+ All Categories
Home > Documents > FIRAS (479)

FIRAS (479)

Date post: 25-Feb-2018
Upload: soran-kahtan
View: 239 times
Download: 0 times
Share this document with a friend

of 26

  • 7/25/2019 FIRAS (479)



    Progress inParticle and

    Nuclear PhysicsProgress in Particle and Nuclear Physics 44 (2000) 3-28


    Electron Scattering and Nuclear Structure at the S DALINAC


    Institut fiir Kerphysik, Technische Universitiit Darmstadt,Schlossgartenstrasse 9, D-64289 Darmstadt, Germany


    Results on ongoing research of elementary electric and magnetic nuclear excitations at the supercon-ducting Darmstadt electron linear accelerator (S-DALINAC) are presented. In the first part of thislecture electric excitation modes in the continuum are discussed by way of two examples employingthe coincident detection of inelastically scattered electrons in an (e,ex) reaction. The first example isthe reaction *sC ( e,en) where the excitation and decay of isoscalar electric monopole and quadrupolegiant resonances has been studied. The results on the strength distribution and the partial exhaustionof energy weighted sum rules are compared to those from RPA and second-RPA (SRPA) predictionsas well as to those from hadronic reactions of the type (p,p) and (p,pn). The second example, a

    discussion of the BZr(e,ep) reaction and its results, can be viewed as a direct proof that in coincidencereactions of the form (e,ex) one is able to isolate and identify narrow weakly excited levels - hereisobaric analog resonances - buried in the continuum and determine their excitation and decay prop-erties and thus subtle nuclear structure properties. The second part of the lecture is concerned withhigh-resolution inelastic electron scattering under 180 which is selective with respect to magneticexcitations. Of those, first systematic studies on the hitherto scarcely explored magnetic quadrupolegiant resonance which is mainly a spin-isospin excitation are presented. As an example, results for*Ca and Zr, in which a strongly fragmented and quenched A42 strength has been detected, arecompared to SRPA and sum rules approaches. Evidence is presented for a new excitation mode, theso called nuclear twist mode, and its parameters are determined. In the third part of the lecture, thepossible use of transverse electron scattering form factors at low momentum transfer for an advc,catctitest of in-medium modifications of vector mesons is critically examined, and finally an outlook is givenon the nuclear physics research program at the S-DALINAC.


    EO, El, E2 excitations in the continuum; electric giant resonances; excitation and decay properties;strength distributions and sum rules; nuclear many-body calculations; M2 giant resonances; frag-mentation and quenching of strength; sum rules; nuclear twist mode; transverse form factors and

    in-medium modifications of vector mesons.Work supported by the DFG under contract number Fti 12/242 Z.

    0146~6410/00/$ - see front matter 0 2000 Published by Elsevier Science BV All rights reserved.PII: SOl46-6410(00)00053-3

  • 7/25/2019 FIRAS (479)


    4 A. Richt er / Pro g. Part . N ucl. Phy s. 44 2000) 3-28


    @ Radiation Physics and(y,y) - Experiments

    @ Free-Electron-Laser

    @ Radiation Physics andPolarizability of the Nucleon

    @ (e,e) at 180 and(e,ex) -Experiments

    @ (e,e) - Experiments

    @ Optics Lab

    Figure 1: Schematic layout of the S-DALINAC an I s experimental stations denoted by 0 throught

    @ in the accelerator and the experimental hall, respectively.

    The topics of this lecture are central ones in the research program of the superconducting Darmstadtelectron linear accelerator (S-DALINAC). Th is accelerator [l] provides continous wave (cw) electronbeams of very high quality between energies E. = 2.5 MeV and (presently) 120 MeV. As indicatedon the floor plan (Fig. 1) of the accelerator and experimental hall, respectively, those beams are

    used for experiments in radiation physics and photon scattering right behind the 10 MeV injectoron position @ Some of the most recent results in the field of nuclear resonance fluorescence arediscussed in the contribution of A. Zilges to these Proceedings. On position @ a recently installedFree-Electron-Laser [2] provides tunable infrared light of wave lengths between 2.5 pm and 10 pmfor experiments in the optics laboratory @ . Experiments on radiation physics at high electronenergies and in the near future - as pointed out in the outlook (Sect. 5) of this lecture on thenucleon polarizabilities - are performed in the experimental hall at position @ . The place forinclusive electron scattering under 180 and exclusive electron scattering experiments of the (e,ex)type is at beam position @ where a large solid angle QCLAM magnetic spectrometer serves as awork horse for these experiments. In fact, in this lecture I will discuss solely electron scatteringexperiments performed at @ and their implications for nuclear structure. Finally, we have also

    recently refurbished our high-resolution electron scattering spectrometer at position @ which wasessential for the discovery of the so called Scissors Mode fifteen years ago at the DALINAC [3]. It isvery exciting that this mode, which in its general properties is now phenomenologically understood [4]and which I have discussed extensively in the last Erice school on the same topic [5] as the presentone is now after a prediction entirely modeled in the spirit of nuclear physics [S] seen also in BoseEinstein condensates [7].

    The lecture is composed of these main parts. Firstly, I will remark on the nature and our presentknowledge of some salient features of electric excitation modes in the continuum. I will illustrate thistopic by way of discussing in some detail two examples: The experimental search for electric monopoleand quadrupole strength in 4sCa with the help of the 4sCa(e,en) reaction and the excitation and decay

    of sharp isobaric analog resonances in the continuum of Zr studied through the Zr(e,ep) reaction.Secondly, I will present the determination of the magnetic quadrupole response, again in 4sCa andZr, and discuss it in the light of extensive model predictions and sum rules. Thirdly, I will try toanswer the question, if - as advocated in the literature - transverse electron scattering form factors

  • 7/25/2019 FIRAS (479)


    A. Richter / Prog. Parr. Nucl. Phys. 44 (2000) 3-28 5

    at low momentum transfer are really suited as a possible test of in-medium modifications of vector

    mesons. Finally, I will give an outlook of our research program at the S-DALINAC.

    Considering the wealth of material presented in the actual lecture, the rather limited space allowrd

    for its written version in these Proceedings forces me to restrict myself essentially only to a summary

    of the various topics I did present and discuss orally. I have tried, however, to give a fairly completelist of references at the end. Nevertheless, I hope that having been asked to present the first lecture

    in the course on Electromagnetic Probes and the Strucure of Hadrons and Nuclei to set the proper

    tone for this topic.


    2.1. First example: electric giant resonances in 4sCa

    Giant multipole resonances are fundamental manifestations of collective behaviour in the atomic nu-

    cleus. Despite considerable experimental and theoretical research on these elementary modes ourunderstanding is still limited [8, 91. While compact strength is found for the lowest multipolarities

    in heavy nuclei and the systematics of their energy dependence are reasonably established. the com-

    plex strength distributions observed in light and medium-mass nuclei represent a challenge even to

    the most advanced theories. Since the giant multipole strengths typically lie in the continuum, i.e.

    above particle thresholds, the dominant relaxation mechanism is another subject of high interest. A

    competition between direct particle emission from the initial particle-hole excitations and mixing into

    a dense background of complex multiparticle-multihole states is expected, but the quantitative role

    of both processes is not clear.

    The most developed microscopic models are based on extensions of the RPA which works best at

    shell closures [8]. Accordingly, data in (semi) magic nuclei form cornerstones for a test of our presentunderstanding. In view of this importance, the almost complete lack of experimental information

    on giant resonances in the doubly closed-shell nucleus 4sCa comes as a surprise. As an example. I

    report here a study of the isovector giant dipole (GDR) and the isoscalar giant monopole (GMR)

    and quadrupole (GQR) modes in 48Ca using coincident electron scattering. This method combines

    two favorable aspects for nuclear structure studies. Effects of the well-understood electromagnetic

    interaction can be separated from the genuine nuclear structure information unlike in the case of

    hadronic probes with their complicated reaction mechanisms. Furthermore, the coincidence condition

    removes the radiative tail from elastic scattering, thereby providing a nearly background-free response.

    Reactions of the type (e,ex) thus provide a versatile and precise method for the study of giant reso-

    nances. So far, experiments have mainly concentrated on charged particle emission which dominatesin lighter nuclei [lo-171. The coincident detection of neutrons in the hostile radiation environment of

    an electron accelerator represents a considerable experimental task, and so far only a few exploratory

    investigations have been performed [18-211. The present results on 4sCa have been obtained with a

    new setup for (e,en) reactions developed at the S-DALINAC [22, 23).

    The expected excitation and decay properties in 4*Ca are sketched schematically in Fig. 2. Electron

    scattering populates the broad, overlapping GMR, GDR and GQR, in a typical energy region of about

    10 - 25 MeV. The neutron threshold is lowest in energy (E, = 9.98 MeV) and dominates continuum

    emission in the giant resonance excitation region into low-lying states of 47Ca. Above 17 2 MeV 2n

    emission becomes energetically possible, and the concidence measurements must be corrected for this.

    The GDR is split into T< = To = 4 and T, = To + 1 isospin parts. The latter decays preferentiallyvia proton emission into 47K.

    The power of the (e,en) reaction is demonstrated in Fig. 3 which compares an inclusive 48Ca(e,e)

    measurement (upper part) with the exclusive data (lower part) for identical kinematics. A suppression

  • 7/25/2019 FIRAS (479)


    6 A. Richt er / Prog. Part . N ucl . Phy s. 44 2000) 3-28

    T = 912

    - 20

    T=3- 15

    a+ 2n =B

    - 10T = 712

    47Ca +

    - 5

    L 0

    @.W AT=O.l(P@l AT=0



    T i: 912


    Figure 2: Excitation and decay modes in electron and proton scattering coincidence experiments inthe giant resonance region (& 2 10 - 25 MeV).

    of the radiative background by almost two orders of magnitude is visible, permitting a clean extractionof the highly fragmented cross section in the giant resonance region.

    10J I I I I I I

    - I 48Ca( e,e)

    E, WV)Figure 3: Comparison of the inclusive (e,e) and the exclusive (e,en) reaction on sC a for identicalkinematics.

    Data were taken at four momentum transfers in the range q = 0.22 - 0.43 fm- in dominantlylongitudinal kinematics. The large solid angle QCLAM magnetic spectrometer at the S-DALINACwas used for electron detection. Decay neutrons were detected with six NE213 liquid scintillatorcounters placed at angles between 0 and 90 (one at about 180) relative to the recoil momentumaxis. Details of the detector geometry and the calibration procedure including rescattering corrections

    from the complex neutron and gamma shielding are described in [22].

    After a 4n integration (for details see (24)) th e resulting form factor summed over 4sCa excitationenergies 11 - 20 MeV is displayed in Fig. 4. The dashed and dotted lines are theoretical El and E2form factors constructed from RPA transition densities (251.

  • 7/25/2019 FIRAS (479)


    Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28

    - Sum


    lo-: E2

    . I

    0. 2 0.4

    9 (fm->

    Figure 4: Formfactor of the 4sCa(e,ern) reaction summed for E, = 11 - 20 MeV. The dashed and

    dotted lines are RPA calculations [25] f or collective El and E2 excitations, and the sohd line is a

    weighted sum of both fitted to the data.

    Assuming excitation energy independence, a decomposition into the relative cross section parts can be

    performed. At the lowest momentum transfers measured here, contributions from E2 are negligible,

    while at the highest momentum transfer El cross sections still dominate, but about 3U are due

    to other multipolarities. By extrapolation to the photon point the measured cross sections can be

    converted to transition strengths presented m Figs. 5 and 6. Note that due to the similarity ofcollective EO and E2 form factors, only the sum of both multipolarities can be determined from the


    An important measure of collective excitations are model-independent energy-weighted sum rules

    (EWSR). For the measured excitation energy range E. = 11 - 25 MeV we find an exhaustion of

    81(12)% for the GDR and 72(11)% of the GQR. The latter value represents an unknown mixture

    of monopole and quadrupole parts. At the photon point the cross section corresponds to B(E2) t(25/16x)B(EO), which can be derived exactly in plane wave formalism, but should also approximately

    hold in distorted wave calculations. Thus, assuming e.g. equal exhaustion of the GMR and GQR, the

    number given above would translate to 46(6)% of the respective EWSRs.

    The GDR in 48Ca has been measured before also in photoabsorption reactions [ZS]. The corresponding

    B(E1) strength distribution (solid squares) is compared in Fig. 5 to the present result. Although

    showing less details because of the limited resolution, the global variation is in agreement with the

    analysis of the (e,en) data.

    The difference in absolute magnitude is still within the systematic uncertainties of both experiments

    The summed monopole and quadrupole strengths displayed in the lower part of Fig. 6 exhibits an

    almost flat distribution from the onset around 12 MeV to the highest energy studied in the present

    experiment. Evidence for similar highly fragmented EO and E2 strength distributions has also beenfound in the doubly magic nucleus 40Ca (151, see upper part of Fig. 6.

    In contrast to the experimental results, RPA calculations predict a compact ISGMR and ISGQR at

    excitation energies of about 18 MeV (see e.g. (27, 281). F or an understanding of the experimental

    observations one has to invoke the coupling to more complex degrees of freedom. One quite successfulapproach based on Green function methods allows for the inclusion of particle-hole (p-h) configuratinns

  • 7/25/2019 FIRAS (479)


    A. Ri chter / Prog. Part . N ucl. Phys. 44 (2000) 3-28

    0.016 20 24

    Excitation Energy MeV)

    Figure 5: Experimental B El) strength distribution derived from the formfactor analysis (histogram).

    Full circles are data from a photonuclear experiment [ZS]. Th e solid line represents a continuum RPAcalculation including lplh@phonon configurations and ground state correlations induced by these

    configurations [29].

    , I I I

    I I I I

    12 16 20 24

    Excitation Energy MeV)

    Figure 6: Comparison of the experimental summed B E0) and B(E2) strength distribution inferredfrom electron coincidence experiments with a continuum RPA calculation including lplh@phononconfigurations and ground state correlations induced by these configurations (solid lines) for 40Ca

    [15, 311 and 4sCa [23, 291.

  • 7/25/2019 FIRAS (479)


    A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28 9

    coupled to low-lying collective vibrations, which is known to be a dominant mechanism for the dampingof giant resonances, and the g.s. correlations induced by them [29]. Within this model, experimentalfindings of significant EO and E2 strengths e.g. in 40Ca at excitation energies well below the mainRPA peak expected around 18 MeV [15, 301 could be traced back to the additional g.s. correlations[31]. Application of this model to giant resonances in 4sCa has been reported in [29]. The predictedB(E1) distribution is included as solid line in Fig. 5. Except for an overall shift of about 1 MeVtowards higher energies good agreement is found for the overall shape and the absolute magnitude.

    Model results of [29] for the (E2+EO) strength in 4*C a are shown as solid lines in the lower part ofFig. 6. The strong fragmentation and the dominance of strength in the interval E v 13 - 18 MeV aresatisfactorily reproduced. The calculations indicate about equal contributions of EO and E2 strengthwith local maxima shifted relative to each other, thereby leading to a rather leveled-out distribution.However, the absolute magnitude is overpredicted by a factor of two. Such a large discrepancy is hardto understand in the light of the almost perfect description of the analogous strength distribution in40Ca deduced from (e,ex) experiments (311. Wh en comparing the strengths in the energy intervalE = 11 - 20 MeV covered in both nuclei a somewhat smaller value S(E2) = 63(g)% EWSR is foundin 4sCa than S(E2) = 76(16)% EWSR observed in 40Ca but the difference is too small to explainthe discrepancy with respect to the model results. On the other hand, it may be in parts be due tothe large amount of EO strength predicted at excitation energies below E = 16 MeV which was notpresent in earlier calculations using the same model [32]. It would be desirable to repeat the multipoledecomposition using transition densities of [29] m order to be more consistent. Alternatively, we arepresently (in collaboration with J. Wambach) developing a model description within the second-RPA(SRPA) approach [33].

    As pointed out in the introductory remarks to this section, understanding the role of direct andstatistical contributions to the decay represents a central question of giant resonance research. Here,electro-induced coincidence experiments provide unique possibilities. The experiment is kinematicallycomplete, so one can reconstruct the excitation spectrum of the residual nucleus 47Ca populated inthe 4sCa(e,en) reaction. Since El cross sections dominate in the investigated momentum transferrange, we choose as an example in Fig. 7 the lowest q value measured where contributions from othermultipoles can be neglected.


    11 /z 24, , 1d3;2i


    II e = 4000 MN

    E:= 11- 17 MaV

    J f ; : ,


    0 2 4 6

    Excitation Energy in Co (t&N)

    Figure 7: Population of states in the residual nucleus 47Ca through the 4sCa(e,en) reaction for kine-matics favoring excitation of the GDR. The dotted areas correspond to a statistical model predictionsnormalized not to overshoot the data.

    Excitation of the g.s. and well-known low-lying levels of 47Ca can be clearly identified in Fig. 7. Theshaded area displays the prediction of statistical model calculations with the code CASCADE modifiedto take isospin properly into account. The calculation is normalized not to overshoot the data. At

  • 7/25/2019 FIRAS (479)


    10 A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28

    higher 47Ca energies good agreement is found, but the experimental population of the g.s. and a groupof 1/2+ and 3/2+ levels at about 2.6 MeV strongly exceeds the statistical expectations. Their wavefunctions exhibit a rather pure single-hole character with respect to the neutron-closed shell in 4sCa[34]. A check of the accuracy of the statistical model results is provided by the good description of thedecay to the first excited state in 47Ca at 2.014 MeV with J = 3/2- which has a more complicatedstructure with large (lp-2h) components [35]. The excess population of single-hole states in 47Ca istherefore interpreted as the signature of direct decay contributions. It corresponds to 39(5)% of thetotal El strength in 4*Ca This fraction is found to be independent of excitation energy within theexperimental uncertainties. Large decay contributions of the IVGDR resonance were also observed in40Ca [15] and generally in &shell nuclei 136). The present results indicate an extension of this featureinto the fp-shell (see also (371).

    Finally, it is instructive to combine and complement the (e,ex) studies discussed here with hadroninduced reactions. Giant resonances in the nuclei 40*4sCa have been studied in proton induced coinci-dence experiments at the NAC, Faure, South Africa in collaboration with groups from Johannesburg,Cape Town and Stellenbosch [38-401. Figure 8 compares the 48Ca excitation (1.h.s) and Ca residualnucleus spectra (r.h.s.) obtained from (e,en) and (p,pn) reactions, respectively. The excitation spec-tra differ considerably, partly due to the different momentum transfers favoring L = 1 for the formerand L = 2,3 for the latter reaction, and partly due to the different reaction mechanisms (isovectorstrength is suppressed in proton scattering). Furthermore, despite the coincidence condition a complexbackground smoothly increasing with E. is expected below the resonance cross sections in the caseof (p,p). The excitation spectra in the daughter nucleus 47Ca demonstrate that the same low-lyinglevels are populated in both experiments. Also, the branching ratios are very similar with exceptionof the decay to the 47Ca g.s. which is much stronger in proton scattering. An explanation has to awaita more detailed analysis of the statistical model predictions for the resonance decay and the role ofvarious background reactions.

    I10 15 20 25 0 2 4

    E, in Ca (t&V) E, in Co (t&V)

    Figure 8: Comparison of (e,en) and (p,pn) studies on giant resonances in 48Ca. L.h.s.: Coincidentexcitation 4sCa excitation spectra. R.h.s: Excitation spectra in the residual nucleus 47Ca.

    Recently, we have also made considerable progress in the quantitative analysis of mixed giant resonance

    strength from the angular correlations to resolved final states [39, 40). This provides e.g. importantinsight into a longstanding and still unsolved problem [41]: for the particularly simple case of the ofa decay from the GR region to the g.s. of 36Ar Initial and final state and emitted particle all have(J = O+) a discrepancy is found in the EWSR fractions of GMR and GQR deduced from electron-and a-induced reactions [16] which casts some doubt on the procedures to convert hadron scattering

  • 7/25/2019 FIRAS (479)


    A. Richter /Pmg. Part. Nucl. Phys. 44 (2000) 3-28 1

    cross sections into transition strengths. Here, 40Ca(p,pcz) results provide an independent test [39].

    Furthermore, succesful analysis of nucleon emission channels is achieved for the first time [40]. It can

    be shown that the main background component - quasifree knockout reactions - can be modeled well

    in the present experiment despite extreme kinematics for this type of reaction [42].

    2.2. Second example: Complete spectroscopy of isobaric analog resonances in Zr

    As discussed in the previous section for the example of 4sCa, (e,ex) experiments provide important

    contributions to our understanding of the excitation and decay properties of giant resonances. How-

    ever, it has also been advocated that such coincidence experiments should be able to isolate and

    identify narrow, weak levels buried in the continuum and allow to determine their decay properties

    which reveal subtle nuclear structure information. Since one can selectively excite different multipoles

    by varying the momentum transfer it has been emphasized that electroexcitation provides a powerful,

    versatile probe. Here, I discuss a recent example which for the first time exploited the full potential

    of this probe to extract the structural details of a single level of long-standing interest 1431.

    Black and Tanner (441 were the first to observe a narrow resonance (I? x 70 keV) in the *Y(p,yc)

    reaction at an excitation energy of 16.28 MeV in Zr This level, sitting just above the peak of the

    giant dipole resonance (GDR) h as since been subject of numerous experimental investigations with

    (p,p) (p,~) (e,p) and (7,~) reactions (for a summary of the experimental information see [45].) The

    basic idea of the experiment is sketched in Fig. 9. There, the hatched area represents the GDR with

    isospm T< : 20 = 5, which predominantly decays by neutron emission to levels in Zr. The 16.28

    MeV state is the isobaric analog (IAR) of a level at 3.160 MeV in OY with spin-isospin quantum

    numbers J = l- and Z, = 20 + 1 = 6, respectively. Due to isospin selection rules only decay by

    proton or -y emission is expected for this Tc + 1 state.

    IAR; Jn=l -; To + 1 GDA; To

    5/2-.-312 ~

    g/2+-T,, + l/2


    To _ 112

    ssZr + n

    sev+p uJn = O+; T,


    Figure 9: Excitation of J; T = 1~ ; To + 1 IAR in Zr and relevant low-lying hole states in the protondecay to Y The hatched area indicates the underlying T = To GDR which preferentially decays via

    neutron emission to sZr.

    So far, one component of this level was deduced [44] to be a vr2d3,2 article configuration coupled to theY ground state wave function, while the parent state itself carries only a small spectroscopic strength

    5 = 0.18 for the analog 2ds,s neutron configuration [46]. 0 ur experiment aimed at discernmg the full

    structure of the J; T, = l-; 6 IAR at E, = 16.28 MeV by measuring the proton decay channels of it

    following electroexcitation in the Zr(e,ep) reactio n One expects a population of low-lying levels In

    Y with dominant hole structure (2pi,s, lgs/z, 2ps/s, lfs,s)-i.

    Measurements were performed at effective momentum transfers qeff = 0.277 fm- and 0.445 fm

    for incident electron energies and scattering angles E, (0,) = 85 MeV (40) and 102 MeV (55),

    respectively. The reasons for the specifice choice of these kinematical settings will become clear in

  • 7/25/2019 FIRAS (479)


    12 A. Richter / Prog. Par . Nucl. Phys. 44 (2000) 3-28

    the discussion below. A set of eight AE-E detector telescopes was used to measure the protons. Thedynamic range of the detector telescopes allowed us to study the 12 - 18.5 MeV excitation energyregion of Zr, feeding levels up to E, = 5 MeV in sQY. The 1.h.s. of Fig. 10 shows the measured crosssections in this excitation region for incident electrons of energy E. = 85 MeV. In the upper part theinclusive inelastic electron scattering spectrum is shown. Here, one only sees broad bumps due to thepredominant GDR strength on top of the radiative tail with no indication of any resolved excitation.The lower part displays the inelastic scattering spectrum gated with coincident proton emission. Thesharp resonance at 16.28 MeV clearly stands out above the GDR, and a further known J = l- IARin Zr at E. = 14.43 MeV is visible.

    Because the parent state in Y exhibits a simple particle-hole (p-h) t ructure, it is instructive to take alook at the shell-model configurations of which the IAR wave function (r.h.s. of Fig. 10) may consist.In good approximation the closed N = 50 shell leads to vanishing neutron contributions. Protonconfigurations are formed by (3si,s, 2&/z) particle and (2pi,s, 2ps,z, lfs,z) hole states. Because of the2 = 40 subshell closure the role of the lgQ/s configuration should be small. In principle, excitation ofthe 2dz.12 shell is also possible, but exluded on the basis of the analysis shown below.





    Excitation Energy in OOZr t V)Figure 10: L.h.s.: Electron scattering spectra at E, = 85 MeV and scattering angle 0. = 40. Top,Singles spectrum, where only broad bumps are seen. Bottom: Spectrum in coincidence with anemitted proton. Note the cross section scale difference. R.h.s.: Microscopic structure of J = l- IARin Zr. Allowed proton p-h transitions are indicated by arrows.

    The excitation spectrum in the final state nucleus Y related to the 16.28 MeV IAR is presented in theleft part of Fig. 11. Proton groups corresponding to the decays into the low-lying levels at E, = 0.00MeV (J = l/2-), Em = 1.51 MeV (J = 5/2-) and E, = 1.74 MeV (J = 3/2-), respectively,are visible, but no evidence for a population of the first excited state at 0.91 MeV (J = g/2-) norto higher-lying states is observed. Using a fit to two Gaussians with the width determined by theg.s. decay, the relative 5/2- and 3/2- line contents could be disentangled. The experiment furthershowed that the dependence of the GDR proton decay on the Zr excitation energy is completelygoverned by the transmission coefficients [47]. Thus, the giant resonance part underlying the IAR canbe determined from the product of the GDR cross section taken from a Lorentzian parametrization[48] times the predicted branching ratios interpolated to the 16.28 MeV region.

    Decay proton angular distributions from the IAR relative to the virtual photon direction are wellfitted by a polynomial function W(0) = Ao. [I + AZ . &(cosO)], with the same AZ coefficient foralll final states. From these angular correlation data the total cross section at the two momentumtransfers for the population of a specific level in ssY is obtained by integrating over proton angles. In

  • 7/25/2019 FIRAS (479)


    A. Richter / Pmg. Part. Nucl. Phys. 44 (2000) 3-28 13

    I,, I30 - PO pi p2 p3 E,= 85 MeV _

    1 I 11 og= 40Op= 160

    20 fi I\,,.

    10 r


    0 :I

    0 1 2 3 4

    Excitation Energy in ? (MeV)


    I I I I,, I l i

    0.2 0.3 0.4 0.5 0.6

    q.,, (fm-7

    Figure 11: L.h.s.: Example of a residual nucleus excitation spectrum in seY for the E, = 16.28 MeVregion in Zr taken at E. = 85 MeV, 0. = 40 and 0, = 160. The fits to determine the IAR decaybranching ratios are indicated. R.h.s.: Inelastic electron scattering form factor of the 16.28 MeV,J = l- level in Zr. The solid line represents the phenomenological wave function of Eq. (2) for thesign combination giving the best fit to the data. The dashed line is due to a n(2p;,is3s,,z) form factordemonstrating the strong difference for a 2d3i2 or 3si/r particle component.

    order to deduce the physical parameters of the resonance from these data, the (e,ep) cross sectionfor the excitation and subsequent decay of the resonance populating a specific level in sgY may bewritten as

    du duZi = dR Mott-1

    IWN (1)

    where (do/dR)Mott is the Mott cross section, IF(q)] th e form factor of the resonance level, Itol itstotal decay width and I?; the partial width of decay to a particular final state. Our data, correctedfor the instrumental resolution, result in a total width of the 16.28 MeV resonance riot = 80(30) keV,in good agreement with earlier results [44, 491. The measured branching ratios Ii/rtor of 65(7) ,26(6) , and 9(3) , to the g.s., second and third excited states in Y comply with the estimates of[50, 511. It should also be remarked that earlier experiments could not separately determine the 5/2-and 3/2- branchings. The partial widths can be determined from this information because we didnot observe any population to the higher levels in sgY and no branchings to isospin forbidden neutronor alpha particle decay channels have been reported in the literature [45].

    The AZ coefficient resulting from the angular correlation data agrees with theoretical estimates ford-wave proton emission. As the three final states populated in ssY are nearly pure single proton holestates, the simplest configuration of the 16.28 MeV 1 ve1 will consist of three lp-lh components withthe particle in the 2dsp shell. The 1g9,s configuration does not contribute significantly since the upperlimit for a possible branching is less than 2 (see 1.h.s of Fig. 11).

    The proton decay branching ratios deduced above and corrected for the d-wave penetrability factorsresult in the follwing wave function of the 16.28 MeV IAR

    116.28 MeV, J;T, = 1-i 6) = ]K (0.422~,,~ * 0.692p3,2 * 0.591fs,r)- 2ds,z) (2)

    relative to the Zr ground state. According to Eq. (2), 18 of the strength are due to a single protonin the 2ds/s shell coupled to the sgY ground state. This corresponds exactly to the 2ds/s neutron singleparticle strength of the parent analog state at 3.160 MeV in Y observed in stripping reactions [46].

    The phenomenological wave function of Eq. (2) can be utilized to calculate the scattering form factor inDWBA. From the four possible sign combinations in Eq. (2), one (+ + -) can immediately be excluded

  • 7/25/2019 FIRAS (479)


    4 A. Richt er / Pro g. Part . N ucl. Phys. 44 2000) 3-28

    by comparison to experiment. The other three are compatible with the data, but the case of equal signs(+ + +) shown in the right part of Fig. 11 provides a superior description. Also shown as dashed curveis the form factor for a pure rr(2p$s3a1,r) configuration. The two experimental momentum transfervalues chosen are sufficient to test the role of a 2ds/r vs. a 3ai/s particle component. Clearly, the datacan be explained without any significant 3ai/r contribution. In passing we note that the wave functions

    for the different sign combinations exhibit a very distinct behaviour at higher momentum transfers,and it may be possible to unambiguously determine the signs of the different components in Eq. (2)with a further measurement at qcff > 0.6 fm-i. Furthermore, the transition strength at the photonpoint is extracted to be B(E1,16.28)?= 7.2(2.3) x lo- * efm*, corresponding to I-r0 = 108(35) eV, ingood agreement with previous work [49-511.

    As the IAR rides on a huge continuum of the Zs states with the same spin forming the giant dipoleresonance, some isospin mixing is expected expressed usually by a spreading width IL. Systematics[52] predict l? G 15 keV in the A = 9 mass region. Its inclusion would lead to an overall reductionof about 20% of the escape widths into the proton channels according to Ptot = xi Ipi + l? whichcannot be excluded on the basis of the present experimental uncertainties. However, the form factorresults - and thus the derived g.s. decay width - would not be affected by such a correction.


    3.1. General remarks

    Magnetic spin and convection currents of the nucleus, because of their elementary nature, are subjectsof continuous experimental and theoretical interest. Magnetic dipole (Ml) transitions have been

    studied intensively with emphasis on the problem of quenching (i.e. a reduction of the transitionstrength with respect to the most advanced model predictions) of the spin part. It is now commonlyaccepted that the quenching results from a combination of coupling to configurations outside themodel spaces via the nuclear tensor force and admixtures of the delta isobar. The latter are small(see [53] for recent work).

    Much less is known about magnetic quadrupole (M2) excitations whose spin part should also be mod-ified by the mechanisms discussed above. The few available data indicate a quenching even strongerthan for the Ml strength [54]. The spin part of the M2 strength is directly related to the J = 2-component of spin-dipole excitations [55, 561 b served in hadron scattering experiments whose spindecomposition is a central goal of recent experimental efforts [57]. The amount of quenching and the

    MZ-strength distributions in ad- and fpshell nuclei are also key ingredients for a detailed modelingof the late stages of heavy stars before a supernova collapse [58, 591 and for the Y-nucleosynthesisprocess [60]. Calculations of the M2 response in nuclei have been performed in various microscopicapproaches [61-63). Although the centroid of the observed M2 strength distribution is roughly repro-duced on the RPA level taking into account one lp-lh excitations, the strong fragmentation of themode can only be described by coupling to the large number of 2p-2h states.

    There is furthermore a fundamental interest in verifying the possible existence of an orbital M2resonance in spherical nuclei. Such an excitation, predicted originally within a fluid-dynamic approachfor finite Fermi systems [64] and named twist mode, can be viewed as a rotation of different layers offluid against each other with a rotational angle proportional to the distance along the axis of rotation.

    Having no restoring force in an ideal fluid, its experimental observation would be direct proof of thezero sound character of giant resonances in nuclei which can be interpreted as vibrations of an elasticmedium, in contrast to the hydrodynamical picture 181. B ac k ward electron scattering presents themost promising tool to search for such a mode [65-671. The results discussed here aim at a solutionof some of these open questions [68].

  • 7/25/2019 FIRAS (479)


    A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28

    3.2. Examples: the magnetic quadrunole response in 4sCa and Zr


    We have chosen to study sC a and Zr as first examples of a systematic investigation of the M2spin quenching as well as to search for experimental indications of the orbital twist mode. Moderndevelopments of SRPA theories [33] provide a promising tool for a realistic description of the M2

    strength distributions in medium-mass and heavy nuclei.

    Electron scattering at 180 is particulary suited for the study of magnetic transitions because ofthe strong suppression of longitudinal excitations including the radiative tail dominated by elasticscattering. Thus, it serves as a filter for transverse excitations. Exceptional features compared tosimilar previous devices can be achieved [69] at the S-DALINAC by the coupling of the 180 system tothe large solid-angle, large momentum acceptance QCLAM spectrometer. This experimental progresspermits investigations [70] even of extremely weak excitations as demonstrated for the example ofan l-forbidden MI transition in 3s (see also the contribution of P. von Neumann-Cosel to theseProceedings).

    An important improvement over previous 180 experiments was achieved by using a 10 MHz pulsedbeam. It allows to determine the time-of-flight (TOF) of electrons with respect to the beam pulse(711, thereby permitting a distinction of electrons scattered off the target from those of backgroundsources (e.g. the Faraday cup or slit systems). With this technique the signal to background ratio inthe measured spectra could be increased by up to an order of magnitude. Compared to the limitedinformation from previous (e,e) experiments, these experimental developments allow an extraction ofthe entire M2 response over large excitation energy regions essential for an answer to the problemsraised above.

    Data were taken at incident electron energies Es = 42.4, 66.4, and 82.2 MeV corresponding to mo-mentum transfers p = 0.38, 0.62, and 0.78 fm-. The resulting spectra are displayed in Fig. 12 for the

    example of 4*Ca. Note the very low background, especially for Eo = 66 and 82 MeV. The variationwith incident energy is compabtible with an interpretation as the remnant radiative tail due to elasticscattering (the effective scattering angle is 178.5). At energies E, > 11 MeV the level density of ex-cited 2- states becomes very high leading to a considerable fragmentation of the transition strength.Thus, the unfolding procedure of the spectra as a superposition of discrete lines applied at lowerexcitation energies is no longer possible. Parts of the M2 strength might be hidden in the backgroundof the spectra.

    O - 4sCa e,e).9 = rao*if-:



    4 a a 10 12 1.4

    Excitation Energy (MeV)

    Figure 12: Upper part: Inelastic electron scattering spectra of 4aCa taken at 0 = 180 and threeincident energies Eo = 42.4, 66.4 and 82.1 MeV.

  • 7/25/2019 FIRAS (479)


    16 A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28

    A solution to this problem is provided by a fluctuation analysis technique based upon a statisticaltreatment, i.e. assuming Wigner-type level spacings and Porter-Thomas intensity distributions (fordetails see (721). To extract the total B(M2)t strength in the excitation energy region covered by theexperiment, an analysis similar to the one in Ref. [73] was performed in the intervals E, = ll- 15 MeV(48Ca) and 7 - 12 MeV (Zr). At higher energies in Zr one probably enters the regime of Ericson

    fluctuations which precludes application of the above method.

    The resulting M2 strength distribution is displayed in the top part of Fig. 13 for the example of Zr.While the centroid is reasonably reproduced, attempts to describe its complex structure by RPAcalculations (middle part) fail independent of details of the residual interaction. One has to invokethe SRPA which extends the model space to include 2p-2h excitations on the correlated ground state.Since both mean-field and collisional damping are included, the SRPA is well suited for a descriptionof the fine structure of nuclear modes [8, 741.

    9 1009d 0,, 1000E

    2 500%

    -2 09g 2000


    04 6 6 1 0 12 14

    Excitation Energy (t V)

    Figure 13: Comparison of the M2 strength distribution in Zr with results of RPA and SRPAcalculations described in the text.

    When evaluated in a basis of RPA states 1~) the strength function takes the form [33]

    SF(E) = -~lm~(Ol~tl~)G,~(E)(~'~~~O)vu

    where P denotes the operator of the perturbing field. In the case of magnetic excitations, P couplesto the current operator

    4 = g & (4V,G(r-r~)}+g~k)(VXzk)J(r-rs))

    where grk and gck) are the orbital and spin g-factors of the le-th nucleon, respectively. Taking intoaccount distortions of the electron in the static Coulomb field of the nucleus, F is then evaluatedby convoluting the current (4) with the distorted waves of the incoming and outgoing electron. TheGreens function in Eq. (3) is given by

    G,,l(E) = (E - E, - Z,,(E) + iq)-l - (E + E, + l&,(-E) - iq)-l (5)

    where E, are the RPA eigenenergies. The coupling to 2p-2h excitations results in a complex selfenergy&I z A,,, - ii r,. After diagonalization of the residual interaction, d, in the 2p2-h subspace it takes

  • 7/25/2019 FIRAS (479)


    A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28 17

    the form

    c,,(E) = ~(vllw, _ ;, + ig(w4 (6)2

    To account for finite energy resolution in the experiment, 11 n Eq. (6) is taken to be finite (typically

    20 keV).

    Details of the calculations are described in [68]. Taking into account coupling to 2p-2h excitationsin the SRPA calculation, the description is greatly improved as shown in the bottom part of Fig. 13.Except for an overall shift of about 500 keV, the features of the M2 strength in sOZr are reproducedremarkably well qualitatively as well as quantitatively.

    In order to see to what extent the present results exhaust the theoretical M2 strengths it is instructiveto plot the running sums as a function of excitation energy (1.h.s. of Fig. 14). The hatched areasindicate the experimental uncertainties dominated by the assumptions on the level densities in thefluctuation analysis. The experimental results exhaust 30% (4sCa) and 21% (sZr), respectively, of theEWSR values calculated within RPA. The short-dashed lines representing the SRPA results with free-nucleon spin g-factors account quite well for the energy dependence, but overshoot the data. Invokingan effective spin g-factor g:f = 0,64g +, simultaneous agreement is achieved for both nuclei in theinvestigated energy ranges. This quenching factor was adjusted to reproduce the Ml data in 4*Ca

    cff -75]. The good agreement with the data demonstrates that (assuming g( - g[ ) the spin quenchingof Ml and M2 strengths is very similar.

    p 200

    2 100

    >& O3 100

    %, 5:

    g 5i

    -0 4 8 12Excitation Energy (MeV) Excitation Energy (MeV)

    Figure 14: L.h.s.:Running sums of the B(M2) strengths in 4*Ca and sZr. The short-dashed and long-dashed lines are SRPA calculations with a free-nucleon and an effective spin g-factor 9: = 0.649?,respectively, which was adjusted to reproduce the Ml strength in 48Ca. R.h.s.: SRPA results for thetotal B(M2) strength distribution in Zr and the decomposition into spin and orbital parts.

    Finally, the possible evidence for an orbital M2 mode is adressed. At present, arguments can only bebased on a decomposition in the SRPA predictions. The r.h.s. of Figure 14 shows the calculated totalB( M2) distribution in eZr and its separation into spin and orbital contributions. One indeed findssignificant orbital strength. The interference pattern leads to a suppression of the total strength atlow excitation energies and an enhancement above approximately 7 MeV. Because of the comparablemagnitudes of spin and orbital strengths, the constructive interference reaches maximum values in themain bump of the M2 resonance around 9 MeV. Thus, the good agreement of the SRPA calculationswith the data (which would be completely spoiled in the absence of the orbital strength) provides a

    strong argument for the presence of the twist mode.

    A visualization of the twist mode is presented in Fig. 15. In the semiclassical prediction as a Fermiliquid 1641, the upper and lower halves of a spherical nucleus rotate against each other. The velocitydistribution of the fundamental mode displayed on the r.h.s. of Fig. 15 corresponds to a constant

  • 7/25/2019 FIRAS (479)


    18 A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28

    angular velocity. Note that orbital M2 modes at higher frequency are also predicted which representmore complicated motions with inner layers of one half rotating against out layers etc. The propertiesof the twist mode can be characterized by its total strength and the mean excitation energy (&)which is related to the nuclear shear modulus ~1 [66, 761. For Zr one finds from the present workB(M2)lt= 780 &fm, (E,) = 9.7 MeV in reasonable agreement with the original prediction 1641,B(A42)lt= 830 ,&fm, (&) = 9.0 MeV. Th e resulting shear mod& expressed in units of the nuclearmatter density p0 = 0.17 fm- are p/p0 = 6.3 MeV (48Ca),and 7.2 MeV (Zr). This corresponds to41% (48Ca) and 47% (Zr), of th e nuclear matter value of 15.34 MeV. The overall reduction and therelative differences in finite nuclei can be understood to arise from surface contributions.

    Figure 15: L.h.s.: Schematic picture of the orbital M2 twist mode predicted by [64]. R.h.s.: Angularvelocity distribution of the fundamental mode.

    Clearly, the results presented here are a starting point only. Evidence for the twist mode is indirect

    so far and a direct proof (e.g. through the different form factor dependence of spin and orbital parts)must await future experiments. For systematic tests of sum-rule predictions [77-811 it would also beof importance to establish these elementary magnetic quadrupole modes over a wide mass range, andexperiments at the S-DALINAC are underway.


    The modification of nucleons and mesons by embedding them into the nuclear medium constitutesa central problem of nuclear physics which is experimentally addressed e.g. in high-energy heavy-ion reactions and electron scattering [82, 831. A n important prediction has been made by Brown andRho [84] that the effective masses should follow an approximate scaling corresponding to the reductionof the pion coupling constant jr. This behaviour can be understood from a restauration of chiralsymmetry at high baryon densities taking into account the scaling properties of QCD (85]. Althoughit seems at first sight remote, electron scattering at low energies and momentum transfers might alsoprovide access to this problem. As an example, in-medium effects on fX and the pmeson mass leadto a reduction of the isovector tensor interaction and a simultaneous enhancement of the spin-orbitforce [86]. The necessity of such corrections has been demonstrated e.g. in studies of magnetic dipole

    transitions in light [87] and heavy [88] nuclei.

    Isovector trqnsverse electron scattering is sensitive to changes of the tensor part of the NN interaction.Therefore, form factors of magnetic transitions can be expected to be modified appreciably. Sucheffects were studied e.g. by Lallena [89] for the form factors of low-lying unnatural parity transitions

  • 7/25/2019 FIRAS (479)


    A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28 19

    in 4sCa. His calculations were carried out in the framework of RPA using the Jiilich-Stony Brookresidual interaction [90]

    v,., = Co(go CT1u2 g; u1 .u2 r1 . T) + ;K(+EVp(E) (7)The calculations allow for a simultaneous variation of mp and f,, expressed by a parameter

    where m* denotes the effective mass. For s = 1 the original interaction of [90] is attained. Thestrength parameters gs and gb of the interaction were fixed to reproduce the energies and transitionstrengths in sPb [91].

    Transitions to the low lying J = 4- and J = 2- states at E. = 6.11 MeV and 6.89 MeV, respectively,in *%a have been investigated in detail by Lallena [89]. Experimental data at low q are availablenow from the measurements described in the previous chapter. The form factors are shown in Fig. 16together with data from MIT/Bates [92] for q > fm-. These are compared to calculations withthe interaction (7) for s = 1 (solid line), 1.2 (dashed line), 1.6 (dotted line) and 2 (dashed-dottedline). Strong effects due to the variation of L are visible. The new data gained on *sCa by our 180experiments previous section clearly provide an upper constraint of e z 1.2 by the behaviour of theM2 transition around the first maximum of the form factor. On the other hand, the results for theM4 transition confirm the need for a value e > 1 already inferred 1891 rom the higher-q data.

    E, = 6.89 MN

    .I = 2-

    0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0

    q, , , f m3 q. , , f m3

    Figure 16: Form factors of the M4 and M2 transitions to the low lying J = 4- and J = 2- states atE, = 6.11 MeV and 6.89 MeV in 48Ca measured in inelastic electron scattering at the S-DALINACand MIT/Bates [92]. The curves represent calculations with the interaction (7) for values t = 1 (solidline), 1.2 (dashed line), and 1.6 (dotted line) and 2 (dashed-dotted line).

    A word of caution is necessary, however, because the calcuations are based on rather severe approx-imations. In particular, QCD sum rules [93] predict a density dependence of the p-meson mass notincluded in the above approach. Before one can draw quantitative conclusions on the effective p-mesonmass, one should reinvestigate the form factors with the very successful SRPA description discussed

    above (with and without variations of the effective masses) to get some insight on the significance ofthe predictions of Ref. [89]. It should also be noted that a recent (p, $) experiment seems to questionthe need for any introduction of effective meson masses [94]. In order to allow some insight, we restrictourselves to a simpler interaction than used above in the calculations of the overall M2 response. Itconsists of a central and tensor piece for r and p exchange including an explicit momentum transfer

  • 7/25/2019 FIRAS (479)




    A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28

    V entral(q) =()[

    -_ 2 f ClQZTlTZ & + fK1 clazTl72 &] ,


    Ken,o, (9) = - (&) y (3~lP~2Q - fllf12Q2) [* + 4,2*] ,

    where Kl and K2 are constants. Variations of the effective mass are restricted to the p-meson.Different values of E are denoted by Fxx (where FlO corresponds to c = 1.0 etc.). Note that for c = 1and q = 0 the interactions (7) and (9) coincide. Before application to our problem the interaction istested for the much-studied form factor of the prominent Ml spin-flip transition in 4sCa [75], givenon the 1.h.s. of Fig. 17. A very good description is obtained rather independent of the choice of L. Avariation between 1 (solid line) and 1.6 (dotted line) leads to a small variation at the first maximumof the form factor only and without effects at higher q. A calculation with the M3Y interaction 1951is practically indistinguishable from the FlO result. A quenching factor of g: = 0.7lgp is includedto achieve qualitative agreement.

    10- '

    l O+0. 0 0.5 1. 0 1. 5 2.0 0.0 0.5 1. 0 1. 5 2.0 2.5 3.0

    qw (fm-9 q, W3

    Figure 17: L.h.s.: Form factor of the prominent Ml spin-flip transition in 4sCa (751 in comparison tocalculations with the interaction (9) and e = 1 (solid line) and 1.6 (dotted line). R.h.s: Dependenceof the M4 form factor on the choice of the interaction (FlO = solid line, M3Y = dashed line, M3Ynox = dashed-dotted line). For M3Y nox, exchange terms are neglected [SS]).

    Calculations for the experimental form factors discussed in Fig. 16 assuming the same spin quenchingare summarized at Fig. 18. The best description for the M4 transition is obtained for e z 1. How-ever, independent of the choice of E the experimental position of the second form factor maximum ispredicted at somewhat too high 4. The q dependence is well described for the M2 excitation for allchoices of e. Here, the first maximum exhibits considerable sensitivity to an in-medium reduction ofmP suggesting an optimum value E = 1.4. Thus, no consistent value of e can be extracted from ananalysis with the Fxx interaction (9).

    One obvious difference to the results of Lallena are much less dramatic effects when increasing e. Theoverall reduction observed with decreasing rnP can be traced back to a modification of the g couplingconstant because of short-range correlations, as shown by Baym and Brown (961. One may speculate

    that these differences mainly arise from the inclusion of MEC effects due to pion and seagull termsby Lallena [89]. At present, one must conclude that, while magnetic form factors at low momentumtransfers exhibit considerable sensitivity to in-medium modifications of vector mesons, the freedomin the fixing parameters of the residual interaction (or the inclusion of MEC corrections) lead toeffects of comparable magnitude. This is demonstrated in the r.h.s. of Fig 17 by comparison of the

  • 7/25/2019 FIRAS (479)


    A . Ri chter / Prog. Part . N ucl. Phy s. 44 2000) 3-28 2

    1o-n0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

    q,,, (fm-1 q.,, (fm-9

    Figure 18: Same as Fig. 16, but calculations with the interaction (9) for values E : 1 (solid line), 1 2(dashed line), 1.4 (dashed-dotted line) and 1.6 (dotted line).

    the M4 form factor calculated with the FlO (solid line) and the M3Y interactions with (dashed) andwithout (dashed-dotted) exchange part. The latter accounts successfully for the global M2 responsein closed-shell nuclei [68]. Thus, while inelastic electron scattering transverse from factors in nucleiare a potentially interesting opportunity to investigate in-medium properties of vector mesons, firstan optimum interaction has to be determined before quantitative conclusions may be possible.

    5. OUTLOOK

    In the previous chapters I have presented a few examples for the relevant contributions of electronscattering at low momentum transfers to our understanding of elementary excitation modes of nuclei.Comcidence experiments permit the decomposition of giant resonance multipole strengths, even mthe case of strongly fragmented and overlapping distributions, and simultaneously provide deeperinsight into the decay mechanisms. On the other hand, as demonstrated for the case of isobaricanalogue states, electron scattering coincidence experiments enable complete spectroscopy of weaktransitions of great physical interest otherwise hardly accessible. Both aspects will be combined inplanned investigations of *Pb through (e,en) and (e,ep) experiments. The doubly magic nucleus

    OsPb forms a cornerstone of modern microscopic models including the coupling to complex degreesof freedom. Such calculations predict significant deviations from simple Lorentzian forms of thestrength distributions (see [97] f or an example). Also, the poperties of the isoscalar giant dipoleresonance (ISGDR) recently identified for the first time [98] could be elucidated further. Isobaricanalog resonances in sPb may be studied by (e,ep) ex p eriments similar to what was shown abovefor Zr.

    Another field where electro-induced particle emission may be of great potential importance are newideas [99] on the nucleosynthesis of the light elements Li, Be, iJIB which are neither produced instellar burning nor in the Big Bang. Recent data indicate that it must be a primary production processwhich is incompatible with previous models of high-energy spallation in the interstellar medium [loo].

    One possible candidate would be inelastic neutrino scattering on C (and eventually 14N, 0) duringsupernova outbursts (601. Electrospallation cross sections, which can be related to te relevant neutrinocross sections by SU(4) symmetry, are a means to test these predictions. However, the experimentsare quite challenging because extremely small branching ratios are expected for the relevant particledecay channels.

  • 7/25/2019 FIRAS (479)


    22 A. Richter / Pmg. Part. Nucl. Phys. 44 (2000) 3-28

    Low-multipolarity magnetic transitions have always been a domain of electron scattering at low mo-mentum trasfers. While previous work mainly focused on Ml excitations 15, lOI], we are now movinginto systematic exploration of the next higher multipol~ity, M2, with special emphasis on the twistmode. The new 180 system at the S-DALINAC has proven to be a versatile intrument for the pre-cise exctraction of magnetic strength functions. One of our goals of the near future are a sytematic

    mapping of the twist mode throughout the nuclear lansdscape and a direct proof of its orbital char-acter by the measurement of selected form factors in heavy nuclei (e.g. 2osPbf. Furthermore, theaccessible momentum transfer will be increased by developments of the apparatus, thereby enablinga first glimpse on M3 modes which form a nearly blank nuclear landscape [102]. E.g., one of thevery few experiments studying M3 strength in the light nucleus 2sMg claims the absence of quenchingin the spin part of the M3 operator [103]. Th s surprising result certainly needs some independentexamination.

    The physics program is closely tied to complementary investigations using polarized proton scatteringand/or charge-exchange reactions at the KVI accelerator in the framework of the EUROSUPERNOVAcollaboration (Aarhus/Bari/Darmstadt/Gent/Groningen/Milano/M~nster). The combined results ofelectromagnetic and hadronic probes have been a particularly powerful tool for our understanding ofthe magnetic dipole response in nuclei (think e.g. of the modification by mesonic exchange currentseven in complex nuclei [104-1061 or the decomposion of spin/orbital and isospin degrees of freedom[107, 1081) and holds the same promise for higher multipol~ities.

    Finally, let me briefly introduce you to another central goal of our experimental activities at the S-DALINAC in the near future: a precision measurement of the pol~izabilities of the proton (and theneutron) using a novel experimental technique. There is a high interest in these elementary propertiesof the nucleon - reflected in several contributions to this school - providing a clear signature of itssubstructure. Thus, their precise knowledge provides a stringent test of models aiming at a descriptionof the quark-meson structure of the nucleon such as chiral perturbation theory [109].

    One promising way to determine the polarizabilities is Compton scattering. At photon energies wellbelow the pion mass these can be extracted in a rather model-independent way from differential crosssections. Use is made of the low energy theorem

    d&e)ub, 0) =dw [ 1w -p + 0(ur4)po nt

    with the structure term p

    = 4 m,~(~)(ww)[~(1icose)2+~(I-cose)2]



    where o and /3 denote the electric and magnetic pol~izabiIities, respectively. From Eq. (11) followsthat forward scattering is mainly sensitive to the sum and backward scatttering to the difference of ~2and ,f?. Experiments results (see [109] f or a summary) scatter considerably with values a z 10 - 15fm3 and /3 x O-4 fm3 and total uncertainties > 1.5 fm3. Recent results come from groups in Saskatoon[llO] and Mainz (1111, but again with errors larger than 1. low3 fm3.

    It is the aim of the experiment planned at the S-DALINAC to achieve uncertainties better than 0.310m3 fm. For this ambitious goal a new experimental technique is employed, sketched schematicallyin Fig. 19. Incident bremsstrahlung photons with energies E7 = 20 - 100 MeV are scattered froma hydrogen target and detected in large-volume NaI counters. Additionally, the recoil proton is

    measured in coincidence allowing a dramatic background suppression which forms the key to theenvisaged precision. The experiment is also unique in the availability of a tunable cw photon beambelow 50 MeV with sufficient intensity which presently exists nowhere else in the world.

    Details of the planned experimental setup are shown in Fig. 20. Electrons are converted to bremsstrahlung

  • 7/25/2019 FIRAS (479)


    A. Richter / Pmg. Part. Nucl. Phys. 44 (2000) 3-28 23

    En = 0.4 - 8.0 MeV P

    Figure 19: Schematic sketch of a new Compton scattering experiment at the S-DALINAC to measurethe proton (and neutron) polarizabilities with high precision. Recoil protons can be measured incoincidence with the scattered photons leading to a dramatic background suppression.

    with a thin (0.1 radiation lengths) converter. A well collimated photon beam impinges on two high-pressure (100 bar) hydrogen targets. These serve as active targets permitting the measurement ofrecoil protons with multi-anode ionisation chambers. The scattered photons are recorded with large1Oxll NaI counters placed under 60 and 140. Additional measurements will be performed at90 where the structure term, Eq. (ll), is directly proportional to a. The setup will be installed atlocation @ in Fig. 1 where high-energy channeling experiments were performed so far. First resultsare expected in early 2001

    Radiator Magnet

    @A LeadEB Polyethylene

    ,Concrete Wall

    Figure 20: Setup of the Compton scattering experiment at the S-DALINAC planned to measure theproton polarieabilities.


    I am very much indebted to my many collaborators at the S-DALINAC and elsewhere. I men-tion in particular P. von Neumann-Cosel, F. Neumeyer, C. Rangacharyulu, B. Reitz, G. Schrieder,K. Schweda, S. Strauch and .I. Wambach for sharing their insight with me into the various topicspresented in this lecture. Furthermore, P. von Neumann-Cosel and K. Schweda have not only con-tributed very much to the physics which I discussed but also helped me in preparing the manuscriptof the lecture. Our longtime collaborator D. Frekers provided the precious and expensive 4sCa target.Finally, A. Faessler is thanked for creating as usual a very stimulating atmosphere in Erice.

  • 7/25/2019 FIRAS (479)


    24 A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28


    [l] A. Richter, in Proc. 5th EPAC, ed 5. Myers et al. (IOP Publishing, Bristol, 1996)

    [Z] A. Richter, Phys. Blitter 54 (1998) 31

    [3] D. Bohle, A. Richter, W. Steffen, A.E.L. Dieperink, N. LoIudice, F. Palumbo, 0. Scholten,

    Phys. Lett. B 137 (1984) 27.

    [4] J. Enders, H. Kaiser, P. von Neumann-Cosel, C. Rangacharyulu, A. Richter, Phys. Rev. C 59

    (1999) R1851.

    [5] A. Richter, Prog. Part. Nucl. Phys. 34 (1995) 261

    [6] D. G y-OdeIin, S. Stringari, Phys. Rev. Lett. 83 (1999) 4452

    [7] O.M. Maragb, S.A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, C.J. Foot, Phys. Rev. Lett.,


    [8] P.F. Bortignon, A. Bracco, R.A. Brogha, Giant Resonances: Nuclear Structure at Finite Tem-

    peratures (Harwood Academic, Amsterdam, 1998).

    [9] Topical Conference on Giant Resonances, Varenna, Nucl. Phys. A 649 (1999)

    [lo] J.R. CaIarco, J. Arruda-Neto, K.A. Griffioen, S.S. Hanna, D.H.H. Hoffmann, B. Neyer, R.E.

    Rand, K. Wienhard, M.R. Yearian, Phys. Lett. B 146 (1984) 179.

    [11) T. Kihm, K.T. Knopfle, H. Riedesel, P. Voruganti, H.J. Emrich, G. Fricke, R. Neuhausen,R.K.M. Schneider, Phys. Rev. Lett. 56 (1986) 2789.

    [12] A. Tanaka, T. Hino, H. Kawahara, N. Nomura, T. Tamae, M. Sugawara, H. Tsubota, H. Miyase,

    Y. Kawazoe, Nucl. Phys. A 489 (1988) 381.

    113) J. P. Fritsch, H.J. Emrich, A. Grasmiick, R. Neuhausen, S. Schardt, N. Zimmermann, J.R.

    CaIarco, M. Potokar, Phys. Rev. Lett. 68 (1992) 1667.

    [14] J. DeAngeIis, J. R. CaIarco, J. E. Wise, H. J. Emrich, Phys. Rev. Lett. 70 (1993) 2872; Phys.

    Rev. C 52 (1995) 61.

    [15] H. Diesener, U. Helm, G. Herbert, V. Huck, P. von Neumann-Cosel, C. Rangacharyulu, A.Richter, G. Schrieder, A. Stascheck, A. Stiller, J. Ryckebusch, J.Carter, Phys. Rev. Lett. 72

    (1994) 1994.

    [16] H. Diesener, U. Helm, P. von Neumann-Cosel, A. Richter, G. Schrieder, and S. Strauch, Phys.

    Lett. B 352 (1995) 201.

    [17] M. Kohl, P. von Neumann-Cosel, A. Richter, G. Schrieder, S. Strauch, Phys. Rev. C 57 (1998)3167.

    [18] G.O. Bolme, L.S. Cardman, R. Doerfler, L.J. Koester Jr., B.L. Miller, C.N. Papanicolas,H. Rothhaas, S.E. Williamson, Phys. Rev. Lett. 61 (1988) 1081.

    [19] R.A. Miskimen, E.A. Ammons, J.D.T. Arruda-Neto, L.S. Cardman, P.L. Cole, J.R. Deininger,S.M. Dolfini, A.J. Linzey, 3 .B. MandeviIle, B.L. Miller, P.E. Mueller, C.N. Papanicolas, A. Ser-

    darevit, S.E. Williamson, Phys. Lett. B 236 (1990) 251; Phys. Rev. C 43 (1991) 1677.

  • 7/25/2019 FIRAS (479)


    A. Richter i Prog. Part. Nucl. Phys. 44 (2000) 3-25 25

    [20] C. Takakuwa, T. Saito, S. Suzuki, K. Takahisa, T. Tohei, T. Nakagawa, A. Abe, Phys. Rev.c 50 (1994) 845

    1211 T. Saito, S. Suzuki, T. Takahisa, C. Takakuwa, M. Oikawa, T. Tohei, T. Nakagawa, K. Abe,Phys. Rev. Lett. 78 (1997) 1018.

    [22] C. Bahr, R. Bijttger, H. Klein, P. von Neumann-Cosel, A. Richter, D. Schmidt, K. Schweda, S.Strauch, Nucl. Instrum. Meth. A 411 (1998) 430.

    [23] S. Strauch, in [9], p. 85~

    1241 S. Strauch, Dissertation D17, Technische Universitit Darmstadt (1998)

    1251 I. Hamamoto, H. Sagawa, X.Z. Zhang, Phys. Rev. C 56 (1997) 3121.

    [26] G.J. OKeefe, M.N. Thompson, Y.I. Assafari, R.E. PyweII, Nucl. Phys. A 469 (1987) 239.

    ]27] P.F. Bortignon and R.A. Broglia, Nucl. Phys. A 381 (1981) 405

    ,281 S. Droidi, V. Klemt, J. Speth, J. Wambach, Nucl. Phys. A 451 (1986) 11

    [29] S. Kamerdzhiev, J. Speth, G. Tertychny, Nucl. Phys. A 624 (1997) 328

    1301 F Zwarts, A.G. Drentje, M.N. Harakeh, A. van der Woude, Phys. Lett. B 125B (1983) 123;

    Nucl. Phys A 439 (1985) 117.

    [31] S. Kamerdzhiev, J. Speth, G. Tertychny, Phys. Rev. Lett. 74 (1995) 3934

    [32] S. Kamerdzhiev, J. Speth, G. Tertychny, J. Wambach, Nucl. Phys. A 577 (1994) 641

    [33] S. Droidi, S. Nishizaki, J. Speth, J. Wambach, Phys. Rep. 197 (1990) 1.

    [34] R. Martin, M. Buenerd, Y. DuPont, M. Chabre, Nucl. Phys. A 185 (1972) 465.

    [35] T.A. Belote, H.Y. Chen, 0. Hansen, Phys. Rev. 142 (1966) 624.

    [36] R.A. Eramzhyan, B.S. Ishkanov, L.M. Kapitonov and V.G. Neudatchin, Phys. Rep. 136 (1986)229.

    [37] B. S. Dolbilkin, R. L. Kondratev, V. P. Lisin, S. Khan, T. Kihm, K. T. Knopfle, H. J. Schulz,Chenlin Wen, J. Friedrich, 2. Phys. A 331 (1988) 107.

    38] P. von Neumann-Cosel, H. Diesener, U. Helm, G. Herbert, V. Huck, C. Rangacharyulu, ARichter, G. Schrieder, A. Stascheck, A. Stiller, J. Ryckebusch, J.Carter, A.A. Cowley, R.W.Fearick, 3.5. Lawrie, S.J. Mills, R.T. Newman, J.V. Pilcher, F.D. Smit, Z.Z. Vilakazi, D M.Whittal, Nucl. Phys. A 569 (1994) 373~.

    [39] J. Carter, A.A. Cowley, H. Diesener, R.W. Fearick, S.V. Fijrtsch, M.N. Harakeh, J.J. Lawrie,S.J. Mills, P. von Neumann-Cosel, R.T. Newman, J.V. Pilcher, A. Richter, K. Schweda, F.D.Smit, G.F. Steyn, S. Strauch, D.M. Whittal, Nucl. Phys. A 630 (1998) 631.

    [40] K. Schweda et al., to be published

    [41] A. van der Woude, in [9], p. 97c.[42) J. Carter et al., to be published.

    [43] P. von Neumann-Cosel, C. Rangacharyulu, A. Richter, G. Schrieder, A. Stascheck, S. Strauch,Phys. Rev. Lett. 78 (1997) 2924.

  • 7/25/2019 FIRAS (479)


    26 A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28

    [44] J.L. Black, N.W. Tanner, Phys. Lett. 11 (1964) 135.

    [45] L. P. Ekstriim, J. Lyttkens-Linden, Nucl. Data Sheets 67 (1992) 579

    [46] S. Michaelson, A. Harder, K.P. Lieb, G. Graw, R. Hertenberger, D. Hofer, P. Schiemenz, E.

    Zanotti, H. Lenske, A. Weigel, H.H. Walter, S.J. Robinson, A.P. Williams, Nucl. Phys. A 552(1993) 232.

    [47] A. Stascheck, Dissertation D17, Technische Hochschule Darmstadt (1996).

    (481 B.L. Berman, J.T. Caldwell, RR. Harvey, M.A. Kelly, R.L. Bramblett, S.C. Fultz, Phys. Rev.162 (1967) 1098.

    [49] M. Hasinoff, G.A. Fisher, S.S. Hanna, Nucl. Phys. A 216 (1973) 221.

    [50] K. Shoda, M. Sugawara, T. Saito, H. Miyase, Nuci. Phys. A 221 (1974) 125.

    [51] W.R. Dodge, E. Hayward, E. Wolynec, Phys. Rev. C 28 (1983) 150

    [52] J. Reiter, H.L. Harney, Z. Phys. A 337 (1990) 121.

    [53] T. Wakasa, H. Sakai, H. Okamura, H. Otsu, S. Fujita, S. Ishida, N. Sakamoto, T. Uesaka, Y.Satou, M.B. Greenfield, K. Hatanaka, Phys. Rev. C 55 (1997) 2909; Phys. Lett. B 426 (1998)257.

    [54] C. Liittge, P. von Neumann-Cosel, F. Neumeyer, A. Richter, Nucl. Phys. A 606 (1996) 183.

    155J F. Osterfeld, Rev. Mod. Phys. 64 (1992) 491

    [56] F.T. Baker, L. Bimbot, C. Djalali, C. Glashausser, H. Lenske, W.G. Love, M. Morlet, E. Tomasi-Gust&son, J. van der Wiele, J. Wambach, A. Willis, Phys. Rep. 289 (1997) 235.

    (571 Proceedings of the International Symposium New Facet of Spin Giant Resonances in Nuclei,Eds. H. Sakai et al. (World Scientific, Singapore, 1998).

    [58] A. Zaringhalam, Nucl. Phys. A 404 (1983) 599.

    [59] J. Cooperstein, J. Wambach, Nucl. Phys. A 420 (1984) 591.

    [60] SE. Woosley, D.H. Hartmann, R.D. Hofmann, W.C. Haxton, Astrophys. J. 356 (1990) 272.

    [61] W. Kniipfer, R. l+ey, A. Friebel, W. Mettner, D. Meuer, A. Richter, E. Spamer, 0. Titze,

    Phys. Lett. B 77 (1978) 367.

    (621 V.Yu. Ponomarev, V.G. Soloviev, C. Stoyanov, A.I. Vdovin, Nud. Phys. A 323 (1979) 446;V.Yu. Ponomarev, V.M. Shilov, A.I. Vdovin, V.V. Voronov, Phys. Lett. B 97 (1980) 4.

    [63] D. Cha, J. Speth, Phys. Rev. C 29 (1984) 636; D. Cha, B. Schwesinger, J. Speth, J. Wambach,Nucl. Phys. A 430 (1984) 321.

    1641 G. Holzwarth, G. E&art, Z. Phys. A 283 (1977) 219; Nucl. Phys. A 325 (1979) 1.

    (651 B. Schwesinger, K. Pingel, G. Holzwarth, Nucl. Phys. A 341 (1982) 1

    [SS] B. Schwesinger, Phys. Rev. C 29 (1984) 1475.

    [67] V.Yu. Ponomarev, J. Phys. G 10 (1984) L177

    1681 P. von Neumann-Cosel, F. Neumeyer, S. Nishizaki, V.Yu. Ponomarev, C. Rangacharyulu, A.Richter, G. Schrieder, D.I. Sober, T. Waindzoch, J. Wambach, Phys. Rev. Lett. 82 (1999) 1105.

  • 7/25/2019 FIRAS (479)


    A. Richter / Prog. Part. Nucl. Phys. 44 (2000) 3-28 21

    [69] C. Liittge, C. Hofmann, J. Horn, F. Neumeyer, A. Richter, G. Schrieder, E. Spamer, A. Stiller,D.I. Sober, S.K. Matthews, L.W. Fagg, Nucl. Instrum. Meth. A 366 (1995) 325.

    [70] B. Reitz, F. Hofmann, P. von Neumann-Cosel, F. Neumeyer, C. Rangacharyulu, A. Richter, G.Schrieder, D.I. Sober, B.A. Brown, Phys. Rev. Lett. 82 (1999) 291.

    [71] P. von Neumann-Cosel, in [9], p. 77~.

    [72] P.G. Hansen, B. Jonson, A. Richter, Nucl. Phys. A518 (1990) 13.

    73] J. Enders, N. Huxel, P. von Neumann-Cosel, A. Richter, Phys. Rev. Lett. 79 (1997) 2010.

    74] J. Wambach, Rep. Prog. Phys. 51 (1988) 989.

    j75] W. Steffen, H.-D. G&, A. Richter, A. Harting, W. Weise, U. Deutschmann, G. Lahm, K.Neuhausen, Nucl. Phys. A 404, (1983) 413.

    [76] S. Nishizaki, K. Ando, Prog. Theor. Phys. 71 (1984) 1263.

    [77] M. Traini, Phys. Rev. Lett. 41 (1978) 1535

    [78] T. Suzuki, Phys. Lett. B 83 (1979) 147.

    [79] S. Nishizaki, K. Ando, Prog. Theor. Phys. 63 (1980) 1599.

    [SO] E. Lipparini, S. Stringari, Phys. Rep. 175 (1989) 103.

    181) D. Kurath, ANL Report 97/14 (1997) 161

    [82] C.M. Ko, V. Koch, G. Li, Annu. Rev. Nucl. Part. Sci. 47 (1997) 505

    [83] M. Soyeur, G.E. Brown, M. Rho, Nucl. Phys. A 556 (1993) 355.

    (841 G.E. Brown, M. Rho, Phys. Rev. Lett. 66 (1991) 2720.

    [85] F. Klingl, N. Kaiser, W. Weise, Nucl. Phys. A 624 (1997) 527.

    [86] M.S. Fayache, L. Zamick, B. Castel, Phys. Rep. 290 (1997) 201.

    [87] M.S. Fayache, P. von Neumann-Cosel, A. Richter, Y.Y. Sharon, L. Zamick, Nucl. Phys. A 627(1997) 14.

    [SS] S. Miiller, G. Kiichler, A. Richter, H.P. Blok, H. Blok, C.W. de Jager, H. de Vries, J. Wambach,Phys. Rev. Lett. 54 (1985) 293.

    [89] A.M. LaIIena, Phys. Rev. C 48 (1993) 344.

    [90] J. Speth, V. Klemt, J. Wambach, G.E. Brown, Nucl. Phys. A 343 (1980) 382

    [91] N.M. Hintz, A.M. LaIIena, A. Sethi, Phys. Rev. C 45 (1992) 1098.

    (921 J.E. Wise, J.S. McCarthy, Ft. Altemus, B.E. Norum, RR. Whitney, J. Heisenberg, J. Dawson,0. Schwentker, Phys. Rev. C 31 (1985) 1699.

    1931 T. Hatsuda, S.H. Lee, Phys. Rev. C 46 (1992) R34.[94] E.J. Stephenson, J. Liu, A.D. Bather, S.M. Bowyer, S. Chang, C. Olmer, S.P. Wells,

    S.W. Wissink, J. Lisantti, Phys. Rev. Lett. 78 (1997) 1636.

    [95] G.F. Bertsch, J. Borysowicz, H. McManus, W.G. Love, Nucl. Phys. A 284 (1977) 399.

  • 7/25/2019 FIRAS (479)


    28 A. Richter / Pmg, Part. Nucl. Phys. 44 (2000) 3-28

    [96] G. Baym, G.E. Brown, Nucl. Phys. A 247 (1975) 395.

    [97] S. Kamerdzhiev, J. Lisantti, P. von Neumann-Cosel, A. Richter, G. Tertychny, J. Wambach.Phys. Rev. C 55 (1997) 2101.

    1981 B.F. Davis, U. Garg, W. Reviol, M.N. H arakeh, A. Bather, G.P.A. Berg, C.C. Foster, E.J.Stephenson, Y. Wang, J. Janecke, K. Pham, D. Roberts, H. Akimune, M. Fujiwara, J. Lisantti,Phys. Rev. Lett. 79 (1997) 609.

    [99] W.C. Haxton, private communication.

    [loo] R. Ramaty, B. Kozlowsky, R. Lingenfelter, Phys. Today 51 (1998) 30.

    [lOl] A. Richter, Prog. Part. Nucl. Phys. 13 (1985) 1.

    [102] C. De Coster, K. Heyde, S. Rambouts, A. Richter, Phys. Rev. C 51 (1995) 3510

    [1031 K.K. Seth, R. Soundranayagam, A. Saha, C. W. de Jager, H. de Vries, B.A. Brown, B.H. Wilden-thal, Phys. Rev. Lett. 74 (1995) 642; Erratum 74 (1995) 3306.

    [104] A. Richter, A. Weiss, 0. Hausser, B.A. Brown, Phys. Rev. Lett. 65 (1990) 2519

    [105] C. Liittge, P. von Neumann-Cosel, F. Neumeyer, C. Rangacharyulu, A. Richter, G. Schrieder,E. Spamer, D.I. Sober, S.K. Matthews, B.A. Brown, Phys. Rev. C 53 (1996) 127.

    [106] P. von Neumann-Cosel, A. Richter, Y. Fujita, B.D. Anderson, Phys. Rev. C55 (1997) 532.

    [107] Y. Fujita, H. Akimune, I. Daito, M. Fujiwara, M.N. Harakeh, T. Inomata, J. Jinecke, K. Katori,H. Nakada, S. Nakayama, A. Tamii, M. Tanaka, H. Toyokawa, M. Yosoi, Phys. Lett. B 365 (1996)29.

    [108] Y. Fujita, H. Akimune, I. Daito, M. Fujiwara, M.N. Harakeh, T. Inomata, J. Janecke, K. Katori,C. Liittge, S. Nakayama, P. von Neumann-Cosel, A. Richter, A. Tamii, M. Tanaka, H. Toyakawa,H. Ueno, M. Yosoi. Phys. Rev. C 55 (1997) 1137.

    (109) V. Bernard, N. Kaiser, U.-G. Meissner, Int. J. Mod. Phys. E 4 (1995) 193.

    [llO] B.E. MacGibbon, G. Garino, M.A. Luca, A.M. Nathan, G. Feldman, B. Dolbilkin, Phys. Rev.C 52 (1995) 2097.

    [ill] J. Ahrends, private communication.