SPIN/ISOSPIN/MULTIPOLE RESPONSE OF THE NUCLEAR CONTINUUM USING HADRON SCATTERING

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SPIN/ISOSPIN/MULTIPOLE RESPONSE OF THE NUCLEAR CONTINUUM USING HADRON

SCATTERING

F. Baker

To cite this version:

F. Baker. SPIN/ISOSPIN/MULTIPOLE RESPONSE OF THE NUCLEAR CONTINUUM US- ING HADRON SCATTERING. Journal de Physique Colloques, 1990, 51 (C6), pp.C6-185-C6-190.

�10.1051/jphyscol:1990615�. �jpa-00230880�

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SPIN/ISOSPIN/MULTIPOLE RESPONSE OF THE NUCLEAR CONTINUUM USING HADRON SCATTERING

F.T. BAKER

Department of Physics and Astronomy, The University of Georgia, Athens, G A 30602, U.S.A.

%sum6

-

Des rbultats rkents des experiences ($,$l) et (&if1) 1 LAMPF, TRIUMF, et SATURNE sont r6sumes.

Abstract

-

(&if')

experiments at LAMPF, TRIUMF, and SATURNE are reviewed.

1

-

INTRODUCTION

In recent years a program to measure spin observables for excitation energies (U) in the nuclear continuum, 10 MeVsw$30 MeV, for inclusive inelastic hadron scattering has resulted in a large base of data for a wide range of targets (12<A<208) and projectile energies (200<EP<800). These data, mostly for cross sections dZu/dRdE (U) and the spin-flip probability S,, for the ($,$I) reaction, have proven very useful for deducing /1,2/ the relative AS=O and AS=l responses of the continuum and for determining /3,4/ the multipole contents of the AS=O and AS=l spectra. More recently data have been acquired which allow separation of S,, into its spin-longitudinal (0.q) and spin-transverse (mq) components, SL and ST. In addition, (a,?!') experiments 151 have been begun a t SATURNE the purpose of which is to separate the AT=O and AT=l responses of the AS=l spectrum. In this talk I will give an overview of all these results.

The talk will be divided into three parts. First I will discuss the systematics of the spin response of the continuum and present our results for the longitudinal/transverse separation of S,, for 4oCa. I will then turn to the multipole decomposition of the angular distributions of the spectra and present evidence for collectivity of spin excitations, particularly the spin dipole. Finally, I will discuss the preliminary results of our (?!,a1) experiments which are aimed at an isospin decomposition of the spin excitations; a more complete discussion of these results was presented earlier in this conference by M. Morlet.

2

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SPIN RESPONSE OF THE CONTINUUM FROM

(8.8')

EXPERIMENTS

Experiments have been performed at LAMPF and TRIUMF at incident energies of 200, 290 318, 580, and 800 MeV on targets 'ZC, 40Ca, 44Ca, 48Ca, 54Fe, QoZr, and zo8Pb. Our published analyses ]1,2/ have focused on the relative spin response as a function of momentum transfer g; here I will instead look at the systematics of the spin properties as a function of qR since many of the features observed are believed now to be related to the concentration of AS=O strength at low W. Figure l(a) typifies all data with q R ~ 2 : S,, is, at high W, substantially larger than the isospin-averaged free nucleon-nucleon (NN) value. This implies that a Fermi-gas model of the nucleus is inappropriate for such (q,w) and that the AS=l nuclear response is substantially enhanced relative to that of a Fermi gas. This relative enhancement of the AS=l strength is illustrated in Figure l(b) where the cross section for AS=O transitions (00) is seen to be only a small fraction of U; ug is given by

uo=u-usnn/. (1)

where cu is the spin-flip probability of AS=l transitions. We have approximated cu as being that for the (appropriately isospin averaged) value for the free NN interaction; this approximation has been shown /3/ to lead to excellent agreement with previous measurements of AS=O strengths.

A convenient way to quantify the qualitative features described above is t o introduce

111

the relative AS=l/(AS=l

+

AS=O) nuclear spin response R,:

b=f1/(fo+f1)

where (2)

fi=u(AS=i)/uf(AS=i) (3)

and uf is the cross section for free NN scattering. Under the assum tion that S,, is relatively insensitive to such things as distortions, Fermi motion, relativistic effects. etc. ?which will be examined in more detail below), one can write that ^'

fi/fo=[Snn/(a-snn )]/[of(AS=l)/ (4)

and R, may be conveniently calculated. R, is thus the raction of the total nuclear response which is AS=l.

Figure 2 shows Rs plotted for a wide range of proton energies and targets for q R ~ 2 . For all nuclei where we have data the response of the nuclear continuum at high w for q R ~ 2 is greater than 80% AS=l.

What is the origin of this enhancement of Rs at high w? Since a given AS=O multipole E will have its

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990615

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COLLOQUE DE PHYSIQUE

12c(p',p"), 3 1 8 MeV

free NN ,S,

F i g u r e 1 F i g u r e 2

peak cross section at q R ~ f l m , e=2, which will peak at qR~2.4, should contribute little to the cross section at qR-2 as should higher multipoles. The e=1, AS=O cross section, due to the giant dipole resonance, is excited primarily via Coulomb excitation and peaks at q R ~ 0 so it also should contribute little to the cross section. The enhancement of Rs is therefore not surprising at qRw-2.

Rs for qR~2.4 is shown in Figure 3; here the same large enhancement is seen for all nuclei except 12C.

L

O 2 5 30 ₃₅ 40

o(MeV)

The enhancement for heavier nuclei can also be understood here even though the AS=O quadrupole angular distribution should be peaking near qR~2.4: for heavy nuclei it is well known that there.is a concentration of a large fraction of the total AS=O quadrupole strength at low win the giant quadrupole resonance (GQR). For lighter nuclei like 12C, however, a well-defined GQR has not been observed; we have multipole decomposed our a0 data for 12C and the distribution of AS=O quadrupole strength deduced is shown in Figure 4; although the errors are large, it is clear that there is substantial quadrupole strength across the region where the heavier nuclei show enhancement which explains the lack of enhancement of Rs for 12C at qR~2.4.

For larger qR (our data extend up to qR~3.7) Rs decreases and appears to approach the Fermi-gas response, Rs=0.5.

I would now like to turn to the results of the longitudinal/transverse separation of the spin response.

40~a($,;') at E,=580 MeV was done at LAMPF; the spin observables DNN, DI,T,, and D,, were measured.

-- - -

The longitudinal (SL) and transverse (ST) spin-flip probabilities are given b y

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At this stage, let us investigate the possible effects of Fermi motion on the predicted SL and ST values.

O l , , , , , ^m ^, ^, ^, ^l ^, ^, , , , , , l

025 30 35 40

w(MeV) F i g u r e 5

In principle, this requires inte rating and averaging over all values of the momentum of the struck nucleoli.

a

A simpler method, and one W ich has been shown /6/ to be a good approximation to full averaging, is to evaluate the t-matrix in the "optimal frame" for each value of q, U. This is done by evaluating the t-matrix everywhere for an effective laboratory kinetic energy

Teff=(EkE - k - ~ ~ ~ t - m ~ ) / m

Popt (7)

where the optimal momentum is given by

P o . t = + [ l + / ~ ] , (8)

Ek is the total energy of the incident particle, and E is the energy of the nucleon with momentum popt.

Popt

T,ff varies rapidly with w and therefore the nature of the effect of using the "optimal frame" depends on the way in which the t-matrix varies with energy. We have used the Lov-Franey 171 t-matrix and use a linear interpolation between the 515 MeV and 650 MeV sets to determine the t-matrix at a given Teff. The results are shown in Figure 5 by the dashed curves. As can be seen, the Fermi averaging has a quite large effect on ST but has little effect on SL.

Finally, one should ask what effects distortions have on the spin observables. It can be anticipated that the effects will not be negligible because of studies we have done /4/ on microscopic DWIAJPWIA calculations which indicate that purely isovector longitudinal transitions have cross sections which are less reduced by distortions by a factor of nearly 4.0 compared t o other transitions; this is because of the longer range of the isovector longitudinal amplitude of the t-matrix compared to other amplitudes. One would therefore expect a considerable enhancement of SL and a slightly reduced ST. Recent RPA calculations performed by Unkelbach indeed show that the distortions do have these qualitative effects, SL increasing by approximately a factor of three compared to plane wave calculations. Similar relults have been obtained in preliminary calculations by Castel. It now appears that a calculation including both distortions and Fermi averaging will quantitatively describe our data. We therefore feel that we are approaching the point where the enhanced AS=l response is understood.

3 - MULTIPOLE DECOMPOSITION OF THE DATA

To determine the multipole content of the AS=l spectrum the spin-flip cross section u S F = d n n is calculated. usF is, to an excellent approximation, due only to AS=l transitions since AS=O transitions have SnnwO at intermediate energies. Shown in Figure 6 are uSF data for fiab=5° for proton scattering from 40Ca (319 MeV), 44Ca (290 MeV), and 4sCa (318 MeV). The striking thing about these data is that usF is

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Ca(i),i)') E,-300 M e V

o (MeV)

virtually identical for all three nuclei even though N increases by nearly 50%. This constancy of aSF is in marked contrast to ( p p ) cross sections /8/ on 40Ca and 48Ca where U in the continuum increases by roughly a factor of two when 8 neutrons are added to 40Ca. This can be qualitatively understood in terms of simple shell-model arguments. For (p,n), no transitions possible in 40Ca are blocked by adding neutrons to the f orbital whereas new transitions become possible so a increases; for (p,pl), transitions from the 40Ca core into 712

the uhI2 shell become blocked and, evidently, this loss of cross section is balanced by added transitions from the uhI2 orbital.

In order t o perform a multipole decomposition of the data we have applied an extension /4/ of the schematic model originally proposed by Boucher et al. /g/. This model uses the spin-isospin sum rules of Suzuki / l 0 and therefore gives an indication of the collectivity of observed spin excitations. The model uses deformed

d

ensity form factors and the Love-Franey /7/ NN force; the predicted angular distributions thus reflect both the multipole and the q dependence of the NN force. The angular range of our data precludes determination of multipoles C>2 but a proposed experiment at LAMPF will extend the angular range for 40Ca. Shown in Figure 7 are predictions for 100% exhaustion at -20 MeV for the spin dipole (AL=l, AS=l, .JT=O-, 1-, 2-) and spin quadrupole (AL=2, AS=l, .JT=1+,2+, 3') resonances (SDR and SQR) in 44Ca;

these are isospin averaged and thus include both the isovector and isoscalar parts of the strengths. The calculations indicate that, althought the isovector strength will dominate, the contribution of the isoscalar strength is not negligible. The influence of the longitudinal isovector part of the force, which has a deep minimum near 81ab=10: is clearly seen for the angular distributions for the 0-, l + , and 3' states; if the t-matrix were independent of q, all angular distributions would resemble those for the natural parity states which are purely transverse. The data, at 3: 5': 7: 9: and 12: are not able to distinguish among the various J's and the angular distributions used in the analyses are the sums for each multi~ole labeled "net" in Figure 7.

Figure 8 shows the results of doing ^~2minimization searches on each 2 MeV bite of our data. There is a pronounced concentration of spin dipole strength the total strength of which is about 150% of the sum rule;

this is indicative that nearly all of the strength is exhausted since the Suzuki sum rule does not include meson-exchange contributions. The summed strength for the spin quadrupole is about 200%, more than would be expected; however, since higher multipoles were not included in the analysis, it is likely that much of this strength is due to contributions from other multipoles. We conclude that, at least for the spin dipole resonance, collectivity (in the sense of there being a concentration of a large fraction of the sum rule strength) of spin excitations exists in nuclei.

Although our results of the SQR are subject to large uncertainties as noted above, there is a systematic decrease with increasing A in the total deduced AL=2, AS=l strength for 40Ca, 44Ca, and 4SCa.

This is in marked contradiction to a predicted /11/ large increase in SQR strength at 48Ca.

These experiments were begun with one of the primary motivations being to search the continuum for missing M1 strength. This has proven to be much more difficult than anticipated since, with increasing U, the momentum transfer at the smallest angles where measurements can be made increases, thus rendering M1 strength "invisible". (It now appears likely that, even if measurements were made at

oO,

detection of small fractions of the M1 strength would not be feasible.) In previous experiments /12,13/ M1 strength has been measured in 44Ca. The angular distributions of our data for 8 MeV<w<l4 MeV show rising a at small

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angles; we therefore analyzed lower W data including the angular distribution for the M1 transition

~ 4 ~ ) - ~ f r j ~ ) u f s , ~ using a DWIA calculation. The results are shown in Figure 9; the larger uncertainties with increasing W are indicative of the difficulty in extracting small M1 strength at large W, particularly in the presence of spin-dipole strength. Our results, 34*11% for 7 MeV<w<ll MeV and 51*14% for 7 MeV<w<l3 MeV are in good accord with the earlier measurements 112,131. If we sum up to 20 Mev, we find 103*38% which is an indication that perhaps all M1 strength can be found at relatively low W.

Similar multipole decompositions are also done on the a0 spectra. It is our feeling that such analyses are the best way to study the AS=O giant resonances since it is clear that the main "background" under the giant resonances, which has previously been treated semiempirically at best, is due to the AS=l transitions.

To improve the use of this method will require data with a larger range of qR.

4 - ISOSPIN DECOMPOSITION OF THE CONTINUUM

As noted above, the schematic model suggests that isoscalar transitions are not negligible in proton scattering; in fact, if isoscalar transitions are not included in our multipole analyses, total spin-dipole strengths deduced far exceed the total amount of strength expected. Nevertheless, the isovector is sufficiently dominant that our conclusions regarding spin collectivity and distributions of spin dipole strength can only be taken seriously for isovector strength. There is practically no information on AT=O, AS=l strength in the continuum. In order to investigate the isospin composition of the continuum a program of inelastic deuteron scattering has been initiated a t the SATURNE syncrotron. The initial experiment, 12c(8,d1) at Ed=400 MeV, was completed last autumn. 12C was chosen because of well-known, strongly excited, isolated isoscalar spin transitions a t 12.71 MeV ( l + ) and 18.3 MeV (2-). Deuterons should excite only isoscalar transitions but both AS=O and AS=l (and possibly AS=2). To isolate the AS=l part of the spectrum we seek an analogy of S,, for deuterons. It may be shown that the probability for transferring one unit of spin to the nucleus is given by

P(1)=(8-2A YY -2PU4K;;)/18. (9)

This would require a tensor polarimeter to measure. Since we have available only a vector polarimeter, POMME 1141, we make the following approximations:

P(2)eo (10)

PYYeA

YY (11)

which lead to

~ ( l ) e ( 4 + 2 A ~ ~ - 6 ~ ; ) / 3 . (12)

One of the purposes of the 12C experiment was to test these approximations. Shown in Figure 10 are the spectra for ^Uand uP(1) measured for 400 MeV deuteron scattering at 4' from 12C; as can be seen, the known AS=O states (2+, O+, 3-) are very effectively suppressed. There is no evidence in the spectrum for any known isovector transitions (particularly the l+ state at 15.1 MeV). Considerable AS=l, AT=O strength is evident in the continuum but not at 20 MeV where evidence for the isoscalar spin dipole has been previously reported 1151. We plan to continue these investigations next by acquiring data for 4oCa which should compliment our

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w (MeV) Figure 10

(5,;') results. However, considerable development of microscopic and/or schematic-model calculations for deuterons will be needed to quantitatively analyze these data.

Finally, there is another possibility for separating isoscalar and isovector components of the spectra.

One could measure ~ S n n for

(if,;)

which should proceed only via AT=l for a T=O target. The 40~a($,if) experiment at 319 MeV has been approved a t LAMPF and should provide further data to help elucidate the nature of isoscalar spin excitations.

5 - CONCLUSIONS

The enhanced spin response at high W in nuclei now appears to be understandable in terms of the concentration of AS=O strength at low U. Separation of the spin response into its transverse and longitudinal parts is consistent with this interpretation in light of preliminary RPA calculations. The multipole decomposition of US,, reveals a spin dipole resonance which exhausts a large fraction of the sum rule and therefore is evidence for spin collectivity in nuclei. New experiments to study isoscalar spin excitations have been shown to be feasible and will proceed.

ACKNOWLEDGEMENTS

The work reported here has resulted from the efforts sf very many people: R. Abegg, D. Beatty, L. Bimbot, B. Bonin, B. Castel, X. Y. Chen, V. Cupps, C. Djalali, J. C. Duchazeaubeneix, G. W. R. Edwards, R. W. Fergerson, C. Glashausser, A. Green, J. Guillot, 0. Hausser, R. Henderson, K. Hicks, K. P. Jackson, R. Jeppesen, K. Jones, G. Kumbartzki, H. Langevin-Jolliet, J. Lisantti, W. G. Love, N. Marty, C. A. Miller, M. Morlet, S. Nanda, L. Rosier, R. Sawafta, B. Storm, E. Tomasi-Gustafsson, W. Unkelbach, J. Van de Wiele, M. Vetterli, J. Wambach, A. Willis, and S. Yen.

The work of the author has been supported by the United States Department of Energy.

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/a/

F. T. Baker et al., Phys. Rev. C40 (19891 18'77.

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