The spin-isospin response

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A 606 (1996) 227-236

The spin-isospin response Carl G a a r d e 1 The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark

Received 10 May 1996

Abstract Three aspects of the response in the spin-isospin channel is discussed. Inclusive data with charge exchange reactions show significant cross sections in the spin-transverse channel beyond contributions from a l p - I h model space. Similar effects are seen in electron scattering. One-proton emission spectra have been obtained to show missing momentum distributions in the quasielastic and dip region. Evidence for coherent pions in charge exchange are presented and discussed in terms of scattering of virtual pions.

1. Introduction Experiments to study the response function in the spin-isospin channel in the quasielastic and the A region have been performed over the last decade and some preliminary conclusions can now be drawn. The interest in the response of the nucleus in this channel is that here the connection to pion-exchange as the carrier of the strong force seems especially simple and strong collective effects are expected in the pion-like i.e. the spin-longitudinal channel both in the nucleon and the A sector of the spectrum. We shall see that these effects are often hidden behind much larger effects in the spin transverse channel, which are not under control and an analysis o f the pion-like channel with sufficient detail has therefore not yet allowed very strong conclusions about the correlation effects in this channel. Recent exclusive experiments have offered a detailed description of the decay of A's in a nucleus. A real breakthrough has been the evidence for coherent pions, and this has led to the construction of a set-up where a detailed study of these pions can be performed. We shall discuss the evidence for the coherent pions. l E-mail:[email protected]. 0375-9474/96/$15.00 Copyright (~) 1996 Elsevier Science B.V. All rights reserved PII S0375-9474(96) 00207 -2

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Another result of these exclusive experiments is the one- and two-proton emission spectra from the dip region following the excitation with the (3He,t) reaction. These spectra carry information on short range correlations in the target ground states.

2. Inclusive reactions Data have been obtained at SATURNE with the (3He,t) [1] reaction and with the (J,2p[IS0]) [2] reaction with tensor polarized beams and at LAMPF with the (l~,ff) [3] reaction to determine the inclusive spectra and for many cases a complete set of spin observables is now available. In Fig. 1 simple (p,n) inclusive spectra [4] are shown at the same energy and angle for the deuteron and ~2C to demonstrate how very different the spectra are in the region above the quasielastic peak. In the lower part of the figure (p,n) spectra for the same targets are shown together with calculated spectra. The deuteron case is calculated in a PWIA with a wavefunction from a Reid soft core potential with (full curve) and without (dashed curve) final state interactions. It is seen that the data are very well described in this model and so are the spin observables [5]. The carbon case is calculated with a continuum RPA for the response function and an eikonal approximation for the distortion. A standard treatment of the distortion gives almost identical results (with the same response function) [6]. In this case we see that this l p - l h approach fails badly not only in the dip region around 150 MeV excitation energy but also in the peak and tail region of the quasielastic part of the spectrum. A more detailed analysis of data on the spin observables with the (1~, if) reaction on J2C [3] shows that the spin longitudinal part of the cross section is reasonably well accounted for in the l p - l h approximation referred to above, whereas the spin transverse part is very much underestimated. The dip-region and also the tail region of the quasielastic peak is therefore dominated by spin transverse excitations. This is also demonstrated in Fig. 2 where data from the A region are compared to calculations [7]. Here a zero degree spectrum is shown, where the separation into spin transfer directions are less model dependent. The situation looks very similar. The spin longitudinal part is reasonably well described, whereas the spin transverse part is severely underestimated. The dip region is filled with spin transverse excitations. We further note that the ratio between longitudinal and transverse cross section for the (1~, if) reaction is very similar to the ratio found with (J,2p[IS0]) [8]. The question is what the origin of this excess cross section is. First we note that two-step processes at the p-n vertex probably only contributes a small fraction of the one-step. The main two-step contribution comes from a scalar-isoscalar times a charge exchange amplitude. The cross section has been estimated in a second order Born approximation and found to be small at the momentum transfers discussed here [4]. Such a process would also contribute for the deuteron target and here we have seen that the one-step process describes the data also in the dip region. Another argument for the dominance of a one-step mechanism is the similarity be-

C. Gaarde/Nuclear Physics A 606 (1996) 227-236

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tween (p,n) and (3He,t) spectra at momentum transfers smaller than say 400 MeV/c. This is demonstrated in Fig. 3, where spectra for the two reactions on 12C at the same momentum transfers are compared. The absorption is quite different for the two reactions and the ratio between one-step and two-step contribution would be different. We would therefore conclude that the charge exchange reactions excite with large cross sections states beyond a l p - l h model space. A similar conclusion can be drawn from a recent analysis of 4He(e,e') data [ 12]. It is found that a two-body term probing pion-exchange correlations in the target gives a significant contribution to the spin-transverse cross section and improves the description of the data very much. A similar analysis of the (p,n) reaction has not yet been attempted and the old question about spin longitudinal correlations in nuclei, for which the (p,n) reaction in principle should be the ideal probe, can therefore not really be discussed in detail before the spin transverse part is better under control.

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reactions

R e c e n t experiments at S A T U R N E have studied charged particle emission f o l l o w i n g excitations with the (3He,t) reaction in a detector with a solid angle c o v e r i n g a significant part o f 4~- [ 1 0 ] . The emphasis has been on the study of A properties in the

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nucleus. In this paper we shall discuss another aspect of data obtained in these experiments.

3.1. One-proton emission spectra In Fig. 4 is shown a spectrum from the 4He(3He,t) reaction at 2 GeV [ 10]. Also shown are the spectra for one- and two-proton decay channels. It is seen that in the dip region the measured yield in the two decay channels accounts almost completely for the inclusive spectrum. At higher excitation energies the pion channel opens and at lower energies the proton energy threshold of 35 MeV cuts into the 1-p spectrum. At still lower energies the inclusive yield corresponds to bound states. In Fig. 5 three spectra of the missing momentum distribution Pmis = q - Pproton projected onto q, are shown for different cuts in the energy transfer. Only the forward going component of Pmis * q/q is shown to avoid efficiency corrections due to threshold and finite solid angle effects. Also shown is the measured momentum distribution for a proton in the g.s. of 4He from an (e,elp) experiment [ 12] and is seen to be in reasonable agreement with the measured distribution for energy transfers (w) in the peak region of the quasielastic response (the electron data are taken at a larger momentum transfer and are therefore not affected by threshold effects). At higher w the missing momentum distribution shows not surprisingly, higher momentum components. The next step would be to calculate this distribution versus energy transfer. Similar data have been obtained also for the deuteron and J2C and 2°sPb. We conclude this section by pointing to the spectra in Fig. 3 demonstrating the complete proportionality between (p,n) and (3He,t) spectra. The experimental momentum distributions as shown in Fig. 5 are therefore to a good approximation a measure of those components in the 4He g.s. wavefunction, that fill the dip region in a (p,n) process.

C. Gaarde/Nuclear Physics A 606 (1996) 227-236

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3.2. Coherent pions Data on coherent pions have been obtained in the same experiments [ 11 ]. The (3He,t) reaction at 2 GeV serves in this study as a source of virtual pions transmitted to the target. The target nucleus takes up part of the transferred momentum of the pion-like quantum, to bring it on to the mass shell as a real pion, to be detected in the detector. The pions are coherent in the sense, that it is the whole nucleus that takes up the momentum and the process then corresponds to elastic scattering of pions off nuclei, but in this case we are talking about scattering of virtual pions, off shell pions. The crucial experiment is then in principle very simple: to measure the momentum of the ejectile and the outgoing pion with sufficient resolution to determine the missing mass so, that the g.s. and the first excited states in the final nucleus can be separated. In Fig. 6 data with the Diogene detector are presented [ ! 1 ] . In the top panel the inclusive spectrum for tritons angles less than 4 ° are shown together with spectra from the different decay channels. In the lower panel the triton angle is limited to the 2.5 to 3.5 ° interval and the yield of one-pion events are shown with and without a gate on the missing mass or rather the excitation energy in IZc to be less than 25 MeV. For this triton angle the momentum transfer q polar angle is around 30 ° where the detector has

233

C. Gaarde/Nuclear Physics A 606 (1996) 227-236

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Fig. 5. Missing momentum distributions projected onto the momentumtransfer q, are shown for different cuts in energy transfer (see Fig, 4). The dots give the measured momentum distribution from 4He(eJp) at the top of the quasielastic peak. full efficiency. It is seen that the yield of these pions from the g.s. region of the final nucleus peaks around an energy transfer of 235 MeV, almost 100 MeV lower than the peak in the yield of the ( l ~ - + l p ) decay channel. This latter channel can be taken as a measure of the quasi-free A production and subsequent decay. The figure also shows that the yield of coherent pions is less than 10% of the inclusive spectrum. They therefore contribute only a small fraction to the shift of the zl peak as observed in the inclusive spectra. Fig. 6 also shows the angular correlation between these g.s. pions and the momentum transfer vector q. Both for 4He and 12C a strong forward peaking is observed and the width of the distributions do correspond to the size of the target nuclei. The poor missing mass resolution makes it difficult to determine the absolute cross section for the coherent pions and a new experimental set-up has been built. The first experiments have been performed and data are on tape to be analyzed. The missing mass resolution should be better then 3 M e V in the new set-up. The very preliminary analysis does show that the g.s. is indeed the final state with by far the largest yield. Several calculations on the coherent pions have been published [ 1 3 - 1 5 ] . In Ref. [13] the approach is based on the A-hole model. A virtual pion is transferred to the target

C. Gaarde/Nuclear Physics A 606 (1996) 227-236

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and propagates through the nucleus by mixing to A-hole-states, and ends up as a onshell pion with the target nucleus taking up the recoil. The coherence is built up in the spin-longitudinal channel with a S • q spin structure ( S is the N ~ A spin transition operator) and probed by the decay of a real pion ( S t . p~.) leaving the target nucleus in a definite state. The angular correlation is then characterized by a ( S t • p ~ ) ( S - q )

i.e.

a (p~, • q) dependence on the momentum vectors. The yield versus energy transfer is a sensitive measure of the residual interaction e.g. the value for g~,~. Results from the paper by Kagarlis and Dmitriev [15] are shown in Fig. 7. In this approach the coherent pions are treated similar to scattering of real pions off nuclei with the transfer of the pion-like quantum from the charge-exchange reaction acting as a source term in the K l e i n - G o r d o n equation. In this model it is easier to follow e.g. the downward shift in energy for the yield of coherent pions. Most of the shift is apparent in the sense that the imaginary part of the pion optical potential removes the yield in the free response region, the zl eats itself. This is shown in the figure where the dashed curve corresponds to no pion rescattering i.e. no optical potential for the scattering of the pions. The crucial information is again the yield of coherent pions versus energy transfer. If we compare Fig. 7 with the data as given in Fig. 6 we see that the model does quite well on this energy dependence and we also note that the no rescattering pions are absorbed and disappear from the coherent channel and comes back as quasi-free decay of the A as e.g. seen in the ( l ~ + l p ) channel in Fig. 6. The downward shift in energy for the yield of coherent pions has another interesting

235

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effect: that the interference between the s-wave and p-wave pion-nucleon interaction is enhanced and the more, the further down the energy is shifted. In the paper by Kagarlis and Dmitriev the s-wave interaction is parametrized on the basis of the free on-shell s-wave data. Very little is known about the off-shell and density behaviour of this interaction, so closely related to fundamental questions such as partial restoration of chiral symmetry. The detailed data underway could hopefully help answering some of these questions.

Acknowledgements This article is dedicated to Gerry Brown on the occasion of his 70th birthday. He has contributed to the discussions on all the subjects in this article. It is surprising that it has taken the experiments so long to come to these rather preliminary conclusions. I think Gerry Brown introduced the name 'pisobars' and here the data on tape on the coherent pions should really help to a much more quantitative understanding. The material presented here is a result of contributions from many people. I especially want to thank C. Ellegaard, J.S. Larsen, T. Sams from NBI, J.L. Boyard, T. Hennino, J.C. Jourdain, B. Ramstein, M. Roy-Stephan from IPN, Orsay, E Radvanyi, P. Zupranski from LNS, Saturne. Discussions with V. Dmitriev and M. Kagarlis have been most helpful.

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