on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

25

Transcript of on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Page 1: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Photoexcitation of Baryon ResonancesBernd KruscheII Physikalisches Institut, Universitat Giessen, Heinrich-Bu-Ring 16, 35392 GiessenReceived XXXThe study of baryon resonances via meson photoproduction reactions on the free pro-ton, nucleons bound in light nuclei and in the nuclear medium is discussed. Special empha-sis is laid on the production of neutral mesons which due to the suppression of non-resonantbackgrounds are particularly well suited for the study of excited states of the nucleon. Ex-periments carried out during the last ten years with the TAPS-detector at the MainzMAMI accelerator have contributed very signicantly to the detailed investigation of thefour lowest lying baryon resonances the P33(1232), the P11(1440), the D13(1520) and theS11(1535). Future experiments with TAPS at the ELSA accelerator have a large potentialfor the investigation of higher lying resonances via many dierent decay channels.1 IntroductionThe study of baryon resonances plays the same role for our understanding of thenucleon as nuclear spectroscopy did for atomic nuclei. In both cases the excitationspectrum of the system does not provide very sensitive tests of models. The cru-cial tests come from the investigation of transitions between the states which aremuch more sensitive to the model wavefunctions. The dominant decay channel ofnucleon resonances is the hadronic decay via meson emission to the nucleon groundstate. However, photon decay amplitudes are also of great interest since the pho-ton couples only to the spin avor degrees of freedom of the quarks and thereforereveals their spin - avor correlations which are related to the conguration mixingpredicted by QCD.Perturbative QCD at high energies deals with the interactions of quarks andgluons. However, our picture of the nucleon has much more to do with eectiveconstituent quarks and mesons that somehow subsume the complicated low en-ergy aspects of the interaction which generate the nucleon many body structureof valence quarks, sea quarks and gluons. The most important step towards anunderstanding of nucleon structure is therefore the identication of the relevantlow-energy eective degrees of freedom. Most nucleon models are based on threeequivalent constituent quarks interacting via some QCD `inspired' interaction. How-ever, models based on quark - diquark (q q2)-congurations were also suggestedand more molecular-like pentaquark (qqq qq) structures have been discussed inthe context with certain `nucleon' resonances.From the experimental point of view the main dierence between nuclear andnucleon structure studies results from the large, overlapping widths of the nucleonresonances and the much more important non-resonant background contributionswhich both complicate detailed investigations of individual resonances. Most nu-cleon resonances have been identied in pion scattering reactions which prot fromthe large hadronic cross sections. However, investigating nucleon resonances only inCzechoslovak Journal of Physics, Vol. 49 (1999), No. 0 A 1

Page 2: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Kruschethe N-channel has two obvious disadvantges: no use is made of the rich informa-tion connected to electromagnetic transition amplitudes and experimental bias mayarise for nucleon resonances that couple only weakly to the N-channel. A com-parison of the excitation spectrum predicted by modern relativistic quark modelsto the experimentally established set of nucleon resonances indeed results in theso-called `missing resonance' problem. Many more states are predicted than havebeen observed. Is this evidence for inept eective degrees of freedom in the modelsor simple experimental bias?During the last ten years the progress made in accelerator and detector technol-ogy has largely enhanced our possibilities to investigate the nucleon with dierentprobes. The new generation of electron accelerators CEBAF at TJNAF in New-port News, ELSA in Bonn, ESRF in Grenoble, and MAMI in Mainz all equippedwith state-of-the-art detector systems have opened the way to meson photopro-duction experiments of unprecedented sensitivity and precision. It is interesting tonote that neutral meson photoproduction moved into the center of interest. Reac-tions involving neutral mesons have the advantage that non-resonant backgroundcontributions are much less important because the incident photon couples onlyto charged mesons. The development of high sensitivity, high resolution photondetectors gave a large push to this eld.With these new tools experiments can proceed along two dierent roads. Theproblem of missing resonances can be attacked by a large scale survey investigatingmany dierent nal states over a large energy range. Alternatively the low lyingresonances P33(1232), P11(1440), D13(1520) and S11(1535) can be studied in greatdetail for precision tests of the models. The present talk is mostly concerned withthe second approach, simply because the majority of the data that became availableduring the last ten years falls in this category.The detailed understanding of the elementary process of resonance excitation onthe free nucleon is the basis for the investigation of baryon resonances in the nuclearmedium. In the case of bound nucleons even properties like mass and width, whichmay be in uenced by the nuclear medium, are mostly unknown. Here photoexcita-tion oers the advantage that due to the small absorption probability of photonsthe complete volume of the atomic nucleus may contribute. This advantage maybe partly lost due to nal state interaction eects if exclusive channels like mesonproduction are used.2 Excitation of baryon resonances on the free proton2.1 The (1232)-resonanceThe (1232)-resonance is certainly the best known exited state of the nucleonwhich has been investigated via many dierent reactions, in particular in the N -nal state, on the free proton but also on bound nucleons. A comparison of the totalphotoproduction cross section for neutral and charged pions (see gure 1) nicelydemonstrates the advantage of the neutral channel. Non-resonant background termswhich contribute strongly to +-production are almost absent for o-production.2 A Czech. J. Phys. 49 (1999)

Page 3: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :

0

1

2

3

200 400 600 800

σ/A

[µb]

x102

γp→πop

γp→π+n

photon energy [MeV]Fig. 1. Total cross section for o and +-photoproduction from the proton. The o-datawere measured with TAPS [1, 2], the +-cross section is taken from SAID [3]It is well known that in photoproduction reactions the I = J = 3=2 -excitationof the nucleon is dominated by the magnetic multipoleM1+. In the simplest picturethe incident M1 photon induces the spin- ip of one of the constituent quarks.However, as far as quantum numbers are concerned the excitation via an E2-photon(E1+-multipole) is also possible. An E2-admixture in the transition strength coulde.g. arise from d-state components in the baryon wave functions connected to tensorforces. The correct prediction of such admixtures is therefore a challenge for nucleonmodels.Experimentally one must determine the ratio REM = E3=21+ =M3=21+ of the elec-tric quadrupole to the magnetic dipole in the isopin 3/2 channel. This may beaccomplished by a measurement of the dierential cross sections and the photonbeam asymmetries in the p(~ ; o)p and the p(~ ; +)n reactions. Such measure-ments were performed at MAMI [4] and at LEGS [5]. Although the extractionof the ratio is not completly model independent (see e.g. discussion in [6] andrefs. therein) all analyses nd a small negative value of the REM -ratio. The re-sults from the Mainz data (2:5 0:1(stat) 0:2(sys))% and the LEGS data(3:1 0:3(stat+ sys) 0:2(model))% are in reasonable agreement.2.2 The second resonance regionThe so-called second resonance region includes the P11(1440), the D13(1520)and the S11(1535) resonances which are all overlapping. Fortunately, the couplingof the resonances to the possible decay channels is quite dierent, which may beexploited by exclusive experiments looking at single and double pion productionand at -photoproduction.Czech. J. Phys. 49 (1999) A 3

Page 4: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Krusche2.2.1 Photoproduction of -mesonsThe photoproduction of -mesons in the second resonance region is completelydominated by the excitation of the S11(1535) nucleon resonance [7] which so far isthe only known nucleon resonance with a strong branching into the N-channel.The dominance of s-wave -production in the S11(1535) excitation range close to the-production threshold is re ected in the typical (E Ethr)1=2 energy dependenceof the total cross section which is shown in gure 2 and the almost isotropic angulardistributions. The data allowed the extraction of precise parameters (mass, width,photon coupling) of the resonance [8].

0

4

8

12

16

680 720 760 800

σ[µb

]

η→2γ

η→3π0 (4γ detected)η→3π0 (3γ detected)

Eγ[MeV]

0

100

695 710 725Eγ[MeV]

σ2 [µb2 ]

Fig. 2. Total cross section for the reaction p( ; )p. The solid line is a Breit-Wigner t.The insert shows the linear (l = 0) rise of the squared cross section at thresholdThe structure of the S11(1535) in terms of the quark model is still hotly debateddue to its unusual branching ratios. The much weaker coupling of the close-by P11and D13 resonances to the N channel can be explained by simple phase spacearguments since they need to decay with relative orbital angular momentum l =1; 2 which is strongly suppressed close to threshold. However, also the second S11-resonance at 1655 MeV has a branching ratio into N of 1 % or less. Glozmannand Rsika [9] have argued, that these decay patterns can be understood as a isospinselection rule in their quark model with quark-diquark clusterization of the nucleon.Their diquark clusters in the nucleon ground state and in the S11(1535) have bothI = 0 but the diquark cluster in the S11(1650) has I = 1. Consequently the decayvia the isoscalar -meson is strongly suppressed for the second S11. Other workeven questioned the very nature of the S11(1535) as a nucleon resonance. Kaiser etal. [10, 11] treated the resonance as a quasi-bound K-state and Bijker et al. [12],failing to explain the S11(1535) properties in their model, suggested a quasi-boundN (penta-quark) state. If such suggestions are correct, the imediate question would4 A Czech. J. Phys. 49 (1999)

Page 5: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :be where are the regular low lying three quark states predicted in the quark modelwith the quantum numbers 1/2,1/2?The precise determination of properties of this state is essential in order to resolvethe problem. Of particular interest is the Q2-dependence of the electromagnetichelicity coupling Ap1=2. For an extended, molecular like objekt one expects a muchfaster drop of the coupling with the momentum transfer than for a conventionalthree-quark resonance. The experimental values show a very atQ2-dependence [13]that is unlike any model prediction. However, those values have very large error barsand were determined with pion electroproduction where the S11 contributes onlyweakly. The recent measurements of -electroproduction with the CLAS-detectorat CEBAF will probably settle this question.A very interesting contribution to our understanding of -photoproduction camerecently from the measurements of the target asymmetry [14] at the Bonn ELSAaccelerator and the photon beam asymmetry [15] at the GRAAL facility in Greno-ble. Dierent analyses of the asymmetries and the angular distributions [16, 17]have clearly born out two important results. The rst concerns the contributionof the D13(1520) resonance. This contribution was rst identied in the angulardistributions [7] via a small s-d-interference term. The photon asymmetry is muchmore sensitive to the D13 and shows indeed the very clear signal expected fromthe tiny eect in the angular distributions. In this sense angular distributions andphoton asymmetries are consistent which each other. However, the models cannott at the same time the target asymmetries in the threshold region. The data showa node around 90o which con icts with the angular distributions and the photonasymmetries if analysed in the framework of the eective Lagrangian [16] or theisobar model [17, 18]. Tiator et al. [17] have analysed this problem in more detailwith a multipole analysis of the p( ; )p reaction based on all three data sets andsome reasonable asumptions like S11-dominance. They could show, that the targetasymmetry data gives rise to a large positive phase dierence between the s- andd-wave multipoles connected with the S11- and D13-excitations. If both resonancescan be parametrized by Breit-Wigner curves (as assumed in the models) the phaseshould be small and negative since the S11 lies only slightly higher in energy andboth have similar widths. Since the D13 is very well established from pion produc-tion experiments this could be another hint to an odd behavior of the S11. Since thediscussion hinges completly on the target asymmetry data, which have considerableuncertainties, a more precise measurement of this observable is highly desirable.So far very few was known about -photoproduction at energies above the secondresonance region. The GRAAL collaboration has published [15] photon asymme-tries up to 1.05 GeV. At the highest photon energies a strong forward peaking ofthe asymmetries develops. Tiator et al. [17] argued, that this behavior is not repro-duced by models that include only the resonances from the second resonance regionand the ususal background contributions. They claim that the asymmetry is bestexplained by a contribution from the F15(1680) resonance. New exciting resultsfor total and dierential cross sections are awaited for the very near future fromexperiments already carried out at GRAAL, at ELSA in Bonn and at CEBAF.Czech. J. Phys. 49 (1999) A 5

Page 6: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Krusche2.2.2 Double pion photoproductionDouble pion photoproduction is a very important reaction channel in the sec-ond resonance region. The cross sections for single meson production (pions and-mesons) and double pion photoproduction are almost equal at incident photonenergies between 600 and 800 MeV. Moreover, most of the rise of the total pho-toabsorption cross section from the dip above the -resonance to the peak of thesecond resonance bump is due to double pion production. This is demonstrated ingure 3 where the total photoabsorption cross section of the proton is compared tothe single and double meson production cross sections.

0

0.2

0.4

0.6

200 400 600 800

total absorptionsingle pion & etadouble pion

Eγ[MeV]

σ[m

b]

Fig. 3. Decomposition of the total photoabsorption cross section of the proton into singleand double meson production reactions.Any detailed interpretation of the second resonance bump requires the under-standing of double pion production. This is not only important for resonances onthe free nucleon. Measurements of the total photoabsorption cross section from nu-clei showed an almost complete depletion of the structure above the -resonance[19, 20, 21] (see below). Some authors [22] interpreted this as evidence for a damp-ing of the excitation of the P11, D13 and S11 in the nuclear medium. However, itwas not even clear if these resonances play an important role for double pion pro-duction which makes such a large contribution to the `bump'. Background termslike the -Kroll-Rudermann (KR) and the -pion-pole term which instead involvethe excitation of the are important at least for the charged double pion channels.Among the possible double pion production reactions p ! +is the onlychannel that was previously measured with any reasonable precision. The totalcross section and invariant mass distributions of the +, p+ and p pairs6 A Czech. J. Phys. 49 (1999)

Page 7: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :were analysed in an early attempt to extracxt the dominant production mechanismby Luke and Soding [23].

0

20

40

60

80

100

300 400 500 600 700 800

Eγ [MeV]

σ[µb

]

DAPHNE

Oset et al.Laget et al.Ochi et al.

Fig. 4. Total cross section for the reaction p ! p+. The data points are fromref. [24]. The dashed, dotted and dash-dotted curves correspond to the calculations from[25, 26, 27]The total cross section which is shown in gure 4 is very small between thresholdat 310 MeV and 400 MeV. It rises sharply from 400 MeV to a maximum at650 MeV. This rise is accompanied by a strong peak at the mass of the -resonance in the invariant mass distribution of the p+-pair. This peak is absentin the p invariant mass. A large contribution of the cross section is thereforeassigned to the p ! ++-reaction via the -KR and the -pion pole term.The energy dependence of the cross section thus re ects the N ! thresholdsmeared by the width of the -resonance. More recent analysis [25, 26, 27], takinginto account the more precise data from the DAPHNE-detector [24] have conrmedthis picture. However, even though the direct contributions from higher resonancesare negligible, it was pointed out by Oset and coworkers [25] that the peak likestructure between 600 and 800 MeV is due to an interference of the sequentialreaction p ! D13 ! ! N with the leading -KR term. This allowed theextraction of the coupling constant of the D13-decay into .The situation is very dierent for the nal states with two neutral pions. Sincethe photon does not couple to neutral particles and the -meson does not decayinto a pair of neutral pions all background terms are forbidden or strongly sur-pressed. Consequently, the neutral channel is best suited for the study of higherlying resonances. Surprisingly, the two models from refs. [25, 26] made very dier-ent predictions. One of them [25] predicted the sequential decay of the D13(1520)resonance, the other [26] the decay of the P11(1440) resonance via a correlated pairCzech. J. Phys. 49 (1999) A 7

Page 8: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Kruscheof pions in a relative s-wave as dominating process. Already the total cross sec-tion (see gure 5) is in better agreement with the prediction from ref. [25]. The

0

5

10

15

300 400 500 600 700 800

Eγ [MeV]

σ[µb

]

Oset et al.Laget et al.Ochi et al.

TAPS 95 (4γ) (very preliminary)TAPS 92 (4γ)TAPS 92 (3γ)DAPHNE

Fig. 5. Total cross section for the reaction p! poo. The data points are from exper-iments with the DAPHNE- [24] and TAPS-detectors [28]. The curves correspond to thesame calculations as in g. 4 .0

1

0 0.2 0.4

m2(πoπo)[GeV2]

coun

ts [a

.u.]

0

1

1 1.5 2

m2(pπo)[GeV2]Fig. 6. Distribution of the invariant mass squared for the oo- and po-pairs from the p ! poo reaction. The histogram shows the data measured with the TAPS detector[28], the dashed line the expectation for pure phase-space behavior and the solid line theresult from ref. [25].problem was solved by the invariant mass distributions measured with TAPS [28](see gure 6). While the oo-mass distribution agrees with phase space the po-8 A Czech. J. Phys. 49 (1999)

Page 9: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :distribution shows a peak at the -mass. Consequently, the sequential decay playsa more important role than the correlated decay. In the meantime data with muchbetter statistical accuracy have been measured with TAPS [29]. It is now possibleto analyse the invariant mass distribtions as function of the incident photon energyand to investigate in much more detail the contribution of the dierent resonances.It came as a complete surprise when the rst measurement of the p ! o+reaction [24] came up with a total cross section that is strongly underestimated bythe predictions from refs. [25, 26] (see gure 7). In the meantime this nding was0

10

20

30

40

50

60

70

300 400 500 600 700 800Eγ [MeV]

DAPHNE (Braghieri et al.)

Tejedor, OsetMurphy, LagetOchi, Hirata

TAPS

Fig. 7. Total cross section for the reaction p ! n+o. The data points are fromexperiments with the TAPS- and DAPHNE-detector. The dashed, dotted and dash-dottedcurves correspond to the models from ref. [25, 26, 27].conrmed by a measurement with the TAPS detector [30] and a similar situationwas found for the n! po reaction [31]. Obviously an important contributionis severely underestimated in the models.Recently Ochi et al. [27] suggested that these ndings can be explained by alarge contribution of the -Kroll-Rudermann term which is negligible for the otherisospin channels. They introduced a form factor at the vertex since the -mesoncontributing to double pion decays in the second resonance region is not on-shell.However, in many other aspects their model is more simplifying than the othersand describes the other charge channels less well.The most sensitive observables for the suggested eects are again the invariantmass distributions of the pion - pion and the pion - nucleon pairs. The predictionfor the -contribution is an enhancement of the pion - pion mass correlation to-wards large invariant masses. Some indication of this behavior was seen for the d ! ppo reaction [32]. However, the interpretation of this result is largelycomplicated by the in uence of Fermi motion and nuclear eects of the bound neu-tron. The TAPS experiments allow for the rst time a comparison of the pion -pion invariant mass distributions for the p ! poo and p ! n+o reactionsfrom the free proton which will nally clarify this question.Czech. J. Phys. 49 (1999) A 9

Page 10: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Krusche3 Excitation of baryon resonances on the bound neutronIn principle there are two possibilities to learn about the isospin structure of thephotoexcitation amplitudes. Coherent photoproduction from light nuclei may beused as an isospin lter while photoproduction from bound nucleons in quasifreekinematics can be used to extract the neutron cross section. The small bindingenergy and the comparatively well understood nuclear structure single out thedeuteron as exceptionally important target nucleus.However, even in the favorable case of the deuteron, the extraction of the ele-mentary n( ; x)n amplitudes requires input from models at least for the o-shellbehavior of the nucleons and the treatment of nal state interactions. For neutralpions predictions were made by several models for the reactions d( ; o)d (see e.g.[33, 34, 35, 36, 37]), d( ; o)np [33, 38, 39] and n( ; oo)n [25, 27].

0

1

2

3

4

5

200 400 600 800

σ [1

00µb

] γd→ηnp, η→πoXγd→πoπ-pp & γd→πoπ+nnγd→πoπonp x 2

γd→πodγd→πonp

sum of all channelsγd→πoX

photon energy [MeV]Fig. 8. Neutral pion photoproduction from the deuteron. The cross section for the nalstates opp and o+nn was decduced from the DAPHNE data [24, 31]. The resultsfor -photopdoduction are from [40] and all other data are taken from [2].The TAPS experiments [7, 2] measured -, coherent and incoherent o- andquasifree 2o-photoproduction. The results for the total cross sections are summa-rized in gure 8. The full line shows the sum of all partial channels. On the otherhand, the inclusive o-production was directly measured by analysing all eventswith at least one o. This result agrees very well with the summed up partial crosssections. Consequently, systematic uncertainties of the partial cross sections, whichall involve complicated analyses and have been measured with two dierent detectorsystems (TAPS and DAPHNE), are very well under control and the contributionof triple pion production apart from the -decays is negligible.10 A Czech. J. Phys. 49 (1999)

Page 11: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :3.1 The (1232)-resonanceIn the -resonance region for the rst time a separation of coherent and breakupo-photoproduction was obtained over the full angular range [2]. The results for thetotal cross sections are compared to model predictions in gure 9. The predictions

0

1

2

3

4

5

6

200 300 400 500

σ [1

00µb

]

photon energy [MeV]Fig. 9. Total single o-photoproduction cross section in the (1232)-resonance regioncompared to predictions. Filled circles: inclusive single o-production, lled triangles: co-herent o-production, open squares: breakup reaction. Full, dash-dotted and dotted curves:predictions from Laget [33], Kamalov et al. [36] and Wilhelm et al. [37] for coherent pro-duction. Long dotted curve: breakup o-production from Schmidt et al. [38]. Long dashed(short dashed) curves: breakup production from Laget [33] without (with) np-FSI.for the coherent process, in particular from Laget [33] and Kamalov et al. [36] arein good agreement with the data. The breakup reaction is overestimated by allmodels. Calculations of this process which do not include nal state interactioneects (FSI) predict cross sections even larger than the measured total inclusivecross section. The calculation by Laget [33] including neutron - proton FSI is muchcloser to the data but still too high. The dierential cross section data [2] underlinethe importance of np-FSI for the breakup channel. The cross section is stronglysuppressed at forward angles for low incident photon energies. In agreement withthe models np-FSI eects are much reduced at pion backward angles since therelative energy of the np-pair rises with the pion angle.The extraction of neutron amplitudes from such data requires a careful treatmentof the FSI-eects as e.g. attempted by Levchuk et al. [39]. A very interesting aspectof this program is connected to the quadrupole strength of the -excitation. Sincethe extraction of the REM -ratio requires the separation of the I = 3=2 component,information about the isospin composition would be very useful.Czech. J. Phys. 49 (1999) A 11

Page 12: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Krusche3.2 The second resonance region3.2.1 Single o-photoproductionThe total cross section for the breakup reaction d ! npo normalized to themass number is compared in gure 10 to the cross section from the free proton. The

20

30

40

50

500 600 700 800

σ/A

[µb]

γp→πop

γd→πonp

photon energy [MeV]Fig. 10. Single o-photoproduction from the proton and the deuteron in the secondresonance region normalized to the mass number. Dashed line: Fermi smeared protoncross section, full line: fermi semared sum of proton and neutron cross section.second resonance bump is much less pronounced on the deuteron. On the proton thestructure is re ected in the angular distributions with the exception of the extremeforward angles, while the deuteron data are almost at as function of incidentphoton energy for all angles. The vanishing of this structure cannot be explainedby nuclear Fermi motion alone. The proton cross section folded with the nucleonmomentum distribution calculated from the deuteron wave function [41] still showsa pronounced peak around 700 MeV (see gure 10). An estimate for the neutroncross section is available from the multipole analysis of pion and photoproductiondata [3]. A momentum folded superposition of proton and neutron cross sectioncannot explain the deuteron data, in particular not at backward angles [2]. This isin sharp contrast to the ndings for - and 2-photoproduction discussed below.Any interpretation of this behavior requires a better understanding of whatcauses the structure in the proton cross section in the rst place. It is certainly notonly due to the excitation of the D13(1520) resonance. It is known [42] that at leastfor backward angles the opening of the -threshold causes a unitarity cusp thatresults in an s-shape like step of the p( ; o)p cross section around the -threshold.12 A Czech. J. Phys. 49 (1999)

Page 13: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :3.2.2 -photoproductionThe electromagnetic excitation of I = 1=2 nucleon resonances involves two in-dependent isospin components namely the isoscalar and the isovector amplitudesleading to I = 1=2 in the nal meson - nucleon system. Since the -meson isisoscalar only these two isospin amplitudes contribute to -photoproduction. Sincethe reaction is dominated by the excitation of the S11(1535) we can directly deducethe isospin composition of the N ! S11 transition. The complete determinationof the relevant amplitudes is possible from the measurement of -photoproductionfrom the proton, the neutron and coherent -photoproduction from the deuteronmaking use of:p / jAIS +AIV j2 ; n / jAIS AIV j2 ; d / jAIS j2 ; (1)where AIS and AIV are the isoscalar and isovector parts. The reaction n( ; )n hasbeen studied via quasifree -photoproduction from 2H and 4He with and withoutcoincident detection of the recoil nucleons.coherent

quasifreethreshold

photon energy [MeV]

σ tot [

µb]

He0

10

20

30

550 600 650 700 750 800

0

1

2

3

4

600 620 640 660

Fig. 11. Total cross section of the reaction 4He( ; )X. The solid line is the result of aparticipant - spectator calculation of the cross section assuming n=p = 2=3.In case of the inclusive measurements the ratio of proton and neutron crosssection was determined in the following way: The measured cross section from thefree proton was folded with the momentum distribution of the bound nucleons andmultiplied with a factor so that the result agreed with the measured cross sectionfor the A( ; )X reaction. In both cases (2H- and 4He-target) agreement was foundwith an energy independent factor except for energies very close to threshold wherenal state interaction eects are important. As an example the result for the heliumtarget is shown in gure 11.Czech. J. Phys. 49 (1999) A 13

Page 14: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd KruscheThe exclusive measurements with detection of the recoil nucleons allow for adirect determination of the neutron/proton cross section ratio. The result for the4He( ; )(n)(p) reactions is shown in gure 12.0

0.2

0 50 100 150 200 250 300

0

1

0

0.2

0.4

0.6

0.8

0 20 40 60

EN,kin,lab [MeV]

dσ/d

E [µ

b/10

MeV

]

(a)

σ n/σ p

(b)

θN,lab [o]

dσ/d

θ [µ

b/ra

d]

proton

neutron

Fig. 12. (a) The kinetic energy dierential cross sections of the recoil nucleons (circles: pro-tons, squares: neutrons) from -photoproduction on 4He within the detector acceptancetogether with the ratio of the two data sets. (b) The angular dierential cross section ofthe recoil nucleons compared with the results from a participant - spectator calculation.The vertical dashed lines indicate the angular range covered by the detector.All experimental results for the ratio of the neutron - proton amplitudes at theS11 peak position are in excellent agreement:* An1=2=Ap1=2 = p0:66 0:07 (deuterium, inclusive) [40]* An1=2=Ap1=2 = p0:68 0:06 (deuterium exclusive) [43]* An1=2=Ap1=2 = p0:67 (0:01)stat (helium, inclusive) [44]* An1=2=Ap1=2 = p0:68 (0:02)stat (0:09)sys (helium, exclusive) [44].14 A Czech. J. Phys. 49 (1999)

Page 15: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :However, the cross section ratio n=p xes only the absolute value of the am-plitude ratio and the above result means that the isoscalar or the isovector part issmall. The sign must be determined from the measurement of the d( ; )d reaction.The upper limit for the cross section of this reaction obtained in [40] and the valuesreported in [43] are so small that they exclude a dominant isoscalar part so thatAn1=2=Ap1=2 < 0. But on the other hand, models of the d( ; )d reaction taking intoaccount this isospin decomposition overstimate the cross section reported in [43] byalmost an order of magnitude. As a test of these models it is desirable to measurethe coherent cross section from a dierent light nucleus. From the facts that thedominant S11-excitation proceeds via a spin- ip amplitude with dominant isovectorcharacter and the quantum numbers of light nuclei we expect qualitatively: 4He: J=0, I=0, only isoscalar non-spin- ip amplitude: very weak signal 2H: J=1, I=0, contribution from isoscalar spin- ip: small signal 3He J=1/2, I=1/2, contribution from isovector spin- ip: largest signalOur experimental results for the 4He( ; )4He-reaction [44] support this picture.The experiment produced only an upper limit for the cross section, no coherentevents were unambigously identied. An attempt to identify the 3He( ; )3He-reaction with TAPS at MAMI will be carred out in spring 2000. In addition thed( ; )d reaction was remeasured with TAPS.3.2.3 Double pion photoproductionDouble pion production from the deuteron was studied with the DAPHNE- andTAPS-detectors. A comparison of +-production from the free proton and from

0

5

10

15

20

200 400 600 800

σ [µ

b]

p(γ,2πo)p 3γ detected

p(γ,2πo)p 4γ detected

d(γ,2πo)np 3γ detected

d(γ,2πo)np 4γ detected

photon energy [MeV]

0

5

10

15

400 500 600 700 800

σ [µ

b]

0

1

2

500 600 700Eγ[MeV]

σ n/σ p

photon energy [MeV]Fig. 13. Left hand side: total cross sections of d( ; 2o)np (lled symbols) and p( ; 2o)p.Right hand side: estimate for the total cross section of n( ; 2o)n (black dots, hatchedarea indicates uncertainty). Dashed and dash-dotted lines: predictions from [25] and [27].Czech. J. Phys. 49 (1999) A 15

Page 16: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Kruschethe proton bound in the deuteron demonstrated that nuclear eects are practi-cally negligible for this reaction [31]. It is therefore reasonable to assume that then( ; o)p- and n( ; oo)n-reactions can be studied via quasifree photoproduc-tion from the deuteron. The o nal state was investigated with the DAPHNE-detector [31, 32], the 2o-channel with the TAPS-detector. The total cross sectionfor 2o production from the deuteron and the extracted neutron cross section [2]are shown in gure 13. The neutron cross section was estimated in a participant -spectator approach. The cross section of p( ; 2o)p and an ansatz for (n( ; 2o)n)were folded with the momentum distribution of the bound nucleons. The ansatzwas varied until the d( ; 2o)np cross section was reproduced. In the meantime datawith much improved statistical quality have been measured which for the rst timeallow the construction of Dalitzplots for this channel [45]. It will be very interest-ing to compare the invariant mass distributions of the pion pair to those from theo channel. The latter show a deviation from phase space that was attributedto a contribution of the -meson [32] which must be absent in the 2o-channel.4 Baryon resonances in nuclear matterThe study of meson photoproduction from atomic nuclei is motivated by twostrongly interconnected aspects namely possible medium modications of baryonresonances and the meson-nucleus interaction. In-medium eects for nucleon reso-nances and mesons can arise from a number of dierent aspects including rathertrivial ones like broadening of excitation functions due to nuclear Fermi motion andvery exciting ones like meson mass modications due to chiral restoration eects: resonance excitation smearing of excitation functions due to nuclear Fermi motion many body absorption processes like NN ! NR resonance damping by dynamic eects (e.g. quark exchange betweennucleons) resonance decays narrowing of resonance widths due to Pauli-blocking of nal states forR! N;N broadening of resonance widths due to additional decay channels likeRN ! NN (collisional broadening) medium modications of meson masses (e.g. lowering of the -mass willincrease the widths of resonances decaying into N) nal state interaction eects absorption of mesons propagation of mesons (and resonances)16 A Czech. J. Phys. 49 (1999)

Page 17: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :Important experimental tools for the study of this eects are: total photoabsorption incoherent (breakup) meson photoproduction coherent meson photoproductionPhotoproduction reactions have the advantage that in contrast to hadron inducedreactions due to the small interaction cross section the complete nuclear volumeis tested. Total photoabsorption measurements are free of FSI eects but are veryunspecic since no nal state and therefore no particular resonances are selected.Coherent photoproduction reactions have the advantage of a rather simple theoret-ical treatment since the nucleus remains in its ground state. On the other hand itis quite dicult experimentally to identify the coherent process. So far this is onlyaccomplished for o-photoproduction in the -resonance region. Breakup mesonproduction reactions are therefore the method of choice in the second resonanceregion.4.1 The (1232)-resonanceCoherent o-photoproduction in the -resonance region is of particular interestas a tool for the study of the -nucleus potential and for possible in-mediummodications of the (1232). The TAPS-results for coherent o-photoproduction

10-1

1

10

0 100 200 300

dσ* /d

Ω/A

[µb/

sr]

Pb(γ,πo)Pb

momentum transfer q [MeV]Fig. 14. Preliminary dierential cross section for the reaction Pb! oPb as function ofthe momentum transfer averaged over incident photon energies from 200 - 250 MeV.from 4He have been published very recently [46]. They have been analysed in theframework of DWIA calculations including an appropriate parametrization of the-nuclear interaction [47]. In this way for the rst time the energy dependence ofCzech. J. Phys. 49 (1999) A 17

Page 18: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Kruschethe -nucleus potential could be determined. There are rst indications that theA-dependence of the potential saturates already for 4He. A much more detailedinvestigation of this questions will be possible when the data from heavier nucleiare included in the analysis. Data have been taken for carbon, calcium, niobiumand lead nuclei. The analysis of this experiments is in the nal stage. As an examplefor the quality of the data the preliminary dierential cross section for coherent o-photoproduction from lead at incident photon energies between 200 and 250 MeVis shown in gure 14.4.2 The second resonance regionA few years ago it came as a complete surprise when measurements of the totalphotoabsorption cross section from nuclei [19, 21, 20] showed an almost completedepletion of the resonance bump in the second resonance region. Dierent expla-nations have been invoked to account for this experimental nding ranging fromtrivial Fermi smearing eects to resonance damping due to quark exchange eects.4.2.1 -photoproductionTotal photoabsorption has the advantage that no nal state interaction eectsmust be accounted for but on the other hand many dierent reaction channels do0

25

50

75

600 800

0

25

50

75

σ η [µ

b]

0

50

100

150

600 800

0

50

100

15012C 40Ca

0

100

200

600 800

σ η [µ

b]

Eγ [MeV]

0

200

400

600 800

Eγ [MeV]

93Nb natPb

Fig. 15. Total cross section for -photoproduction from nuclei. The solid lines are theresults from a BUU-model calculation [48], the dashed curves the results of an -meanfree path Monte Carlo model [49].18 A Czech. J. Phys. 49 (1999)

Page 19: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :contribute and not all of them are related to resonance excitation. It is therefore de-sirable to investigate the resonances in this region with selective reactions. The mostselective one is certainly -photoproduction as probe for the S11(1535)-resonance.A detailed investigation of this reaction from light to heavy nuclei [50] foundno unexplained depletion of the in-medium strengths. The measured cross sections(see gure 15) were very well reproduced by dierent models taking into accountthe trivial eects like Fermi smearing, collisional broadening and Pauli-blocking.This was somewhat surprising in view of the results from total photoabsorptionthat could not be explained by such eects.4.2.2 Inclusive o-photoproductionIn the meantime we have extended this work to inclusive o-photoproductionfrom nuclei which is more sensitive to the D13(1520)-resonance since the S11-resonance plays only a minor role. Inclusive o-production means that all eventswith at least one neutral pion in the nal state are accepted and the detectionprobability of the observed pion is used for an event-by-event eciency correction.Events with more than one neutral pion are counted with the approriate multiplic-ity. The total inclusive cross section therefore represents the cross section sum ofall possible channels wheighted with their individual neutral pion multiplicities.

1

1.5

2

2.5

100 200 300 400 500 600

(σ/A

2/3 )/

(σ(12

C)/

12.2/

3 )

40Ca(γ,πo)X93Nb(γ,πo)XnatPb(γ,πo)X

pion lab momentum [MeV]Fig. 16. Preliminary total cross sections for the reactions A ! oX forA = 40Ca;93Nb;nat Pb scaled by A2=3 and normalized to carbon.Preliminary results are shown in gures 17 and 16. The mass number dependenceof the cross section indicates the expected strong FSI eects. This is demonstratedin gure 16. The cross sections scale almost perfectly like A2=3 for momenta largerCzech. J. Phys. 49 (1999) A 19

Page 20: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Kruschethan 200 MeV, indicating that only pions from the nuclear surface regions areobserved. The excitation probability of the (1232) resonance via pion absorptiondecreases at smaller pion momenta where the nuclei become more transparent forpions.The excitation functions for inclusive o-photoproduction are shown in gure 17.In comparison to the deuteron the second resonance bump is much less pronounced0

50

100

150

200

250

σ/A

[µb]

d(γ,πo)X

0

20

40

60

80

100

120

12C(γ,πo)X

0

20

40

60

80

200 400 600 800

40Ca(γ,πo)X

0

10

20

30

40

50

200 400 600 800

Pb(γ,πo)X

photon energy [MeV]Fig. 17. Preliminary total cross sections for inclusive o-photoproduction scaled to themass number. The three curves for the heavy nuclei correspond to the BUU-calculation ofEenberger et al. [51, 52]. Standard BUU: dotted; -absorptive part from -hole model:dashed; additional medium modication of D13 (300 MeV collisional width): dash-dotted.for heavy nuclei. Predictions in the framework of the standard BUU-model [51,52], which described the -production data very well, are not in agreement withthe pion data. In particular the cross section in the second resonance region isstrongly overestimated. A more carefull treatment of the -excitation using the-absorptive part from -hole models improves the situation in the -resonanceregion. The remaining discrepancy at this energies is attributed to multiple particleabsorption processes like NN ! N, which are not included in the model.Reasonable agreement in the second resonance region is only obtained whenadditional medium eects are considered. The authors discuss e.g. the possibility20 A Czech. J. Phys. 49 (1999)

Page 21: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :of a modied decay width of the D13(1520) resonance into the N-channel causedby a medium modication of the -spectral function due to the coupling of the-meson to D13-hole-states. However, the net eect is small since on one hand sidethe primary absorption cross section is lowered due to the broadening of the D13but on the other side the decay branching of the D13 into the double pion channel isincreased. The data in the second resonance region are reproduced in the model ifan ad hoc collisional broadening of the D13-resonance of 300 MeV is introduced.However, such a large broadening is probably not realistic.4.2.3 Double o-photoproductionFrom the subset of data with more than two detected photons cross sections for2o-photoproduction from nuclei were derived (see gure 18). So far only resultsbelow the -production threshold were obtained because the statistical quality ofthe data was not good enough to separate the background originating from !3o-decays. Double o-production is of special interest since the results for the0

1

2 12C

σ/A

[µb]

40Ca

0

0.5

200 300 400 500

93Nb

200 300 400 500 600

natPb

Eγ[MeV]Fig. 18. Preliminary results for the total cross section of double o-photoproduction fromnuclei normalized to the mass number. The open symbols are obtained from events withtwo identied o-mesons, the full points from events with one pion and at least one furtherphoton. The latter are practically background free only below the -production threshold.The curves show the prediction from [48].elementary cross section from the proton have borne out the important contributionfrom the sequential D13(1520)-decays. A comparison of the preliminary results tomodel predictions seems to indicate an even stronger overestimation of the dataCzech. J. Phys. 49 (1999) A 21

Page 22: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd Kruschethan in case of inclusive o-photoproduction. The situation is not much improved byan introduction of in-medium eects like collisional broadening of the D13 [51, 52].Due to the large absorption probability of the pions, reactions with two pions in thenal state originate almost exclusively at the surface of the nuclei where in-mediumeects are less eective. The situation for this channel is completely open. New datawith much better statistical quality taken with TAPS at MAMI in 1999 will allowa much more detailed investigation of this reaction also above the -threshold.Apart from the investigation of the second resonance region this experiments willalso provide data for a detailed investigation of the pion - pion interaction in thenuclear medium. It was recently predicted by Rapp et al. [53] that a medium modi-ed scalar-isoscalar pion - pion interaction should lead to a signicant enhancementof the cross section close to the double pion production threshold. Such eects areof relevance for the behavior of the in-medium chiral condensate and are hotly de-bated. Very recently Aouissat et al. [54] have argued that a reduction of the sigmameson mass caused by partial restoration of chiral symmetry in nuclear matter willlead to an even stronger enhancement of the -strength in the I = J = 0 channel.5 OutlookThe photoproduction of mesons is certainly a very powerful tool for the studyof nucleon resonances on the free and bound nucleon. In the near future, bothstrategies, the search for the missing resonances as well as the detailed investigationof low lying resonances oer many yet unexplored possibilities.In case of the low lying resonances polarization degrees of freedom will becomemore important as already demonstrated for -photoproduction. In particular thestudy of resonances that contribute only weakly like e.g. the P11(1440) state canprot from more complete experiments.A more detailed study of the electromagnetic properties of resonances will be at-tempted via decay chains like R! (1233)! No or R! S11(1535)! N resulting in o or nal states. For some resonances, in particular the (1232),it may even be possible to study e.g. the magnetic moment via the realingmenttransition ! which is possible due to the large width of the resonance. Asa rst step in this direction the recent TAPS experiments measuring double o-photoproduction have for the rst time clearly identied the o nal state in the-region.The search for the missing resonances will not only prot from the higher incidentphoton energies now available at Jlab and at ELSA. According to quark modelpredictions many of the 'missing' resonances couple only weakly to the N -channel.It is therefore very important to look for these states in all possible nal states likeN, N!, N, N0 and even in more complicated cascade decays like , . Firstencouraging results were already reported for the 0N -channel [55].The TAPS-detector will participate in this program at the ELSA accelerator inBonn. It is planned to operate TAPS in conjunction with the Crystal Barrel (CB)detector which was already moved from CERN to Bonn. The CsI-modules of theCB-detector will cover the largest part of the solid angle while the fast counting22 A Czech. J. Phys. 49 (1999)

Page 23: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :TAPS-modules will be used in the forward angular range.The planned setup is shown in gure 19. The experimental program at ELSA willcenter around the more complicated nal states involving high photon multiplicities.As discussed above nal states like oo, o , o are of high interest. Furthermorethis program is the ideal complement to the experiments carried out with the CLAS-detector at Jlab which has only very limited photon detection capabilities but allowsvery detailed studies of reaction channels with not more than one neutral particle.30˚

Fig. 19. Planned combined setup of the TAPS detector and the CB-detector. The TAPS-detector is congured as forward wall covering angles up to 30o.Acknowledgement: I gratefully acknowledge the contributions of all membersof the TAPS/A2-collaborations who participated in the experiments. This workwas supported by the DFG (SFB 201).Czech. J. Phys. 49 (1999) A 23

Page 24: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Bernd KruscheReferences[1] M. Fuchs et al., Phys. Lett., B368:20, 1996.[2] B. Krusche et al., Eur. Phys. J., A6:309, 1999.[3] R. Arndt et al. VPI and SU Scattering Analysis Interactive Dialin.[4] R. Beck et al., Phys. Rev. Lett., 78:606, 1997.[5] G. Blanpied et al., Phys. Rev. Lett., 79:4337, 1997.[6] R. Beck et al., Phys. Rev., C61:35204, 2000.[7] B. Krusche et al., Phys. Rev. Lett., 74:3736, 1995.[8] B. Krusche et al., Phys. Lett., B397:171, 1997.[9] L.Y. Glozman and D.O. Riska. Phys. Lett., B366:305, 1996.[10] N. Kaiser, P.B. Siegel, and W. Weise. Phys. Lett., B362:23, 1995.[11] N. Kaiser, T. Waas, and W. Weise. Nucl. Phys., A612:297, 1997.[12] R. Bijker, F. Iachello, and A. Leviatan. Phys. Rev., D55:2862, 1997.[13] V. Burkert. Proc. of the Exciterd Baryons 1988, edts. G. Adams, N.C. Mukhopadhyayand P. Stoler, World Scientic 1988, 1988.[14] A. Bock et al., Phys. Rev. Lett., 81:534, 1998.[15] J. Ajaka et al., Phys. Rev. Lett., 81:1797, 1998.[16] N.C. Mukhopadhyay and N. Mathur. Phys. Lett., B444:7, 1998.[17] L. Tiator, D. Drechsel, G. Knochlein, and C. Bennhold. Phys. Rev., C60:35210, 1999.[18] G. Knochlein, D. Drechsel, and L. Tiator. Z. Phys., A352:327, 1995.[19] Th. Frommhold et al., Phys. Lett., B295:28, 1992.[20] Th. Frommhold et al., Z. Phys., A350:249, 1994.[21] N. Bianchi et al., Phys. Lett., B299:219, 1993.[22] M.M. Giannini and E. Santopinto. Phys. Rev., C49:R1258, 1994.[23] D. Luke and P. Soding. Springer Tracts in Modern Physics, 59:39, 1971.[24] A. Braghieri et al., Phys. Lett., B363:46, 1995.[25] J.A. Gomez Tejedor and E. Oset. Nucl. Phys., A600:413, 1996.[26] L.Y. Murphy and J.M. Laget. DAPHNIA/SPhN, 96-10:1, 1996.[27] K. Ochi, M. Hirata, and T. Takaki. Phys. Rev., C56:1472, 1997.[28] F. Harter et al., Phys. Lett., B401:229, 1997.[29] M. Wolf. PhD thesis, Giessen University, publication in preparation, 1999.[30] W. Langgartner. Diploma thesis, Giessen University, publication in prep., 1999.[31] A. Zabrodin et al., Phys. Rev., C55:R1617, 1997.[32] A. Zabrodin et al., Phys. Rev., C60:5201, 1999.[33] J.M. Laget. Phys. Rep., 69:1, 1981.[34] P. Bosted and J.M. Laget. Nucl. Phys., A296:413, 1978.24 A Czech. J. Phys. 49 (1999)

Page 25: on - jazz.physik.unibas.ch filePhoto excitation of Bary on Resonances Bernd Kr

Baryon Resonances : : :[35] F. Blaazer, B.L.G. Bakker, and H.J. Boersma. Nucl. Phys., A590:750, 1995.[36] S.S. Kamalov, L. Tiator, and C. Bennhold. Phys. Rev., C55:98, 1997.[37] P. Wilhelm and H. Arenhovel. Nucl. Phys., A593:435, 1995.[38] R. Schmidt, H. Arenhovel, and P. Wilhelm. Z. Phys., A355:421, 1996.[39] M.I. Levchuk, V.A. Petrun'kin, and M. Schumacher. Z. Phys., A355:317, 1996.[40] B. Krusche et al., Phys. Lett., B358:40, 1995.[41] M. Lacombe et al. Phys. Lett., B101:139, 1981.[42] K.H. Altho et al. Z. Phys., C1:327, 1979.[43] P. Homan-Rothe et al., Phys. Rev. Lett., 78:4697, 1997.[44] V. Hejny et al., Eur. Phys. J., A6:83, 1999.[45] V. Kleber. diploma thesis, Giessen University, publication in preparation, 1999.[46] F. Rambo et al., Nucl. Phys., A660:69, 1999.[47] D. Drechsel et al., Nucl. Phys., A660:423, 1999.[48] M. Eenberger, A. Hombach, S. Teis, and U. Mosel. Nucl. Phys., A614:501, 1997.[49] R.C. Carrasco. Phys. Rev., C48:2333, 1993.[50] M. Robig-Landau et al., Phys. Lett., B373:45, 1996.[51] M. Eenberger. PhD thesis, Giessen University, 1999.[52] J. Lehr, M. Eenberger, and U. Mosel. Nucl. Phys., A:in press, 2000.[53] R. Rapp et al., Phys. Rev., C59:R1237, 1999.[54] Z. Aouissat et al., Phys. Rev., C61:R12202, 2000.[55] R. Plotzke et al. Phys. Lett., B444:555, 1998.

Czech. J. Phys. 49 (1999) A 25