ELASTIC AND INELASTIC SCATTERING AT LOW

AND INTERMEDIATE ENERGIES

E. Stephenson

To cite this version:

E. Stephenson. ELASTIC AND INELASTIC SCATTERING AT LOW AND INTER-MEDIATE ENERGIES. Journal de Physique Colloques, 1990, 51 (C6), pp.C6-85-C6-98.<10.1051/jphyscol:1990607>. <jpa-00230870>

HAL Id: jpa-00230870

https://hal.archives-ouvertes.fr/jpa-00230870

Submitted on 1 Jan 1990

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

COLLOQUE DE PHYSIQUE Colloque C6, suppldment au 11-22, Tome 51, 15 novembre 1990

ELASTIC AND INELASTIC SCATTERING AT LOW AND INTERMEDIATE ENERGIES

E.J. STEPHENSON

Indiana University Cyclotron Facility, Bloomington, IN 47405, U.S.A.

Rdsumd - Une revue est prdsentde des expdriences rdcentes et des analyses au sujet de diffusion dlastique et indlastique dans lesquelles les phdnomenes de polarisation sont trks importants. Les sujets qui concernent des ions legers et des dnergies moyennes sont accentuds.

Abstract - A review is made of recent experiments and analysis concerning elastic and inelastic scattering in which polarization phenomena play a crucial role. Topics involving light ions and intermediate energies are emphasized.

I. INTRODUCTION

In his summary at the Osaka meeting in 1985, Prof. Willy Haeberli [Ha 861 identified polarization transfer experiments, and especially the high precision achieved for proton-induced reactions, as one of the highlights of the meeting. In this talk, I will illustrate some of the new measurements that have been made in this area. Theorists, of course, would like to have polarization transfer measurements of a precision comparable to what can now be routinely achieved for analyzing powers. This has led to continued work to improve the reliability and precision with which such experiments can be done. The last few years have seen the capabilities of the world's intermediate energy laboratories expand in this direction. Some examples include:

- an additional solenoid has been added to the TRIUMF facility to provide longitundinal polarization at the MRS spectrometer,

- a solenoid has also been added for longitudinal spin at Osaka [Yo 871 and work has begun on a polarimeter for the high resolution RAIDEN spectrometer [Ka 871,

- polarization transfer has begun operation at Saturne [Bo 901,

- the nucleon physics line has come into operation at LAMPF, with an emphasis on ($,S) reactions, and a new optically-pumped ion source has been installed to increase the negative ion intensity,

- and IUCF has rebuilt its spin-transfer system, including precession solenoids, in-beam polarimeters, and the focal plane polarimeter, to take advantage of the high-resolution opportunity offered by the new K600 magnetic spectrometer [Op 90).

Polarimeter efficiencies have not greatly increased, but data handling techniques are improving. The IUCF focal plane polarirneter, for example, includes electronic rejection of unscattered, and therefore useless, events in less than 2 ps so that valuable computer time is not spent on this task. When additional experimental luminosity is available, the increased rates for useful data naturally lead to improved statistical precision.

With any experiment where precision is improved, it becomes increasingly important to consider sys- tematic limitations to the measurements. At intermediate energy, our knowledge of the absolute size of an analysing power enters at the level of about 3%. These calibrations have relied on standard double-scattering experiments, some of them now fairly old [Ho 681, in which the first and second scatterings were arranged to resemble each other as closely as possible so that formulas similar to the e = A2 relation between asymmetry and analyzing power could be used to deduce the analyzing power. In conjunction with the recent construc- tion of new polarimeters for both beam lines and spectrometers has come a remarkable jump in the precision with these devices can be calibrated absolutely. Now, several groups [Sr 89, C1 89, Ev 901 have realized that when the first scattering is chosen so that A FZ 1, either that analyzing power or the polarization incident on the second scatterer can be known with great precision. In elastic scattering from a spin-0 target, the outgoing normal-component polarization p' is related to the analysing power A and the beam polarization p through

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990607

COLLOQUE DE PHYSIQUE

If the incident polarization is positive and A is also large and positive, the outgoing polarization is very close to 1 (p = 0.8 and A = .95 yields p' = 0.994, for instance), and large positive values of p' for negative beam polarization imply values of A very close to one. The amplifying effect of this relation allows relatively poorly known polarization measurements to yield extremely accurate values of either p' or A.

Another example (which was exploited some time ago at lower energies [Ke 721) is the precise measure- ment of A in p+12C elastic scattering [Wi 901 made by measuring the transfer coefficients, D S ~ f and DLLt, when they are close to zero and applying the relationship

In figure 1, these measurements are shown at three energies. The quadratic relationship allows the analyzing power of the point at E = 190 MeV and B = 19.0" to be determined rather precisely as A = 0.9994:::::::. In addition, the continuity of DsL, and DLL, with angle and energy shows that near this point, A = 1 exactly.

Fig. 1 - Preliminary results of DLL, and DSLJ measurements for p+12C elastic scattering at 200, 190, and 180 MeV. The solid lines are guides connecting points at the same energy. The angles at each en- ergy are (from top to bottom) 17.0" and 18.1" at 200 MeV, 17.g0, 19.0°, and 20.1" at 190 MeV, and 19.9" and 21.0' at 180 MeV. The 180 and 200 MeV measure- ments are preliminary, and do not repre- sent the full statistical recision available. The dashed circles are coutours where A = 0.96, 0.98, 0.99, 0.995, and 0.999 as one moves toward the origin.

At the same time that considerable advances are being made in the technology of polarization ex- periments, the questions that people wish to address are advancing beyond a simple description of elastic scattering in terms of the optical potential and of reactions in terms of a distorted wave calculation in which the transition to an excited state is modelled in either a collective or a simple impulse approximation form. In this talk, I will illustrate some of the new physics ideas in the area of elastic and inelastic scattering that rest predominantly on polarization experiments. A number of these ideas depend on polarization transfer measurements as well as the more traditional analyzing power and cross section data.

11. BEYOND THE OPTICAL POTENTIAL

Since most reaction calculations rely on distorted wave techniques to describe the relative motion of projectiles and ejectiles with respect to the target nucleus, global optical potentials are still of considerable utility. This is particularly true for systems whose outgoing energies span a wide range, such as (p,2p), (p,pn) and (e,elp) experiments. An analysis to appear shortly [Va 901 by Varner, et al., covers 40 5 A < 209 and 16 5 E(MeV) 5 65 (much the same range as Becchetti and Greenlees [Be 691) and includes both proton and neutron data. A very extensive analysis within the framework of the Dirac relativistic picture covering 40 5 A 5 208 and 65 < E(MeV) 5 1040 has just appeared [Ha 901, and a more complete analysis extending to lighter nuclei is underway. Changes from earlier relativistic model work include surface-peaked imaginary potentials, which appear to be important [CO 891 for the reproduction of large-angle elastic scattering experiments [Mi 861.

A continuing concern of global optical model parametrizations is the extent to which the results and level of success of the model are constrained by the choice of radial shape function for the potential. It is therefore useful to have available a number of cases in which the potential shape has been modified. Typically this is

done by adding a series of functions, Fourier-Bessel, for example, to the standard potential shape. A number of such potentials for light ion scattering in fact agree well with double-folding predictions using the Paris interaction [Er 891. This applies even for the spin-orbit parts [Er 901. The one difficulty lies with deuterons, which generally require a less diffuse potential surface than the folding prescription provides [Er 871. This problem is likely to be related to breakup in the nuclear surface, and has been parametrized by assuming a smaller effective size for the deuteron [Er 891.

A considerable effort is also being made to describe nucleon-nucleus elastic scattering, particularly at low energies, through the use of a dispersive optical model. This model divides the real, central potential into two parts, one that is fixed or weakly energy dependent, usually referred to as the Hartree-Fock potential, and another that is computed using a dispersion relation from the imaginary potential [Ma 821. The imaginary and spin-orbit terms in the potential, including the well parameters of the Hartree-Fock term, are determined empirically from elastic scattering angular distributions of the cross section and analyzing power using chi square minimization techniques. The potential is determined at a number of energies, and then extrapolated to negative values, where is can be used to determine the bound state properties of the nucleus. The dispersive term in the central potential vanishes at the Fermi energy, and both the real and imaginary terms obey symmetry relations about the Fermi energy. Modifications to the usual fitting approach, such as the use of iterative moments [Ma 89a], as well as the use of dispersion relations directly [To 901, do a good job of describing elastic scattering of both neutrons [A1 901 and protons.

The dispersive optical potential, when extrapolated to negative energies, can be used to predict with considerable success the single particle energies of various shell model orbitals with their rms radii and spreading widths. The energy dependence of the full potential makes possible estimates of the nucleon effective mass. The imaginary part of the potential is related to estimates of occupation probabilities and spectroscopic factors.

The combination of a fixed central term with a dispersive central term often generates potential shapes that do not resemble Woods-Saxon forms. To the extent that the choice of Woods-Saxon shapes has perhaps overly restricted optical model phenomenology, these new shapes often improve the description of elastic scattering measurements. This shows up particularly for deuteron scattering [Wa 901, where the dispersive techniques can be applied with equal success, but it is not so clear how to interpret the bound state properties associated with a deuteron projectile.

At the previous polarization conference, relativistic descriptions were being applied for the first time to the study of spin-l scattering, and tested against angular distributions of cross section, vector and tensor analyzing powers in high-energy deuteron scattering [Se 851. A simple folding model appeared to produce insufficient "spin-orbit" coupling (by a factor of two) to explain the observed Ay and Ayy angular distributions [Sa 861. Since then, various calculations, such as those using the Kemmer equation [KO 891, have resolved this difficulty.

Coupled-channel descriptions of collective transitions have now been successfully modelled using the relativistic Dirac equation. Calculations at 497.5 MeV [Sh 881 show that strong transitions, such as the 3- in 40Ca, have a discernable influence on the reproduction of the elastic scattering beyond O,, = 40°, and need to be considered in the productions of global potentials for elastic scattering.

Besides analyses that consider only the central and spin-orbit degrees of freedom, the elastic scattering of protons from nuclei with spin affords the opportunity to observe the effects of spin-spin forces [Fe 601 of either a spherical ( a . I) or tensor 3(a . r ) ( I . r ) - ( U - I ) character. Recent work (I3C from [Pr 901, 15N from [Na 901, and 29Si and 31P from [Na 861) has concentrated on spin-$ targets and higher bombarding energies to avoid the complications from compound nucleus effects [Th 761 and quadrupole spin-flip [B1 751. The measurements have concentrated on DNN,, usually referred to more simply as the Wolfenstein parameter D. While high precision is needed to see the usually small differences from one, calibration with a spin-0 target where D = 1 helps to resolve many experimental difficulties and calibrate the analyzing power of the double scattering polarimeter. Among these experimental results, the largest deviations from one are for I3C and I5N, shown in figure 2. Nakano [Na 901 reports that the best optical model calculations, shown by the dashed line, require both spherical and tensor spin-spin terms, although use of a tensor potential alone does not drastically worsen agreement. The solid curves shown on the same plots are impulse approximation calculations [Pr 901 based on the Paris nucleon-nucleon interaction [Ge 831. Good agreement is obtained for I3C, and the substantially larger depolarization observed for I5N is at least qualitatively reproduced. A decomposition of the impulse approximation into spherical and tensor contributions to an effective optical potential would be most helpful in evaluating the results of the phenomenological optical model calculation, and in particular deciding to what extent the spherical and tensor potentials contribute.

COLLOQUE DE PHYSIQUE

Fig. 2 - Angular distribution measure- 1.00

ments of the depolarization parameter in elastic proton scattering from I3C at 0.98

72 MeV [Pr 901 and 15N at 65 MeV [Na 901. The dashed line is an optical D 0.96

model containing both spherical and ten- sor spin-spin potentials. The solid lines 0.94

are impulse approximation calculations from ref. [Pr 901. 0.92

Both elastic and inelastic scttering of intermediate energy protons offers a rather direct way to study the effective nucleon-nucleon interaction in the nuclear medium. Because the central part of the nucleon- nucleon force is relatively small at these energies, the spin-orbit and tensor interactions can be studied with greater clarity. The weakness of the interaction as a whole also permits the use of distorted-wave impulse approximation calculations (in which a single nucleon-nucleon scattering becomes the perturbing interaction) with some confidence.

While a number of studies use the free nucleon-nucleon form of the interaction, it is expected that modifications will occur inside the nucleus from Pauli blocking in the final state, and the motion of the target nucleons. This was well illustrated by the spin rotation experiment on p+208Pb elastic scattering from TRIUMF in comparison to the relativistic model predictions of Horowitz [Mu 871.

The relative simplicity of elastic scattering also makes it an important testing ground for the assumptions behind an impulse approximation treatment. A simple t p approximation does not include the full complexity of nuclear motion when p is taken to be the average nuclear density. The motion of nucleons in a shell structure can be treated by full-folding calculations. Results by Elster [El 901 based on the Bonn interaction and Crespo [Cr 901 show relatively small modifications to the impulse approximation results. Larger changes that produce calculations in better agreement with elastic scattering data are reported by Arellano [Ar 901. The differences among these calculations are not well understood. Ambiguities arise, for example, in the treatment of Coulomb effects [Cr goal.

111. BEYOND THE IMPULSE APPROXIMATION

Although the impulse approximation does surprisingly well in some cases as a description of inelastic scattering, it is by no means universally successful, even in cases when it can be argued that the structure being studied is well described (by comparison to electron scattering formfactors, for example). It is often the case that calculations using different models of the effective interaction agree better among themselves (since they share a common origin in nucleon-nucleon scattering measurements) than they do with experimental results. It is then worthwhile to ask whether any form of the interaction is capable of describing the growing body of (p,p) and (p,p') data. If a form could be established empirically that was independent of mass and varied smoothly with energy, the differences with various theoretical density-dependent forms would provide guidance to theorists seeking to understand the origins of additional medium effects, or perhaps better constraints on the nucleon-nucleon interaction.

Of particular note in this regard is the work of Jim Kelly [Ke SO], who has studied the way in which the isoscalar central and spin-orbit terms in the effective interaction compare with a large body of low- lying inelastic scattering transitions for a number of bombarding energies. Cross section and analyzing power

measurements for transitions including both surface- and interior-peaked formfactors are used to constrain an empirically-adjusted effective interaction. The formfactors originate to whatever extent possible in electron scattering data. The same interaction is used to generate the distorted waves in the entrance and exit channels, thus maintaining the internal consistency of the calculations. Density-dependence, modelled on the Hamburg prescription [Ge 831, is included. The results are shown in figure 3 for a few transitons in the 1sO(p,p')160 reaction at 180 MeV, and provide a generally superior description of the data as compared to calculations (shown by the dashed lines) based on a theoretical interaction which includes density dependence.

Fig. 3 - Fits, shown by the solid curves, to the cross section and analyzing power data for 180 MeV protons exciting the first I-, 3-, and 2+ states in laO. The fit ignored measurements beyond 2.7 fm-l. Impulse approximation calculations based on the free (dotted) and density-dependent (dashed) Paris-Hamburg inter- action are shown for comparison. This interaction was the basis for the fitted interaction.

The density-dependent corrections usually reduce the cross sections at momentum transfers less than 1 fm-l and increase them near 2 fm-l. At the same time, the spin-dependence, as shown in the analyzing power, is much improved. In modifying the interaction, Kelly allowed the real central, imaginary central, and real spin-orbit terms to vary. All of these terms in the interaction became weaker by about 20%, especially near g = 0, in a way not anticipated in the theoretical interaction. This was true even for states with a particularly small density dependence.

These studies have been carried out on 28Si and 40Ca, as well as 160, and at energies up to 500 MeV. Despite the increased absorption associated with the opening of the pion channel, the reproduction is still excellent, as shown for the 160(p,p')160 transition to the 3- state in figure 4. The density-dependence remains large, as shown for the real and imaginary central terms shown in figure 5, in contrast to the expected decline in Pauli blocking effects [Ra SO]. Even the elastic is well reproduced, in some aspects better than the relativistic calculations that brought much initial attention to Dirac phenomenology [Sh 83, C1 831, as shown in figure 6. It should be emphasized that our theoretical understanding of these effective interaction results, which so beautifully summarize the content of a large body of experimental data, is still inadequate.

No similar work has yet been done to establish an empirical tensor interaction. For isospin-changing (AT = l) reactions, that interaction is expected to be dominated by the exchange [Br 841 of the longer- range pion and shorter-range p-meson. This interaction is easily studied in (p,n) reactions or through the

COLLOQUE DE PHYSIQUE

Fig. 4 - Angular distribution measurements of the cross section, analyzing power A, induced polarization P, and the five polarization transfer coefficients Dij for the '60(p,p')160 reaction to the lowest 3- state using 489 MeV protons. The dashed curves are impulse approximation calculations based on the 515 MeV interaction of Franey and Love [Fr 851. The solid curves are a best-fit interaction. Note that for this transition, A, FZ P, DNNt X 1, DSL, M -DLS!, and DLLI x Dss,, as would be the case for elastic scattering.

- -T- - - - I Im too

Fig. 5 - The empirical effective interac- tion for the real central (top) and imagi- nary central (bottom) terms at 489 MeV The interaction is shown as a function of momentum transfer q for four densities: 0 fm-' (circles), 0.6 fm-l (dots), 1.0 fm-l (triangles), and 1.4 fm-' (squares).

Fig. 6 - Cross section, analyzing power A, and spin rotation parameter Q for 489 MeV proton scattering from 40Ca. The curves are described in figure 4.

observation of isovector stretched states, since their spin-flip character suppresses the contributions of the large central term, and the spin-orbit amplitude is anyway small [Lo 811. In figure 7, the polarization transfer coefficient D s s is shown at 200 MeV [Ol 851 and 350 MeV [La 891 for the '60(p,p')'60 reaction to the 4- state at 18.98 MeV excitation. Both calculations, which agree well despite the change in bombarding energy, utilize a free interaction [fi 851. Plotted as a function of momentum transfer, the two data sets agree well with each other, but not with impulse approximation calculations.

The nature of the discrepancy can be illustrated through the measurement of complete sets of proton polarization-transfer coefficients. Then combinations may be created (in the approximation where Oleb = O,,, the excitation energy vanishes, and distortions are not important), such as [B1 821

1.0

0.6

Fig. 7 - Measurements of the polarization 0.6

1 1 1 1 1 1 1 1 1 1 1 - - - -

cc-. 0.4 - transfer coefficient D s s for the

160(p,p')160 reaction to the 4-, T = 1 0.2 - stretched state at 18.98 MeV. The data is DSS. 0.0 - from 200 MeV (open circles) [Ol 851 and 350 MeV (dots) [La 89). Impulse approx- -0.2 - imation calculations for 200 (dashed) and -0.4 - 350 MeV (solid) utilize the free Franey- -0.6 - Love interaction [Fr 851.

-0.0 - - -1 .o 1 1 1 1 1 1 1 1 1 1 1

0 100 200 300 400 500 600

q (MeV/c)

C6-92 COLLOQUE DE PHYSIQUE

which are separately sensitive to the spin-longitudinal and transverse nuclear structure functions, xL and xT, and the corresponding KMT [Ke 591 amplitudes, E and B. The unpolarized cross section is ao. A plot of D1 and Dz for the 160(p,p')160, 4- transition is shown in figure 8 along with calculations based on the Love-Franey [Fr 851 and density-dependent Bonn [Na 841 interactions.

Numerous authors [CO 87, for example] have calculated an enhancement of the spin-longitudinal response over the simple predictions shown in figure 8 of a particle-hole model. Instead, that spin combination is suppressed experimentally in favor of the one containing the transverse amplitude. This result is similar to

I I I I I I I I I I - - -

D2 - - -

I I I I I I I I I 0 l 0 20 30 40 50

Fig. 8 - Preliminary measurements for the polarization transfer combinations D1 and D2, as discussed in the text, for the 160(p,p')160 reaction to the 4-, T = 1 state at 18.98 MeV. The proton bombard- ing energy is 200 MeV. The impulse ap- proximation calculations use the Franey- Love [Fr 851 and the density-dependent Bonn [Na 841 interactions.

earlier observations from LAMPF [Ca 841 that failed to show a expected pion-like enhancement of the nuclear response.

Brown and Rho [Br 891 have suggested that there are additional medium modifications, arising from the effective nucleon mass and exchange current corrections, to the meson exchange model of the tensor interaction. One prediction of this model is a large (~1.6) increase in the p-meson coupling, something that may also explain the location [CO 901 of l+ strength in 'aspb. Figure 9 shows a simple model of the momentum transfer dependence of the tensor force using

30 - 20 -

Fig. 9 - Momentum transfer dependence 10 - of the effective isovector tensor interac- tion based on a simple model of rr and VT -io - p exchange. The solid (dashed) curves include (omit) an enhancement to the p- meson coupling strength.

-40 - -50

\-.____----* - - -60 - I I I I l I

0 l 2 3

q (fm-l)

where q is the momentum transfer, m is the meson mass, and f is the meson-nucleon coupling constant. At momentum transfers where the measurements shown in figure 7 are available, the enhancement (dashed to solid curve) substantially reduces the strength of the tensor interaction. Figure 10, which compares a free interaction calculation with (solid) and without (dashed) this change, indicates by its improved agreement that this modification is helpful.

Fig. 10 - Angular distribution of the po- larization transfer coefficient Dssr in the 160(p,p')170 reaction to the 4-, T = 1 state at 18.98 MeV. The proton bombard- ing energy is 200 MeV. The solid (dashed) calculations use. the interaction of [Fk 851 modified (unchanged) by the enhance- ment to the p-meson coupling.

The two 4-, T = 0 transitions in 160(p,p')160 at 17.74 and 19.80 MeV are admixed with the T = 1 [Ca 831. Recent measurements of DNNt at IUCF [Op 901 showed similar values for the two states while impulse approximation calculations showed larger differences (dashed lines in figure 11) that originate in the isospin mixing. The weaker tensor force from the modified model reduces the effects of this mixing on DNNr, explaining the small observed experimental difference. Unlike studies of bound state excitation energies, angular distributions of polarization transfer observables give us the chance to look at the momentum transfer dependence of these changes.

17.74 MeV 19.80 MeV

Fig. 11 - Angular distributions of f iN, for the T = 0 transitions in 160(p,p')160 at 17.74 and 19.80 MeV. The proton bombarding energy is 200 MeV. The solid (dashed) calculations use the interaction of [Fr 851 modified (unchanged) by the enhancement to the p-meson coupling.

C6-94 COLLOQUE DE PHYSIQUE

While quantities such as D1 and Dz are useful in assessing the size of the tensor interaction, it is important to stress that this does not exhaust the information present in proton-induced polarization transfer measurements, nor does it represent the end of the difficulties we have with understanding the effective interaction and the structure of the states excited through it. Measurements of quantities such as the analyzing power, induced polarization P, and some of the in-plane transfer coefficients, DSL~ and D ~ s l , are also sensitive to the relative phase among the central, spin-orbit, and tensor amplitudes [MO 821. Specific combinations, such as P - A and DSLt + DLS,, are sensitive to exchange contributions and the presence of nuclear currents [Lo 841. In cases where the transition density is isospin mixed, new variations appear for all of the spin observables. Additional information is available if we also detect the y-ray from the decay of the state excited in such transitions [Pi 901.

Measurements at IUCF have recently been completed for the cross section and analyzing power for the T = 0 and T = 1, O+ -t 0- transitions in 160(p,p')160 at 200 MeV [Sa 891. These kinds of studies are attractive since the final state spin constrains the pertinent structure to only the spin-dependent longitudinal transition density (not observed in electron scattering), and the analyzing power and spin rotation functions vanish unless the model is relativistic (contains coupling through the Dirac lower components) or contains explicit exchange. In figure 12 the T = 0 transition cross section and analyzing power are shown. Both non-relativistic (using the interaction of [Fr 851 with exchange) and relativistic [Ro 891 calculations closely resemble each other and not the measurements.

Fig. 12 - Cross section and analyzing power angular distributions for the 200 MeV proton inelastic excitation of the 0-, T = 0 state at 10.957 MeV in 160. The solid (dashed) curves are impulse ap- proximation calculations that utilize a non-relativistic (relativistic) model.

Again for the T = 0 and T = 1, l+ transitions in I2C, measurements of some coefficients, such as D N N ~ which is sensitive primarily to the size of the interaction components, agree well while other combinations, such as P - A , do not, as shown in figure 13. There have been interactions that have reproduced more closely the trends of P - A, such as a relativistic calculation for the T = 0 transition [Ro 891 and the Paris-Hamburg

Fig. 13 - Angular distributions of the po- larization transfer coefficient DNNc and the P - A difference for the l+ transitions at 12.71 and 15.11 MeV in I2C. The pro- gon bombarding energy is 200 MeV. The solid curves use the interaction of [Fr 851. The long and short dashed curves use the free and density-dependent Bonn interac- tion [Ma 891.

T=O, 12.71 MeV T=l, 15.11 MeV 1.0

0.0

0.6

0.4

1 .o

0.0

0.6

0.4

0.2

P-A 0.0

-0 .2

-0.4

-0.6

-0.8

-1.0

interaction [Ge 831 for the T = 1; unfortunately neither calculation leads to a more consistent description of all the observables. The general conclusion is that while the main aspects of the effective interaction and its role in nuclear excitations is well understood, the more subtle features, including exchange or the larger momentum transfer regions, are not well described in even our best models, and should be the subject of continued experimental and theoretical work.

Among the contributions to this meeting is the first announcement [MO 901 of a polarization transfer measurement in deuteron inelastic scattering as a way to locate isoscalar spin-flip strength. The A S = 1 spin-flip probability for spin-l, I I , ,

S1 = [4 - A,, - P" - 2Ki: ]/g ,

Fig. 14 - The inelastic 12C(d,d') spectrum at O = 4" and E d = 400 MeV. The lower panel shows the spin-flip cross section based on the S> observable.

5 10 15 20

Excitation energy (MeV)

C6-96 COLLOQUE DE PHYSIQUE

was changed for experimental reasons to

to make a quantity measurable with the vector and tensor polarized beam at Saturne [Ar 881 and the focal plane polarimeter POMME [Bo 901, which is primarily sensitive to the vector polarization component of the scattered deuterons. The results for 400 MeV deuterons are shown in figure 14. They exhibit very small values of S? for the 2+ (4.44 MeV), 0+ (7.65 MeV), and 3- (9.64 MeV) AS = 0 states, and larger values for the l+ (12.71 MeV) A S = 1 state. Such information could form an important complement to studies with the (p,n) reaction, which is primarily sensitive to isovector transitions, and (p,pf), which is sensitive to both. Further, the use of a spin-l deuteron beam opens the possibility to look for two-particle-two-hole correlations through the observation of A S = 2 strength.

What is needed is a different polarimeter, perhaps based on back-angle d+p scattering, that is sensitive to the tensor deuteron polarization. Figure 15 shows the A, and A,, analyzing powers at two energies. Since these analyzing powers arise from the interference of the amplitudes for particle exchange and quasi-elastic scattering, they have very little energy dependence and can be used with thick analyzers.

d+p elastic scattering

::: 'j 0 .5

Fig. 15 - Angular distribution measure- ments of the vector A, and tensor Ayy analyzing power for d f p elastic scatter- ing at a deuteron energy of 79 MeV [St 831 and averaged over 93-145 MeV [Ca 901.

I am indebted to the generous help of J. M. Cameron, T. B. Clegg, H. Clement, J. J. Kelly, W. G. Love, L. Ray, R. L. Varner, B. von Przewoski, R. L. Walter, and Y. Wang in the preparation of this talk. This work was supported in part by the US National Science Foundation.

A1 90 M. A. Alohali, et al., contribution to this conference. Ar 88 J . Arvieux, et al., Nucl. Instrum. Meth. A273 (1988) 48. Ar 90 H. F. Arellano, et al., Phys. Rev. C 41 (1990) 2188; contribution to this conference. Be 69 F. D. Becchetti and G. W. Greenlees, Phys. Rev. 182 (1969) 1190. B1 75 J. S. Blair, M. P. Baker, and H. S. Sherif, Phys. Lett. B60 (1975) 25. B1 82 E. Blezynski, M. Blezynski, and C. A. Whitten, Jr., Phys. Rev. C 22 (1982) 2063. Bo 90 B. Bonin, et al., Nucl. Instrum. Meth. A288 (1990) 379; and Nucl. Instrum. Meth. A288 (1990)

389. Br 84 G. E. Brown, Spin Ezcitations in Nuclei, ed. F. Petrovich, et al., (Plenum, New York, 1984) p. 233. Br 89 G. E. Brown and Mannque Rho, Phys. Lett. B222 (1989) 324; and G. E. Brown and Mannque Rho,

"In Medium Stiffening of the Nucleon-Nucleon Spin-Isospin Interaction", private communication. Ca 84 T. A. Carey, et al., Phys. Rev. Lett. 53 (1984) 144. Ca 90 J. M. Cameron, private communication; see also M. Garcon, et al., "Spin Observables of Nuclear

Probes," ed. C. J. Horowitz, et al.'(Plenum, New York, 1988) p. 357. C1 83 B. C. Clark, et al., Phys. Rev. Lett. 50 (1983) 1644. C1 89 M. Clajus, et al., Nucl. Instrum. Meth. A281 (1989) 17. CO 87 J . Cohen, J. Phys. G: Nucl. Phys. 13 (1987) 1497. CO 89 E. D. Cooper, Nucl. Phys. A495 (1989) 483. CO 90 G. CO' and A. M. Lallena, Nucl. Phys. A510 (1990) 139. Cr 90 R. Crespo, et al., Phys. Rev. C 41 (1990) 2257.

Cr 90a R. Crespo and J. A. Tostevin, to be published. El 90 Ch. Elster, et al., Phys. Rev. C 41 (1990) 814. Er 87 M. Ermer, et al., Phys. Lett. B188 (1987) 17. Er 89 M. Ermer, et al., Phys. Lett. B224 (1989) 40; and contribution to this conference. Er 90 M. Ermer, et al., contribution to this conference. Ev 90 P. D. Eversheim, et al., Phys. Lett. B234 (1990) 253. Fe 60 H. Feshbach, Nuclear Spectroscopy, Part B, ed. F. Ajzenberg-Selove (Academic Press, New York,

1960) p. 1033. Fr 85 M. A. Franey and W. G. Love, Phys. Rev. C 31 (1985) 488. Ge 83 H. V. von Geramb, The Interaction between Medium Energy Nucleons in Nuclei, ed. H. 0. Meyer

(American Institute of Physics, New York, 1983) p. 44. Ha 86 W. Haeberli, J . Phys. Soc. Jpn. 55 (1986) Suppl. p. 543. Ha 90 S. Hama, et al., Phys. Rev. C 41 (1990) 2737. Ho 68 B. Hoistad, et ab, Nucl. Phys. A119 (1968) 290. Ka 87 0. Kamigaito, et al., RCNP Annual Report - 1987. Ke 59 A. K. Kerman, H. McManus, and R. M. Thaler, Ann. Phys. 8 (1959) 551. Ke 72 P. W. Keaton, Jr., et al., Phys. Rev. Lett. 29 (1972) 880. Ke 90 J . J . Kelly, et al., Phys. Rev. C 41 (1990) 2504 and references therein. Ko 89 R. E. Kozack, et al., Phys. Rev. C 40 (1989) 2181. La 89 B. W. Larson, M. S. Thesis, Simon Fraser University, 1989. Lo 81 W. G. Love and M. A. Franey, Phys. Rev. C 24 (1981) 1073. Lo 84 W. G. Love and J. R. Comfort, Phys. Rev. C 29 (1984) 2135.

Ma 82 C. Mahaux and H. Ng8, Nucl. Phys. A378 (1982) 205. Ma 89 R. Machleit, private communication.

Ma 89a C. Mahaux and R. Sartor, Nucl. Phys. A493 (1989) 157. Mi 86 C. A. Miller, et al., Phys. Lett. bf B169 (1986) 166. MO 82 J. M. Moss, in Spin Ezcitations in Nuclei, ed. F. Petrovich, et al. Plenum, New York, 1984 p. 355. MO 90 M. Morlet, et al., contribution to this conference. Mu 87 D. P. Murdock and C. J. Horowitz, Phys. Rev. C 35 (1987) 1442. Na 84 K. Nakayama, et al., Nucl. Phys. A431 (1984) 419. Na 86 T. Nakano, et al., RCNP Annual Report 1986, p. 3. Na 90 T, Nakano, et al., Phys. Lett. B240 (1990) 301. 01 85 C. Olmer, Antinucleon- and Nucleon-Nucleu~ Interactions, ed. G. E. Walker, et al., (Plenum, New

York, 1985) p. 261. Op 90 A. K. Opper, contribution to this conference. Pi 90 J. Piekarewicz, et al., Phys. Rev. C 41 (1990) 2277.

C6-98 COLLOQUE DE PHYSIQUE

Pr 90 B. von Przewoski, et al., to be published; contribution to this conference. Ra 90 L. Ray, Phys. Rev. C 41 (1990) 2816. Ro 89 E. Rost, private communication (computer program DREX). Sa 86 F. D. Santos, et al., J. Phys. Soc. Jpn. 55 (1986) Suppl. p. 942. Sa 89 R. Sawafta, e t al., IUCF Scientific and Technical Report, May 1988 - April 1989, p. 19. Se 85 N. van Sen, et al., Phys. Lett. B156 (1985) 185. Sh 83 J. R. Shepard, et al., Phys. Rev. Lett. 50 (1983) 1443. Sr 89 J. Sromicki, et al., Phys. Rev. C 40 (1989) R1111. St 83 E. J. Stephenson, et al., IUCF Scientific and Technical Report - 1983, p. 58.

Th 76 W. J. Thornpson, et al., Phys. Lett. B62 (1976) 245. To 90 W. Tornow, Z. P. Chen, and J. P. Delaroche, to be published in Phys. Rev. C . Va 90 R. L. Varner, et al., to be published.

Wa 90 Y. Wang, private communication. Wi 90 S. W. Wissink, et al., contribution to this conference. Yo 87 M. Yosoi, et al., RCNP Annual Report - 1987.