North Carolina
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17O+p: two recent results Observation of a new resonance at Elab,R= 194.1 0.6 keV in 17O(p,a)18F Measured resonance strength wg = (1.6 0.2) meVImportant consequences in nova nucleosynthesis2) Experiment at CSNSM, OrsayPhysical Review Letters, in press
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The problem of primordial 7Li abundance(h = ratio of the baryon number to the photon number, equivalent to the baryonic density)A problem of the rates of the reactions involved in SBBN ?Coc et al., Fields et al,
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The 12 main reactions involved in SBBNPublication: P. Descouvemont, A. Adahchour, C. Angulo, A. Coc, E. Vangioni-Flam, ADNDT 88 (2004) 203-236.A new BBN Compilation R-matrix method Statistical treatment of uncertaintiesUpdate and supersede the NACRE compilation for the reactions:Website: http://pntpm3.ulb.ac.be/bigbang
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Other nuclear reactions affecting 7Li production?
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What do we know about 7Be(d,p)8Be ?No data at BBN energies! How to extrapolate?
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The 7Be+d reactions
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New experiment set up7Be beamFC Cup
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7Be beam: energy and isobar contamination
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Proton spectrag.s. and first excited state in 8BeHigher energy excited states in 8Be: 40% of the counting rate26 hours
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Results : astrophysical S-factorKavanagh 1960: measurement at a lab angle of 90O above the BBN energiesLouvain-la-Neuve experiment 2004: measurement at BBN at 16 anglesHigh energy levels (about 40% of total events) not observed previouslyAngular distribution: isotropicC. Angulo et 17, Astrophysical Journal Letters 630 (2005) L105-L108 Negligible effect in BBN: 7Li problem persists
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Effective energyIntegral 1Integral 2
Chart2
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1535907003.17469
1354281927.54399
1192359979.58693
1048198255.84709
920026714.695559
806234282.519791
705355997.165247
616061110.473248
537142078.474528
467504373.830694
406157060.543278
352204075.838109
304836168.542005
263323447.250697
227008495.188658
195300011.923945
167666945.060806
143633077.722233
122772040.082631
104702715.442886
89085013.3794593
75615984.3657798
64026251.9765473
54076740.3596173
45555676.1104437
38275845.0233978
32072085.4341828
26799001.0181696
22328876.9799256
18549784.5675064
15363859.7784243
12685742.9989103
10441167.1397489
8565682.60551698
7003508.16383061
5706497.4709868
4633211.66348611
3748089.04421282
3020703.48000933
2425103.68615638
1939226.10468244
1544374.58904367
1224760.58885966
967097.986183568
760247.170173739
594903.350816006
463324.505200533
359094.722362523
276919.065356841
212446.402499709
162116.973985413
123031.755760076
92840.9599876964
69649.2710608058
51935.6582891134
38485.8315685712
28335.6149448027
20723.7055288372
15052.462227958
10855.5307882792
7771.259315944
5520.9923956346
3891.452837861
2720.5286697165
1885.8799715755
1295.8663071748
882.3715609745
595.169753565
397.5336193687
262.8381572363
171.954743094
111.2684403901
71.1825451578
45.0008098394
28.0998164126
17.3221852283
10.5362367906
6.3198486331
3.7360006658
2.1752655467
1.2466160395
0.7026857629
0.3892890186
0.2117973235
0.1130679602
0.059175224
0.030332431
0.0152124922
0.0074567443
0.0035682258
0.0016648456
0.0007563826
Ecm (MeV)
Yield (rel. units)
figure effec energy
Estoppingexp(-2pieta)/stoppingmu=1.56491661712.014101986
1.713.81E-011.29E-171.80E+101.80E+10cm=0.22302017087.01692860980.381364492117992993951.8856
1.73.79E-011.30E-171.63E+101.63E+100.38136449211.00E-05
1.693.77E-011.32E-171.47E+101.47E+100.12935169910.0007563826
1.683.75E-011.33E-171.32E+101.32E+100.12935169911.00E-05
1.673.72E-011.35E-171.19E+101.19E+100.34122086132505222660.87742
1.663.70E-011.36E-171.07E+101.07E+100.34122086131.00E-05
1.653.68E-011.37E-179.67E+09
1.643.66E-011.39E-178.69E+09
1.633.64E-011.40E-177.80E+09
1.623.61E-011.42E-177.00E+09
1.613.59E-011.43E-176.27E+09
1.63.57E-011.44E-175.61E+09
1.593.55E-011.45E-175.02E+09
1.583.52E-011.47E-174.48E+09
1.573.50E-011.48E-174.00E+09
1.563.48E-011.49E-173.57E+098.48E+10
1.553.46E-011.50E-173.17E+09
1.543.43E-011.52E-172.82E+09
1.533.41E-011.53E-172.51E+09Eff=0.37
1.523.39E-011.54E-172.22E+09
1.513.37E-011.55E-171.97E+09
1.53.35E-011.56E-171.74E+09
1.493.32E-011.57E-171.54E+09
1.483.30E-011.58E-171.35E+09
1.473.28E-011.59E-171.19E+09
1.463.26E-011.60E-171.05E+09
1.453.23E-011.61E-179.20E+08
1.443.21E-011.62E-178.06E+08
1.433.19E-011.63E-177.05E+08
1.423.17E-011.64E-176.16E+08
1.413.14E-011.65E-175.37E+08
1.43.12E-011.66E-174.68E+08
1.393.10E-011.67E-174.06E+08
1.383.08E-011.67E-173.52E+08
1.373.06E-011.68E-173.05E+08
1.363.03E-011.69E-172.63E+08
1.353.01E-011.70E-172.27E+08
1.342.99E-011.70E-171.95E+08
1.332.97E-011.71E-171.68E+08
1.322.94E-011.72E-171.44E+08
1.312.92E-011.73E-171.23E+08
1.32.90E-011.73E-171.05E+08
1.292.88E-011.74E-178.91E+07
1.282.85E-011.74E-177.56E+07
1.272.83E-011.75E-176.40E+07
1.262.81E-011.76E-175.41E+07
1.252.79E-011.76E-174.56E+07
1.242.77E-011.77E-173.83E+07
1.232.74E-011.77E-173.21E+07
1.222.72E-011.78E-172.68E+07
1.212.70E-011.78E-172.23E+07
1.22.68E-011.79E-171.85E+07
1.192.65E-011.79E-171.54E+07
1.182.63E-011.79E-171.27E+07
1.172.61E-011.80E-171.04E+07
1.162.59E-011.80E-178.57E+06
1.152.56E-011.80E-177.00E+06
1.142.54E-011.81E-175.71E+06
1.132.52E-011.81E-174.63E+06
1.122.50E-011.81E-173.75E+06
1.112.48E-011.81E-173.02E+06
1.12.45E-011.82E-172.43E+06
1.092.43E-011.82E-171.94E+06
1.082.41E-011.82E-171.54E+06
1.072.39E-011.82E-171.22E+06
1.062.36E-011.82E-179.67E+05
1.052.34E-011.82E-177.60E+05
1.042.32E-011.82E-175.95E+05
1.032.30E-011.83E-174.63E+05
1.022.27E-011.83E-173.59E+05
1.012.25E-011.83E-172.77E+05
12.23E-011.83E-172.12E+05
0.992.21E-011.83E-171.62E+05
0.982.19E-011.83E-171.23E+05
0.972.16E-011.82E-179.28E+04
0.962.14E-011.82E-176.96E+04
0.952.12E-011.82E-175.19E+04
0.942.10E-011.82E-173.85E+04
0.932.07E-011.82E-172.83E+04
0.922.05E-011.82E-172.07E+04
0.912.03E-011.82E-171.51E+04
0.92.01E-011.81E-171.09E+04
0.891.98E-011.81E-177.77E+03
0.881.96E-011.81E-175.52E+03
0.871.94E-011.81E-173.89E+03
0.861.92E-011.80E-172.72E+03
0.851.90E-011.80E-171.89E+03
0.841.87E-011.80E-171.30E+03
0.831.85E-011.79E-178.82E+02
0.821.83E-011.79E-175.95E+02
0.811.81E-011.78E-173.98E+02
0.81.78E-011.78E-172.63E+02
0.791.76E-011.77E-171.72E+02
0.781.74E-011.77E-171.11E+02
0.771.72E-011.76E-177.12E+01
0.761.69E-011.76E-174.50E+01
0.751.67E-011.75E-172.81E+01
0.741.65E-011.75E-171.73E+01
0.731.63E-011.74E-171.05E+01
0.721.61E-011.74E-176.32E+00
0.711.58E-011.73E-173.74E+00
0.71.56E-011.72E-172.18E+00
0.691.54E-011.72E-171.25E+00
0.681.52E-011.71E-177.03E-01
0.671.49E-011.70E-173.89E-01
0.661.47E-011.69E-172.12E-01
0.651.45E-011.69E-171.13E-01
0.641.43E-011.68E-175.92E-02
0.631.41E-011.67E-173.03E-02
0.621.38E-011.66E-171.52E-02
0.611.36E-011.65E-177.46E-03
0.61.34E-011.65E-173.57E-03
0.591.32E-011.64E-171.66E-03
0.581.29E-011.63E-177.56E-04
8.67E+10
The results are corrected by 1 effect:g.s. counts at 5.5 MeV --> 61% of total counts, as at low energies
figure effec energy
Ecm (MeV)
Yield (rel. units)
Effective energy
EEcmexp(-2pieta)Estoppingexp(-2pieta)mu=1.56491661712.014101986
5.5451.24E+005.399E-036.68E-031.713.81E-011.29E-171.80E+101.80E+10cm=0.22302017087.0169286098
5.4951.23E+005.205E-036.38E-031.73.79E-011.30E-171.63E+101.63E+10
5.4451.21E+005.015E-036.09E-031.693.77E-011.32E-171.47E+101.47E+10
5.3951.20E+004.828E-035.81E-031.683.75E-011.33E-171.32E+101.32E+10
5.3451.19E+004.644E-035.54E-031.673.72E-011.35E-171.19E+101.19E+10
5.2951.18E+004.463E-035.27E-031.663.70E-011.36E-171.07E+101.07E+10
5.2451.17E+004.286E-035.01E-031.653.68E-011.37E-179.67E+09
5.1951.16E+004.112E-031.643.66E-011.39E-178.69E+09
5.1451.15E+003.942E-031.633.64E-011.40E-177.80E+09
5.0951.14E+003.775E-031.623.61E-011.42E-177.00E+09
5.0451.13E+003.612E-031.613.59E-011.43E-176.27E+09
4.9951.11E+003.452E-031.63.57E-011.44E-175.61E+09
4.9451.10E+003.297E-031.593.55E-011.45E-175.02E+09
4.8951.09E+003.145E-031.583.52E-011.47E-174.48E+09
4.8451.08E+002.996E-031.573.50E-011.48E-174.00E+09
4.7951.07E+002.852E-031.563.48E-011.49E-173.57E+098.48E+10
4.7451.06E+002.711E-031.553.46E-011.50E-173.17E+09
4.6951.05E+002.575E-031.543.43E-011.52E-172.82E+09
4.6451.04E+002.442E-031.533.41E-011.53E-172.51E+09Eff=0.37
4.5951.02E+002.313E-031.523.39E-011.54E-172.22E+09
4.5451.01E+002.188E-031.513.37E-011.55E-171.97E+09
4.4951.00E+002.067E-031.53.35E-011.56E-171.74E+09
4.4459.91E-011.950E-031.493.32E-011.57E-171.54E+09
4.4349.89E-011.924E-031.483.30E-011.58E-171.35E+09
4.160E-024.08E-021.473.28E-011.59E-171.19E+09
Eff = 1.151.463.26E-011.60E-171.05E+09
1.453.23E-011.61E-179.20E+08
1.443.21E-011.62E-178.06E+08
1.433.19E-011.63E-177.05E+08
1.423.17E-011.64E-176.16E+08
1.413.14E-011.65E-175.37E+08
1.43.12E-011.66E-174.68E+08
1.393.10E-011.67E-174.06E+08
1.383.08E-011.67E-173.52E+08
1.373.06E-011.68E-173.05E+08
1.363.03E-011.69E-172.63E+08
1.353.01E-011.70E-172.27E+08
1.342.99E-011.70E-171.95E+08
1.332.97E-011.71E-171.68E+08
1.322.94E-011.72E-171.44E+08
1.312.92E-011.73E-171.23E+08
1.32.90E-011.73E-171.05E+08
1.292.88E-011.74E-178.91E+07
1.282.85E-011.74E-177.56E+07
1.272.83E-011.75E-176.40E+07
1.262.81E-011.76E-175.41E+07
1.252.79E-011.76E-174.56E+07
1.242.77E-011.77E-173.83E+07
1.232.74E-011.77E-173.21E+07
1.222.72E-011.78E-172.68E+07
1.212.70E-011.78E-172.23E+07
1.22.68E-011.79E-171.85E+07
1.192.65E-011.79E-171.54E+07
1.182.63E-011.79E-171.27E+07
1.172.61E-011.80E-171.04E+07
1.162.59E-011.80E-178.57E+06
1.152.56E-011.80E-177.00E+06
1.142.54E-011.81E-175.71E+06
1.132.52E-011.81E-174.63E+06
1.122.50E-011.81E-173.75E+06
1.112.48E-011.81E-173.02E+06
1.12.45E-011.82E-172.43E+06
1.092.43E-011.82E-171.94E+06
1.082.41E-011.82E-171.54E+06
1.072.39E-011.82E-171.22E+06
1.062.36E-011.82E-179.67E+05
1.052.34E-011.82E-177.60E+05
1.042.32E-011.82E-175.95E+05
1.032.30E-011.83E-174.63E+05
1.022.27E-011.83E-173.59E+05
1.012.25E-011.83E-172.77E+05
12.23E-011.83E-172.12E+05
0.992.21E-011.83E-171.62E+05
0.982.19E-011.83E-171.23E+05
0.972.16E-011.82E-179.28E+04
0.962.14E-011.82E-176.96E+04
0.952.12E-011.82E-175.19E+04
0.942.10E-011.82E-173.85E+04
0.932.07E-011.82E-172.83E+04
0.922.05E-011.82E-172.07E+04
0.912.03E-011.82E-171.51E+04
0.92.01E-011.81E-171.09E+04
0.891.98E-011.81E-177.77E+03
0.881.96E-011.81E-175.52E+03
0.871.94E-011.81E-173.89E+03
0.861.92E-011.80E-172.72E+03
0.851.90E-011.80E-171.89E+03
0.841.87E-011.80E-171.30E+03
0.831.85E-011.79E-178.82E+02
0.821.83E-011.79E-175.95E+02
0.811.81E-011.78E-173.98E+02
0.81.78E-011.78E-172.63E+02
0.791.76E-011.77E-171.72E+02
0.781.74E-011.77E-171.11E+02
0.771.72E-011.76E-177.12E+01
0.761.69E-011.76E-174.50E+01
0.751.67E-011.75E-172.81E+01
0.741.65E-011.75E-171.73E+01
0.731.63E-011.74E-171.05E+01
0.721.61E-011.74E-176.32E+00
0.711.58E-011.73E-173.74E+00
0.71.56E-011.72E-172.18E+00
0.691.54E-011.72E-171.25E+00
0.681.52E-011.71E-177.03E-01
0.671.49E-011.70E-173.89E-01
0.661.47E-011.69E-172.12E-01
0.651.45E-011.69E-171.13E-01
0.641.43E-011.68E-175.92E-02
0.631.41E-011.67E-173.03E-02
0.621.38E-011.66E-171.52E-02
0.611.36E-011.65E-177.46E-03
0.61.34E-011.65E-173.57E-03
0.591.32E-011.64E-171.66E-03
0.581.29E-011.63E-177.56E-04
8.67E+10
The results are corrected by 1 effect:g.s. counts at 5.5 MeV --> 61% of total counts, as at low energies
results from E
countssigma totstats%sys%cos
5.55 MeVtotal2773742130.9925461516
gs + 1st135249363130.956304756
others142151383130.9744254538
solid angle9.85E-02srad5%
beam particles7.14E+107%
1.71 MeVtotal1051.41028
gs + 1st64610.81328
others41390.51628
solid angle9.80E-02srad5%
beam particles1.48E+1126%
D content1.72E+1910%
Sheet3
Ecmsigma(E) (barn)exp(2pieta)*ES(E) (MeV-barn)
0.5830.069238327
0.6220.095633132
0.6530.122130037
0.6600.134529339
0.6690.152128543
0.6810.140727539
0.6910.149526740
0.6990.145826138
0.7050.145825737
0.7190.152124738
0.7310.154623937
0.7460.152123135
0.7610.150822234
0.7760.143321431
0.7930.154620632
0.8080.170919934
0.8240.163419332
0.8390.184718735
0.8540.183518133
0.8690.184717633
0.8850.192317133
0.9010.196016633
0.9170.194816131
0.9330.201115732
0.9700.206114831
1.0090.204814029
1.0480.213613228
1.0690.208612827
1.0870.211112627
1.1070.243812330
1.1250.272712033
1.1460.276511732
1.1650.266411430
1.1860.233711226
1.2040.209911023
1.2440.173410518
1.2640.173410318
1.2830.162110216
Cross section and S factor
ElabEcmds/dw (mb/sr)ds/dwx4pi (barn)exp(2pieta)*ESfactormu=1.56491661712.0141019864.9518333324EmaxEminEbinErr1Err2Eeffecsolid anglebeamD contentcountscounts_corrDsigma/Domega(lab)Dsigma/Domega(cm)Sigma_tot (barn)S-factor (MeV-barn)stats%syste%totalerror bar(stat)
0.7490.5835.51E+006.92E-02383277.0169286098all0.380.1310.2490.0120.2370.3689.80E-021.48E+111.51E+191051260.580.590.007469.6all0.090.280.370.97.5
0.80.6227.61E+009.56E-0233132all1.230.990.240.080.161.159.85E-027.14E+101.51E+1927743051.428.8130.740.3863445.0all0.0180.130.150.8386.3
0.8390.6539.72E+001.22E-0130037g.s+1st0.380.1310.2490.0120.2370.3689.80E-021.48E+111.51E+196476.80.350.360.004545.9g.s0.110.280.400.74.5
0.8490.6601.07E+011.34E-0129339g.s.+1st1.230.990.240.080.161.159.85E-027.14E+101.51E+191352186117.5818.750.2356727.4g.s0.0230.130.160.6235.7
0.860.6691.21E+011.52E-0128543
0.8750.6811.12E+011.41E-0127539degcos
0.8890.6911.19E+011.50E-012674070.9925461516
0.8990.6991.16E+011.46E-0126138170.956304756Compared to Paker
0.9060.7051.16E+011.46E-01257370.9744254538ParkerPresentfactor
0.9240.7191.21E+011.52E-0124738120.9781476007beforenow10042.92.3
0.940.7311.23E+011.55E-01239370.97628652730.00600.006210028.53.5
0.9590.7461.21E+011.52E-01231350.32920.3512
0.9780.7611.20E+011.51E-01222340.00390.0038
0.9980.7761.14E+011.43E-0121431averaged Kavanagh27.227.4(present)0.22620.1712
1.0190.7931.23E+011.55E-0120632(0.96-1.20)0.9910.690.495.5 MeV
1.0390.8081.36E+011.71E-01199340.650.611.71 MeV
1.0590.8241.30E+011.63E-0119332
1.0790.8391.47E+011.85E-0118735
1.0980.8541.46E+011.83E-0118133coulomb barrierFINAL RESULTS
1.1170.8691.47E+011.85E-0117633z16
1.1380.8851.53E+011.92E-0117133z24Ecmsig_tot(mbar)err staterr sysS(MeV-b)err staterr systot error
1.1580.9011.56E+011.96E-0116633a112ALL0.377.50.82.110133
1.1790.9171.55E+011.95E-0116131a271.1538675045166
1.1990.9331.60E+012.01E-0115732rho5.8833035351.23333333332.014101986
1.2470.9701.64E+012.06E-0114831Vc5.87425071557.0169286098GS+1st0.374.50.51.36122
1.2971.0091.63E+012.05E-011402928.21.1523643127144
1.3471.0481.70E+012.14E-011322828
1.3751.0691.66E+012.09E-011282726Gamow window for T=0.1-1 GK
1.3981.0871.68E+012.11E-0112627260.1435.0
1.4231.1071.94E+012.44E-0112330290.4735.0
1.4471.1252.17E+012.73E-011203332
1.4731.1462.20E+012.76E-011173232
1.4981.1652.12E+012.66E-011143030
1.5251.1861.86E+012.34E-011122626
1.5481.2041.67E+012.10E-011102323
1.61.2441.38E+011.73E-011051818
1.6251.2641.38E+011.73E-011031827.2
1.6491.2831.29E+011.62E-0110216
Cross section and S factor
2.85428519952.85428519951.82137118681.8213711868
5.91215062395.91215062393.6221929493.622192949
kavanagh60
c.m. energy (MeV)
S-factor (MeV barn)
T = 0.8 GK
figures poster debrecen
The results are corrected by 1 effect:g.s. counts at 5.5 MeV --> 61% of total counts, as at low energies
c.m. energy (MeV)
sigma (mb)
figures poster debrecen
26.5041478822125.86711651559.62573803320.85752890040.85752890040.66949001310.669490013135
31.68580138327.441173664544.98553059750.8143728310.8143728310.63604551390.636045513935
36.6183836348
39.3402842126
43.3361384297
38.7397178388
39.881469139
38.0290788321
37.4567170455
37.611857506
37.0013814796
35.0549336645
33.5242251944
30.6931777796
31.9008919277
34.0812231565
31.5139046851
34.5094400256
33.2778001401
32.560640154
32.8676453577
32.5793394746
31.4545079275
31.620404119
30.511068301
28.6002619322
28.2451198931
26.7938446023
26.5010589659
29.8714728938
32.6704356404
32.3505501984
30.4977476689
26.1509142636
23.0391867488
18.2754094767
17.9355116086
16.4747983756
Kavanagh
Present, partial
Present, total
c.m. energy (MeV)
S-factor (MeV barn)
T = 0.8 GK
angular distri
angular distribution
totalgs+1st2nd+3rd
anglemb/srmb/srmb/sr
164.77.655614.125722498941153.7584202132
163.38.376817.183021755950184.1452408562
161.89.0914035.445141513799415.9535822421
160.49.819148.457090788127646.961112755
159.010.5124562.2951198377165807.8927257546
157.611.2224762.9532060556173747.9343056442
156.211.9221655.190066345150667.4290017058
154.812.6225765.8406740697176818.1142266464
153.413.3223159.3465094728156757.7036685724
152.014.0125766.2198083119171868.137555426
150.614.6921655.8247995309152647.4715995296
149.215.3826267.93280682180828.2421360593
147.916.0620753.8516958673145627.3383714724
146.516.7315139.418510581397546.2784162479
145.217.4307.859655241819112.8035076675
angular distri
Sheet1
Ebeam = 5.3 MeV in LAB = 1.18 MeV in CM5.79E+05
5 degrees12 degrees5.81E+05
thicknessthicknessafter target (keV)after target (keV)5.85E+05
ug/cm2umEbeamEcmEbeamEcm5.91E+05
6506.99129028712002675.88E+05
7508.067401646801514.14E+05
8008.605201164621035.79E+05
9009.6820044146325.54E+05
100010.757.82006.21E+05
6.19E+05
593075.10
5.63E+05
At 5 degrees:5.80E+05
A beam of 5.3 MeV produces a 21.66 MeV proton, after a in 6.45 um (0.6 mg/cm2) it ends with 21.65 MeV5.90E+05
A beam of 5.3 MeV 7Be ends with 1.63 MeV after the target and produces a proton of 18.19 MeV5.91E+05
In a 300 um Si (LEDA):5.92E+05
A proton of 21.65 MeV loses 1.35 MeV5.83E+05
A proton of 18.19 MeV loses 1.60 MeV5.84E+05
If we put a Mylar foil of 12 um before the detector:5.80E+05
A proton of 18.19 MeV loses 40 keV6.11E+05
A proton of 21.65 MeV loses 40 keV6.07E+05
This is negligible.5.79E+05
If we put an Al foil of 10 um5.97E+05
A proton of 18.19 MeV loses 60 keV5.69E+05
A proton of 21.65 MeV loses 50 keV5.68E+05
This is negligible.6.06E+05
5.70E+05
At 12 degrees:5.71E+05
A beam of 5.3 MeV produces a 21.28 MeV proton, after a in 6.45 um (0.6 mg/cm2) it ends with 21.65 MeV5.79E+05
A beam of 5.3 MeV 7Be ends with 1.63 MeV after the target and produces a proton of 18.00 MeV5.95E+05
The situation is similar as with 5 degrees5.90E+05
6.04E+05
6.03E+05
5.76E+05
5.94E+05
6.01E+05
6.12E+05
6.18E+05
5.89E+05
6.06E+05
5.70E+05
6.04E+05
6.13E+05
5.95E+05
5.82E+05
6.05E+05
5.59E+05
5.81E+05
5.92E+05
5.81E+05
5.94E+05
5.97E+05
6.24E+05
5.77E+05
5.94E+05
5.95E+05
5.85E+05
5.76E+05
5.92E+05
5.63E+05
6.06E+05
6.09E+05
5.92E+05
5.86E+05
5.80E+05
5.93E+05
5.91E+05
5.99E+05
6.17E+05
5.93E+05
5.88E+05
5.89E+05
5.87E+05
6.03E+05
5.83E+05
5.91E+05
5.90E+05
6.02E+05
5.90E+05
5.99E+05
5.68E+05
6.09E+05
5.98E+05
6.01E+05
5.83E+05
5.89E+05
5.76E+05
5.75E+05
5.90E+05
5.84E+05
5.99E+05
6.12E+05
5.61E+05
5.91E+05
5.67E+05
6.05E+05
5.75E+05
5.68E+05
5.97E+05
5.76E+05
0.588
T = 1 GK
T = 0.5 GK
Gamow window
Sheet2
for a CD de 500 um at 12 cm from target (4.8-18 deg) followed by a LEDA of 300 um at 60 cm from target (4.8-11.8 deg)irradiation beam 6.72E10 7Be particles
lab angEpDE1E1time/mTOF at 48 cm time 39852 s
521.662.3119.3516.377.91 average 1.6875E6 part / s
621.632.2819.3516.377.91
721.582.3619.2216.427.91protons detected 2774
821.542.3219.2216.427.91
921.482.3419.1416.467.91solid angle 9.8482E-2 srad 5 % error
1021.472.3719.1016.477.91
1121.42.4218.916.557.91cross section
1221.32.3319.016.547.91 tot g.s. + 1st rest
mbarn 2.7846E+01 1.9083E+01 8.7634E+00
error 0.17 0.17 0.16
Sheet2
11
11
11
11
11
11
11
11
Delta E MeV (in 500 um)
TOF (ns) for 48 cm
picture for 300+500 um
CD labEpEp after 500 umtime/mTOF (70 cm)DE(1)LEDA labEp(2)DE(2)9.84E+061.1777777778
at 62 cm(after 300 um)9.79E+06
4.821.719.416.3511.442.310.40.5695844.917.911.499.81E+06
5.721.619.316.3911.482.410.50.805855.317.791.509.87E+06
6.721.619.316.4111.482.310.61.0266645.817.81.469.85E+06
7.621.619.216.4211.502.310.71.2320266.217.691.531.01E+07
8.521.519.116.4611.522.410.81.4219366.717.581.559.94E+06
9.521.519.116.4711.532.310.91.5963947.217.561.569.82E+06
10.421.419.016.5111.562.4111.75547.617.481.539.83E+06
11.321.318.916.5511.592.411.11.8989548.117.361.561.00E+07
12.221.318.916.5611.592.411.22.0270568.517.361.559.85E+06
13.121.218.816.6211.632.411.32.1397069.017.241.539.70E+06
14.021.118.616.6811.672.511.42.2369049.417.021.629.94E+06
14.921.018.516.7211.712.511.52.318659.916.911.631.00E+07
15.821.018.516.7411.722.511.62.38494410.316.911.599.80E+06
16.720.918.416.7911.752.511.72.43578610.816.821.579.90E+06
17.620.818.316.8411.792.511.82.47117611.216.71.579.83E+06
18.420.718.216.8911.822.511.92.49111411.716.581.599.80E+06
9.96E+06
9.98E+06
9.90E+06
9.83E+06
9.88E+06
9.89E+06
9.93E+06
1.01E+07
9.92E+06
9.86E+06
9.95E+06
1.00E+07
9.73E+06
9.83E+06
9.82E+06
1.00E+07
9.91E+06
9.89E+06
9.72E+06
9.67E+06
9.76E+06
9.94E+06
9.75E+06
9.80E+06
9.68E+06
9.92E+06
9.88E+06
9.88E+06
9.80E+06
9.88E+06
9774737.0000
9.94E+06
9869626.4802193250.32888889
6.5
LEDAEp(2)LEDA
CD labEpEp aftertime/mTOFDE(1)usedafterDE(2)labsolid ang
at 3 cm500 um(at 6.5 cm)in 500 umat 9.5 cm300 umin 300 umat 9.5 cm(sr)
18.420.718.216.891.102.527.80.004881
21.820.317.717.131.112.630.10.007681
25.019.817.017.441.132.832.30.009941
28.119.416.517.721.152.827.814.561.9534.40.0117412.841.95
31.018.915.818.111.183.130.113.742.0636.40.0121113.082.06
33.718.415.118.521.203.334.412.832.2938.30.0124813.32.29
36.318.014.618.881.233.436.412.22.3540.10.0128213.412.35
38.717.513.819.361.263.738.311.242.5941.80.0131513.72.59
40.917.113.219.801.293.940.110.412.8143.50.0134313.92.81
43.016.712.620.281.324.143.59.4863.11445.00.0136714.133.114
45.016.412.120.741.354.345.08.7623.28846.50.0138514.33.288
46.816.011.321.391.394.746.57.6113.71947.90.0139514.683.719
48.615.710.821.941.434.947.96.7963.97449.20.0139714.93.974
50.215.410.222.581.475.250.45.6024.56850.40.0138715.214.568
51.715.19.523.311.525.651.64.3115.22951.60.0136515.565.229
53.114.88.824.221.576.052.82.656.18552.80.0132816.0056.185
angle = 28.1Ep(2)
ElabEpEp aftertime/mTOFDE(1)afterDE(2)
7Be500 um(at 6.5 cm)in 500 um300 umin 300 um
5.319.416.517.721.152.814.561.951.92
5.019.216.317.861.163.014.341.911.94
418.615.618.241.193.013.562.0152.015
317.9214.818.751.223.212.652.12.13
2.517.5814.418.961.233.212.212.212.17
217.2213.919.291.253.311.622.312.24
1.516.8313.519.631.283.411.162.32.3
116.413.019.981.303.410.562.422.42
0.816.212.820.161.313.410.362.42.4
0.615.9912.520.391.333.59.992.482.48
0.515.8812.420.451.333.59.872.522.52
angle = 41
p0Ep(2)
ElabEpEp aftertime/mTOFDE(1)afterDE(2)
7Be500 um(at 6.5 cm)in 500 um300 umin 300 um
5.317.313.519.571.273.810.812.72.72
5.017.213.419.671.283.810.672.72.73
416.812.920.051.303.9102.92.9
316.412.420.441.334.09.463.02.95
2.516.212.220.621.344.09.23.02.99
21611.920.841.354.18.823.13.12
1.515.811.721.031.374.18.63.13.12
115.511.321.411.394.28.043.33.27
0.615.3211.121.631.414.27.763.33.32
0.5215.2811.121.651.414.27.763.33.3
p1
5.314.39.623.231.514.75.64.0
5.014.179.523.341.524.75.524.0
413.88.924.081.574.94.534.4
313.458.524.671.604.93.864.7
2.513.268.225.221.645.13.3144.8
213.077.925.631.675.22.625.3
1.512.877.626.121.705.31.885.7
112.667.326.651.735.40.9746.3
0.612.487.027.231.775.50.2686.7
0.5212.446.927.471.795.60.16.8
picture for 300+500 um
TOF (ns)
DE in 500 um Si (MeV)
500um + 300um
DE in 300 um de Si (MeV)
DE in 500 um Si (MeV)
500um+1.5mm
TOF (ns)
DE in 500 um Si (MeV)
CD at 3 cm, LEDA at 9.5 cm (lab angles 28 to 53 deg)
picture for 500um+1.5mm
DE1 in 500 mm of Si (MeV)
DE2 in 300 mm of Si (MeV)
Lab angles covered: 28 - 53 degrees
DE1 in 500 mm of Si (MeV)
DE2 in 300 mm of Si (MeV)
lab angle: 28 deg
2.771893.96763
2.777673.98121
2.783513.99489
2.78944.00868
2.795354.02262
2.801364.03693
2.807434.0514
2.813554.06601
2.819734.08077
2.825964.09568
2.832254.11073
2.83864.12593
2.8454.14127
2.851454.15674
2.857974.17236
2.864564.18842
2.87134.20503
2.878114.22205
2.884984.23931
2.891914.2568
2.897984.27451
2.903824.29245
2.909654.31062
2.915624.3291
2.921734.34787
2.927874.36688
2.934014.38613
2.940174.40602
2.946344.4263
2.952524.4469
2.95874.46782
2.96494.48905
2.971114.5106
2.977334.53245
2.983554.55462
2.989784.5771
2.996024.59994
3.002264.62358
3.00854.64762
3.014754.67207
3.021014.69692
3.027274.72234
3.033524.74838
3.039784.77495
3.046044.80203
3.05234.82965
3.058564.85801
3.064824.88696
3.071074.9165
3.077324.94665
3.083574.97781
3.089815.00973
3.096055.04239
3.102435.07583
3.109035.11033
3.115655.14571
3.122285.18228
3.129535.22006
3.136935.25927
3.144385.29966
3.15195.34122
3.159475.38457
3.167095.42938
3.174775.47484
3.182095.52085
3.189445.56864
3.196825.61803
3.204245.66953
3.211685.72334
3.219155.77937
3.226655.83838
3.234195.90041
3.241745.96609
3.249336.03592
3.256946.11015
3.264586.18999
3.272246.27713
3.279936.37207
3.287646.47694
3.295386.59629
3.303146.73696
3.310926.91982
3.318947.14545
3.327237.11365
3.335577.08183
3.343957.04999
3.352387.01814
3.360866.98612
3.369386.95383
3.377956.9215
3.386566.88913
3.395226.85673
3.40391
3.41265
3.4214
3.43017
3.43897
DE1 in 500 mm of Si (MeV)
DE2 in 300 mm of Si (MeV)
lab angle: 41 deg
Ep iniDE1DE2DE1+DE2Ep iniDE1DE2DE1+DE2De1 carDe2 car17.30383.837622.77189
500um300um17.30383.837622.771896.609513.772.726.4917.28313.841342.77767
19.97932.3681982.303764.67195817.28313.841342.777676.619013.82.736.5317.26233.845032.78351
19.95852.3694582.308334.6777880.717.26233.845032.783516.628543.92.96.817.24163.848712.7894
19.93782.3707042.312934.68363417.24163.848712.78946.638113.992.956.9417.22083.852372.79535
19.9172.3719432.317584.68952317.22083.852372.795356.647724.012.99717.20013.856012.80136
19.89632.3731752.322264.69543517.20013.856012.801366.657374.063.127.1817.17943.859632.80743
19.87562.3743932.326984.70137317.17943.859632.807436.667064.083.127.217.15863.863242.81355
19.85482.3755972.331744.70733717.15863.863242.813556.676794.193.277.4617.13793.866822.81973
19.83412.3767942.336534.71332417.13793.866822.819736.686554.243.327.5617.11713.870392.82596
19.81332.3779772.341364.71933717.11713.870392.825966.696354.223.37.5217.09643.873952.83225
19.79262.3791532.346234.72538317.09643.873952.832256.706217.07573.877482.8386
19.77192.3803152.351144.73145517.07573.877482.83866.716084.694.018.717.05493.880992.845
19.75112.381472.355954.7374217.05493.880992.8456.725994.6548.6517.03423.884492.85145
19.73042.3826182.360144.74275817.03423.884492.851456.735944.864.419.2717.01343.887972.85797
19.70962.3837452.364344.74808517.01343.887972.857976.745944.934.669.5916.99273.891532.86456
19.68892.3848722.368534.75340216.99273.891532.864566.756095.114.8369.94616.9723.895412.8713
19.66822.3859782.372714.75868816.9723.895412.87136.766715.1785.27210.4516.95123.89932.87811
19.64742.3870842.37694.76398416.95123.89932.878116.777415.275.7210.9916.93053.903192.88498
19.62672.3881692.381084.76924916.93053.903192.884986.788175.366.32611.68616.90973.907082.89191
19.60592.3892542.385254.77450416.90973.907082.891916.798995.496.72212.21216.8893.912012.89798
19.58522.3903182.389434.77974816.8893.912012.897986.809995.576.7712.3416.86833.917262.90382
19.56452.3913822.39364.78498216.86833.917262.903826.8210816.84753.922572.90965
19.54372.3924252.397774.79019516.84753.922572.909656.8322216.82683.927942.91562
19.5232.3934682.401944.79540816.82683.927942.915626.8435616.8063.933382.92173
19.50222.394492.40614.8005916.8063.933382.921736.8551116.78533.938882.92787
19.48152.3955122.410264.80577216.78533.938882.927876.8667516.76463.944442.93401
19.46082.3965132.414424.81093316.76463.944442.934016.8784516.74383.950072.94017
19.442.3975072.418584.81608716.74383.950072.940176.8902416.72313.955762.94634
19.41932.3986832.422494.82117316.72313.955762.946346.902116.70233.961512.95252
19.39852.400652.425384.8260316.70233.961512.952526.9140316.68163.967322.9587
19.37782.4026452.428224.83086516.68163.967322.95876.9260216.66093.97322.9649
19.35712.4046752.430984.83565516.66093.97322.96496.938116.64013.979142.97111
19.33632.4067332.433684.84041316.64013.979142.971116.9502516.61943.985142.97733
19.31562.4088262.436324.84514616.61943.985142.977336.9624716.59863.991212.98355
19.29482.4109472.438894.84983716.59863.991212.983556.9747616.57793.997342.98978
19.27412.4130962.44144.85449616.57793.997342.989786.9871216.55724.003532.99602
19.25342.415282.443834.8591116.55724.003532.996026.9995516.53644.009783.00226
19.23262.4174992.446214.86370916.53644.009783.002267.0120416.51574.01613.0085
19.21192.4197392.448514.86824916.51574.01613.00857.024616.49494.022483.01475
19.19112.4220142.450754.87276416.49494.022483.014757.0372316.47424.028933.02101
19.17042.4243242.452924.87724416.47424.028933.021017.0499416.45354.035433.02727
19.14972.4266552.455024.88167516.45354.035433.027277.062716.43274.0423.03352
19.12892.4290212.457054.88607116.43274.0423.033527.0755216.4124.048633.03978
19.10822.4314152.459014.89042516.4124.048633.039787.0884116.39124.055333.04604
19.08742.4338442.46094.89474416.39124.055333.046047.1013716.37054.062093.0523
19.06672.4363012.462724.89902116.37054.062093.05237.1143916.34984.068913.05856
19.0462.4387862.464474.90325616.34984.068913.058567.1274716.3294.075793.06482
19.02522.4412992.466154.90744916.3294.075793.064827.1406116.30834.082743.07107
19.00452.4438472.467764.91160716.30834.082743.071077.1538116.28754.089753.07732
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13.98543.3411144.188427.529534
13.96473.346634.205037.55166
13.94393.3521884.222057.574238
13.92323.3577884.239317.597098
13.90243.3634234.25687.620223
13.88173.36914.274517.64361
13.8613.3748194.292457.667269
13.84023.3805734.310627.691193
13.81953.3864884.32917.715588
13.79873.392554.347877.74042
13.7783.3986544.366887.765534
13.75733.4048144.386137.790944
13.73653.4110234.406027.817043
13.71583.4172884.42637.843588
13.6953.4236024.44697.870502
13.67433.4299654.467827.897785
13.65363.4363774.489057.925427
13.63283.4428384.51067.953438
13.61213.4493554.532457.981805
13.59133.4559214.554628.010541
13.57063.4625434.57718.039643
13.54993.4692144.599948.069154
13.52913.4759344.623588.099514
13.50843.4827034.647628.130323
13.48763.4895214.672078.161591
13.46693.4963954.696928.193315
13.44623.5033184.722348.225658
13.42543.5102974.748388.258677
13.40473.5173184.774958.292268
13.38393.5243954.802038.326425
13.36323.5315284.829658.361178
13.34253.5387034.858018.396713
13.32173.5459344.886968.432894
13.3013.5532144.91658.469714
13.28023.560554.946658.5072
13.25953.5679284.977818.545738
13.23883.5753625.009738.585092
13.2183.5828455.042398.625235
13.19733.5903845.075838.666214
13.17653.5979725.110338.708302
13.15583.6056095.145718.751319
13.13513.6135335.182288.795813
13.11433.6215765.220068.841636
13.09363.6296965.259278.888966
13.07283.6378795.299668.937539
13.05213.6461255.341228.987345
13.03143.6544485.384579.039018
13.01063.6628415.429389.092221
12.98993.6708985.474849.145738
12.96913.6783465.520859.199196
12.94843.6858085.568649.254448
12.92773.6932915.618039.311321
12.90693.7007955.669539.370325
12.88623.7083135.723349.431653
12.86543.7158525.779379.495222
12.84473.7234055.838389.561785
12.8243.7309795.900419.631389
12.80323.7385675.966099.704657
12.78253.7461696.035929.782089
12.76173.7537926.110159.863942
12.7413.7614226.189999.951412
12.72033.7690736.2771310.046203
12.69953.7767386.3720710.148808
12.67883.784416.4769410.26135
12.6583.7921036.5962910.388393
12.63733.799816.7369610.53677
12.61663.8075316.9198210.727351
12.59583.8152597.1454510.960709
12.57513.8230017.1136510.936651
12.55433.8307577.0818310.912587
12.53363.8385277.0499910.888517
12.51293.8463047.0181410.864444
12.49213.85426.9861210.84032
12.47143.8622856.9538310.816115
12.45063.8703986.921510.791898
12.42993.8785396.8891310.767669
12.40923.8867016.8567310.743431
12.38843.8948916.8242910.719181
12.36773.9031026.7918210.694922
12.34693.9113416.7593110.670651
12.32623.9196016.7267710.646371
12.30553.9278896.6941910.622079
12.28473.9361916.6615910.597781
12.2643.9445216.6289510.573471
12.24323.9528726.5962810.549152
12.22253.9612446.5635810.524824
12.20183.9696376.5308510.500487
12.1813.9780516.4980910.476141
12.16033.986646.4650810.45172
12.13953.9952716.4320110.427281
12.11884.0039376.3988910.402827
12.09814.0126386.3657210.378358
12.07734.0213816.3324910.353871
12.05664.0301526.2992210.329372
12.03584.0389656.2658910.304855
12.01514.0478136.2325110.280323
11.99444.056786.1989610.25574
11.97364.0662236.1647310.230953
11.95294.0757296.1304110.206139
11.93214.0852916.0960110.181301
11.91144.0949096.0615310.156439
11.89074.104596.0269610.13155
11.86994.1143555.9922710.106625
11.84924.1243025.9573210.081622
11.82844.1343195.9222710.056589
11.80774.144425.887110.03152
11.7874.1545915.8518310.006421
11.76624.1648395.816459.981289
11.74554.1751575.780979.956127
11.72474.1855525.745389.930932
11.7044.1960245.709689.905704
11.68334.2065595.673899.880449
11.66254.2171715.637999.855161
11.64184.227865.601989.82984
11.6214.2386125.565889.804492
11.60034.2494415.529679.779111
11.57964.2603685.493329.753688
11.55884.2715195.456659.728169
11.53814.2827685.419849.702608
11.51734.2941085.38299.677008
11.49664.3055395.345839.651369
11.47594.3170685.308629.625688
11.45514.3286885.271289.599968
11.43444.3403925.233829.574212
11.41364.3521945.196229.548414
11.39294.3640875.158499.522577
11.37224.3760645.120649.496704
11.35144.3881325.082669.470792
11.33074.4002915.044559.444841
11.30994.4125415.006319.418851
11.28924.4250644.967689.392744
11.26854.4377484.928829.366568
11.24774.4505444.88989.340344
11.2274.4634664.85069.3140660.06625064970.153781008
11.20624.4765074.811239.287737
11.18554.489664.77179.261361.33E+07
11.16484.5029324.7329.2349321.36E+07
11.1444.5163164.692149.2084561.34E+07
11.12334.5298194.652119.1819291.35E+07
11.10254.5434414.611919.1553511.35E+07
11.08184.5571754.571559.1287251.35E+07
11.06114.5710214.531039.1020511.36E+07
11.04034.5850354.490279.0753051.36E+07
11.01964.5994064.4499.0484061.33E+07
10.99884.6139314.407519.0214411.35E+07
10.97814.6284914.365978.9944611.35E+073.8
10.95744.6432054.324218.967415
10.93664.6580524.282268.940312
10.91594.6730534.240098.913143
10.89514.6881944.197728.885914
10.87444.7034754.155158.858625
10.85374.7189034.112378.831273
10.83294.7344714.069398.803861
10.81224.7501794.026218.776389
10.79144.7661323.982688.748812
10.77074.7824353.938658.721085
10.754.798923.894368.69328
10.72924.8155873.849818.665397
10.70854.8324363.8058.637436
10.68774.849463.759948.6094
10.6674.8668063.714428.581226
10.64634.8844183.668528.552938
10.62554.9022543.62238.524554
10.60484.9203283.575748.496068
10.5844.9386333.528858.467483
10.56334.9572043.481588.438784
10.54264.9760973.433858.409947
10.52184.9952633.385738.380993
10.50115.0146883.337248.351928
10.48035.0343793.288378.322749
10.45965.0543643.239088.293444
10.43895.0748183.189128.263938
10.41815.0956083.138688.234288
10.39745.116723.087788.2045
10.37665.1381613.036418.174571
10.35595.1599732.984518.144483
10.33525.1822612.931938.114191
10.31445.2049272.878818.083737
10.29375.2279712.825158.053121
10.27295.2513932.770958.022343
10.25225.2753822.715947.991322
10.23155.2999522.66017.960052
10.21075.3250122.603567.928572
10.195.3505552.546337.896885
10.16925.376632.488347.86497
10.14855.4034822.429247.832722
10.12785.4309292.369297.800219
10.1075.4589712.308497.767461
10.08635.4876152.246837.734445
10.06555.5173092.183677.700979
10.04485.5477662.119427.667186
10.02415.5789792.054097.633069
10.00335.6110251.987577.598595
9.982585.6443031.919297.563593
9.961845.6785331.849657.528183
9.94115.7138551.778457.492305
9.920365.7506051.705217.455815
9.899625.7887621.629967.418722
9.878885.8284871.552477.380957
9.858145.8700391.472377.342409
9.83745.9135721.389447.303012
9.816665.959171.303567.26273
9.795926.0073091.214057.221359
9.775186.0587241.119867.178584
9.754446.1134991.020877.134369
9.73376.1723690.916037.088399
9.712966.2359010.8045347.040435
9.692226.3061320.6834586.98959
9.671486.3850570.5499736.93503
9.650746.4778490.3966666.874515
7Be
p
DE1
DE2
p0
p1
target
DE1 + DE2 (MeV)
DE1 in 500 mm of Si (MeV)
lab angle: 41 deg
6.60951
8.63784
6.61901
8.65812
6.62854
8.67851
6.63811
8.69903
6.64772
8.71972
6.65737
8.7408
6.66706
8.76206
6.67679
8.78347
6.68655
8.80505
6.69635
8.8268
6.7062
8.8487
6.71608
8.87077
6.72599
8.893
6.73594
8.91537
6.74594
8.93791
6.75609
8.96144
6.76671
8.98593
6.77741
9.01089
6.78817
9.03615
6.79899
9.06169
6.80999
9.08751
6.82108
9.11362
6.83222
9.14001
6.84356
9.16694
6.85511
9.19437
6.86675
9.2221
6.87845
9.25015
6.89024
9.27891
6.9021
9.30814
6.91403
9.33776
6.92602
9.36777
6.9381
9.39816
6.95025
9.42894
6.96247
9.4601
6.97476
9.49165
6.98712
9.52359
6.99955
9.55596
7.01204
9.5892
7.0246
9.62291
7.03723
9.6571
7.04994
9.69177
7.0627
9.72708
7.07552
9.76309
7.08841
9.79969
7.10137
9.83688
7.11439
9.87469
7.12747
9.9133
7.14061
9.95258
7.15381
9.99252
7.16707
10.03315
7.18039
10.07485
7.19377
10.11739
7.20721
10.16074
7.22085
10.20495
7.23477
10.25029
7.24878
10.29658
7.26286
10.34447
7.27734
10.39374
7.29198
10.44455
7.30671
10.49663
7.32156
10.54997
7.3365
10.60521
7.35154
10.66201
7.36668
10.71898
7.37999
10.77563
7.39331
10.83408
7.40664
10.89416
7.41998
10.95638
7.43333
11.02093
7.44668
11.08773
7.46004
11.15753
7.47342
11.23038
7.48679
11.3069
7.50017
11.38759
7.51355
11.47271
7.52693
11.56345
7.54032
11.66152
7.5537
11.76741
7.56709
11.88324
7.58047
12.01358
7.59386
12.16526
7.60723
12.35915
7.62083
12.59582
7.63466
12.57508
7.64852
12.55434
7.6624
12.5336
7.67629
12.51286
7.69021
12.49212
7.70414
12.47138
7.7181
12.45064
7.73207
12.4299
7.74606
12.40916
7.76005
7.77406
7.78816
7.80241
7.81667
3.83762
4.67021
3.84134
4.67691
3.84503
4.68362
3.84871
4.69035
3.85237
4.6971
3.85601
4.70387
3.85963
4.71066
3.86324
4.71746
3.86682
4.72428
3.87039
4.73112
3.87395
4.73797
3.87748
4.74484
3.88099
4.75173
3.88449
4.75863
3.88797
4.76555
3.89153
4.77302
3.89541
4.7809
3.8993