Elastic scattering of polarized protons by 6Li

Nuclear Physics A496 (1989) 189-204 North-Holland, Amsterdam

ELASTIC SCATI'ERING OF POLARIZED PROTONS BY 6Li* (I). Optical-model analysis M. HALLER, M. BETZ, W. K R E T S C H M E R , A. R A U S C H E R , R. S C H M I T T 1 and W. S C H U S T E R

Tandemlabor der Universitiit Erlangen-Niirnberg, Erlangen, Fed. Rep. Germany Received 9 August 1988 (Revised 20 December 1988)

Abstract: The differential cross sections and the analyzing power for the 6Li(p, p) elastic scattering were measured over the proton laboratory-energy range from 1.6 to 10 MeV (tr) and from 2.8 to 10 MeV (A). The data are well described by optical-model calculations, only if the geometrical parameters are allowed to depend strongly on the energy. The magnitudes of the volume integrals and the root mean square radii are in good agreement with predictions of microscopic theories. Nevertheless, there are resonant structures in the energy dependence of these parameters as well as in the experimental excitation functions. They correspond to a well known resonance at E~m = 1.6 MeV and to a broad resonance structure at E~m = 4 MeV, which may be identified as a superposition of resonances recently predicted by refined resonating-group calculations. NUCLEAR

R E A C T I O N S 6Li(polarized p , p ) ; E = l . 6 - 1 0 MeV; measured tr(E, 0), A(E, 0); deduced optical-model parameters. Enriched target.

1. Introduction Since some years, the A = 7 mirror nuclei VBe and 7Li have been the object of many experimental and theoretical investigations. Besides the general interest in developing nuclear models for the structure of these nuclei, there are special reasons: The reaction 6Li(n, t)4He is the dominant breeding process for tritium in fusion reactors, and the capture 3He(c~, y)7Be is part of the pp cycle and a key reaction for the understanding of the solar neutrino problem ~). Due to the difficulties of direct experimental studies at the very small energies of interest, it is important to develop a microscopic model for the structure of 7Be and 7Li, which describes the experimental thresholds and resonances in a wide energy range. This has been done by H o f m a n n et al. 2.3) in the framework of refined multichannel and multistructure resonating-group calculations, which predicted some additional resonances near 10 MeV excitation energy in 7Be. Some of these predicted resonances with J " = 1-, 3 or ~-, and T = ½, should be found in the elastic * Supported by the Deutsche Forschungsgemeinschaft. Present address: FAG Kugelfischer, Erlangen, Fed. Rep. Germany. 0375-9474/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

190

M. Hailer et al. / Elastic scattering (1)

scattering of protons at 6Li. Measurements of this reaction may serve as a test for the theoretical resonating-group calculations. Usually, the optical model formalism is applied to scattering processes, which are dominated by the direct reaction mechanism, i.e. mainly for heavy target nuclei and medium energies. As recently suggested by Dave and Gould in an investigation of unpolarized neutron scattering cross sections 4), the optical model application may be extended to small mass numbers and small energies, even if broad resonances are present. Another interesting question is, whether the predictions of microscopic models 5), which are originally designed for large mass numbers, agree with the results of optical-model calculations for 6Li(p, p) scattering. If there are resonances, they should influence the results of the optical-model calculations, which will be discussed in the following sections. More detailed examination of the resonance parameters can be achieved by a complicated phase-shift analysis, which is subject of the subsequent paper.

2. The experiment Since the amount of existing polarized data was very poor, we measured complete angular distributions (laboratory angles between 30 ° and 165 ° in steps of 5°) of the differential cross section and the analyzing power of 6Li(p, p) scattering in a wide lab-energy range (1.6-10 MeV and 2.8-10 MeV, respectively) and in small steps (200 keV steps below 3 MeV, 100 keV steps between 3 and 6 MeV, 500 keV steps above 6 MeV). The measurements were carried out at the Erlangen Tandem accelerator facility. The polarized proton beam was produced by a Lamb-shift type ion source, accelerated by an EN Tandem and focussed into a 4~- scattering chamber, which is shown in fig. 1. A long collimator, consisting of a scattering and an antiscattering diaphragm of 3.0 and 3.2 mm diameter, respectively, guided the beam to the exchangeable target. Sixteen surface-barrier detectors were mounted in steps of 10° on two rotatable rings, which were turned by 5° between two runs. In this way, 28 scattering angles between 30 ° and 165 ° in steps of 5° could be measured in two runs, with overlaps at 90 ° and 95 °. Collimators in front of each detector limited their solid angles to values between 0.012 msr (30 °) and 0.15 msr (160°); thus compensating the increase of the cross section at forward angles. Target current and beam polarization were measured on-line by a combination of 4He polarimeter and Faraday cup at the exit of the scattering chamber. The polarization was switched from up to down every 10 seconds, and the digitized beam current was accumulated and stored separately for each spin orientation. The beam current accumulation was stopped during the dead time of the corresponding ADC. Special difficulties arose from the target preparation, because Li is hygroscopic and forms quickly LifO and LiOH in the air. Initially, LiF on a backing of Ni was used, which caused problems because of interfering lines from inelastic scattering at F and Ni. These lines could be removed by using a sandwich target

M. Hailer et al. / Elastic scattering (I)

191

Fig. 1. View from above into the 4rr scattering apparatus.

A1-6Li-C, and, with further improvement, C-6Li-C. With this latter kind of target (50 ixg/cm 26Li), which had to be stored in vacuum, very clean spectra were obtained, as can be seen in fig. 2. The ~H and 160 background lines result from air moisture, which had penetrated through the very thin and porous carbon backings. The transmission through the Tandem accelerator decreases at small energies. Below 2.8 MeV proton energy, only the larger beam current of the unpolarized ion source was sufficient. So at these small energies between 1.6 and 2.6 MeV only cross-section measurements have been performed. The polarized beam had a constant (within : e l % ) polarization of typically 68%. Angle-dependent normalization factors, which depend primarily on the different solid angles of the detectors, were determined by elastic scattering of a low energy (3.4 MeV) proton beam at a thin Au target. This scattering cross section is well described by the Rutherford formula. Normalization errors and systematic errors, arising from spin correlated flipping of the beam axis, were estimated to be small compared with the statistical errors which include the errors from background subtraction in the spectra. As the exact determination of the target thicknesses of the 6Li targets was not practicable, we got the overall normalization of the absolute cross section by adjusting our data between 1.8 and 2.8 MeV to corresponding data of McCray 6). The data of ref. 6) include

192

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M. Hailer et al. / Elastic scattering (I) SO00

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very small energies ( E >~ 0.4 MeV), a n d t h e r e f o r e are well d e s c r i b e d by the Rutherf o r d f o r m u l a , at least at f o r w a r d angles. This is not the case for o u r d a t a starting at E = 1.6 MeV. T a k i n g into a c c o u n t an overall n o r m a l i z a t i o n error o f 5% given in ref. 6), we d e t e r m i n e d a 7% overall n o r m a l i z a t i o n e r r o r for o u r cross section data. The a n g u l a r d i s t r i b u t i o n s o f the d a t a are c o m p a r e d with o p t i c a l - m o d e l (see sect. 3) a n d p h a s e - s h i f t c a l c u l a t i o n s (see the f o l l o w i n g p a p e r ) . S o m e insight into r e s o n a n c e structures can be o b t a i n e d from e x c i t a t i o n functions, which are d i s p l a y e d in fig. 3. The differential cross section shows a p e a k b e l o w 2 MeV, which has a l r e a d y been a n a l y z e d , for e x a m p l e by M c C r a y 6), a n d a s s i g n e d to be a ~5 resonance. A b r o a d e r structure a p p e a r s at 4-5 M e V a n d indicates a d d i t i o n a l r e s o n a n c e s , which have been s u g g e s t e d b y recent r e s o n a t i n g - g r o u p c a l c u l a t i o n s 3). Very s i m i l a r is the s h a p e o f the total elastic cross section (without R u t h e r f o r d scattering), which is shown in fig. 4. It has b e e n c a l c u l a t e d in a p h a s e - s h i f t analysis, which fitted all e x p e r i m e n t a l data.

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where f is the normal W o o d s - S a x o n form factor

f(r, r~, a,) = [1 + e x p ( r - r~A'/3)/ax] ' The Coulomb-potential Vc(r) corresponds to the potential of a homogeneously charged full sphere with the radius reAl/3; Vo, WD and Vso are the depths of the real, imaginary, and spin-orbit potential, respectively. The spin-spin interaction, which is comparatively small and has little influence on ~r and A, has been neglected. In general, the imaginary part of the optical potential consists of a volume and a surface term. The former has been omitted here, because at energies far below 30 MeV only absorption at the nuclear surface is important. Also an imaginary part of the spin-orbit potential turned out to be unimportant for 6Li(p, p) scattering as well as in other earlier analyses of proton scattering (e.g. ref. 7)). in the case of low energy scattering on heavy target nuclei one usually calculates the compound nucleus contributions within the Hauser-Feshbach formalism. This procedure is not applicable to the light nucleus ++Li, because of its small level density; i.e. there are not enough levels within the energy resolution of the experiment and thus the usual statistical assumptions are not valid. In the absence of resonances the observables are described by an optical potential with an only weakly energy-dependent parameter set. If, however, resonances are present, a good description of all observables can probably be only achieved with strongly energy-dependent parameters. First the data were fitted for each energy separately, using the resulting parameters as starting values for the subsequent energy. The computer code G O M E L ~) was used, which also calculates errors of the parameters, according to a 10% increase of the X 2 type error function, and the correlation coefficients between them. In this first fitting procedure (I) the following parameters were kept fixed to avoid ambiguities: q, = 1.25 fm, ro = 1.20 fm, a~ = 0.40 fm, a .... = 0.40 fm. The other parameters were fitted simultaneously, with the exception of V,.o and r, .... which were kept fixed below 2.8 MeV, since at these energies only cross-section data, to which the spin-orbit parameters are not sensitive, have been measured.

196

M. Hailer et aL / Elastic scattering (1)

The resulting description of the data, as shown in fig. 5 (solid curves), is quite good; there is only a slight discrepancy in the analyzing power in the forward angular region at energies below 5 MeV, where resonances are predicted (compare the discussion of the excitation functions at the end of sect. 2). The resulting fit parameters of procedure (I) are shown in fig. 6 as function of c.m. energy. Below 3 MeV a resonance structure is seen in all but the (fixed) spin-orbit parameters. It corresponds to the 1.6 MeV resonance in the excitation functions discussed above. The value of the spin-orbit potential is larger than usual, but it was not possible to describe the data with a significantly smaller value. The real potential increases with energy, whereas the usual behaviour is a slight decrease ~). An attempt to fit the data in the usual way with linearly energy-dependent opticalmodel parameters was performed in procedure (II), where ~(0) and A(O) for E~ab = 3, 5, 7, and 9 MeV were analyzed simultaneously. To avoid ambiguities, the parameters were varied alternatingly over several fit runs. The resulting parameters are listed in table 1, and the description of the data is shown in fig. 7. It is of course not as good as from procedure (I), especially at very small energies, but the energy dependence of the potential depths is much more reasonable. Therefore, in a third procedure (III) the potential depths Vo, WD, V~o and imaginary potential diffuseness al were kept fixed with the appropriate values according to table 1. The remaining free parameters ro, ao, r~, r~.... a .... were fitted analogously to procedure (I), leading to a similarly good description of the data as shown in fig. 5 (dashed curves). Only at the smallest energies there are some discrepancies, probably resulting from the constant Vo, compared with its strong structure in procedure (I) (see fig. 6). The varied parameters of procedure (III) are plotted in fig. 8. Similarly to the results of procedure (1) (fig. 6), there are structures which correspond well to the resonance in the total cross section (fig. 4), especially r~, which is narrower than before. These structures appear independently from the special fitting procedure applied. It was not possible to describe both cross section and analyzing power, if the geometry parameters were not allowed to vary strongly with energy. We may conclude that there are energy regions where due to the presence of compound-nucleus resonances, a proper description of the data is not possible with a weakly energy-dependent optical potential. This is not the case, as has been shown in ref. 4), if only unpolarized cross-section data are analyzed.

4. V o l u m e integrals and root mean square radii

For a comparison of different analyses of experimental data or theoretical predictions, usually volume integrals and root mean square (r.m.s.) radii are considered. In this way parameter ambiguities (Vr ~ and Wa~) and the influence of the special radial dependences of the form factors are drastically reduced. These quantities are defined as follows:

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M. Hailer et al. / Elastic scattering (I) TABLE

201

1

Optical-model p a r a m e t e r s o f p r o c e d u r e ( l I ) (see text), depending linearly on the lab energy E rc Vo r0

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this work, and with the predictions of the microscopic model 5) according to Jeukenne, Lejeune and Mahaux (JLM). Apart from the resonances, the magnitude of the volume integrals and the root mean square radii of our proton-scattering analysis agree both with the results of the neutron scattering and the JLM predictions. Because of the applied local-density approximation, the validity of the JLM model was originally restricted to mass numbers A/> 12. Although A = 6 for 6Li(p, p), the application of the JLM model seems practicable if we neglect resonance effects. These effects are not present in JLM nor in the neutron-scattering analysis, where all optical-model parameters are linearly energy dependent. The unpolarized cross section of elastic neutron-scattering at various target nuclei f r o m 6Li t o 13C, in the energy range between 7 and 15 MeV, has been analyzed by Dave et aL 4). In that analysis, unpolarized neutron data have been described with

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O~

6 6 Ec... [ MeV ]

4

~...[HeV]

Fig. 9. Real and imaginary volume integrals per mass unit, calculated from the parameters of procedure (III) (see fig. 8). The solid curves belong to a neutron-scattering analysis 4), they are Coulomb corrected and extrapolated to the corresponding energy range. The dashed curves show the prediction of the JLM model 5).

fm

fm 10

i

,

i

,

i

,

i

,

i

,

i

,

i

,

10

i

I I l l l l F l l l n l l l l l

•

8

l°

6 e e . e

9

. . . . . . . . . . . . . . . . . . . . . . . . . .

2 0

i

I

i

I

2

,

I

,

I

4

,

I

,

I

fi

,

I

,

I,

I

t

2

fl

Ec...(HeY)

i

I l l

,

4

I

i

In

I

i

I

6 B F-.c... [ HeV I

Fig. 10. Real and imaginary root mean square radii, calculated from the parameters of procedure (II1) (see fig. 8). The curves are the same as in fig. 9.

linearly energy-dependent potential depths and constant geometry parameters, although the description was, according to the authors, not as good as for heavier nuclei, especially in regions of resonances. For our proton scattering analysis, however, both cross section and analyzing power could not be described simultaneously with constant geometry parameters, even if all potential depths were adjusted. As pointed out in ref. 4), the parameter set from neutron scattering can also describe the unpolarized 6Li(p, p) cross sections of ref. ,2) after applying a Coulomb correction by adjusting Vo and WD. This parameter set could not, however, describe our data 13), with discrepancies mainly in the analyzing power.

5. Conclusions

The cross section and analyzing power of 6Li(p, p) scattering in the energy range between 1.6 and 10 MeV lab energy are well described by optical-model calculations.

204

M. Hailer et al./ Elastic scattering (I)

The p a r a m e t e r s do not, however, d e p e n d smoothly on energy, but show a strong peak at Ecru = 1.6 MeV, c o r r e s p o n d i n g to a w e l l - k n o w n r e s o n a n c e , a n d a b r o a d structure at Ec.m = 4-5 MeV, where further r e s o n a n c e s are predicted (see the following paper). The same structures are f o u n d in the total elastic cross section (fig. 4). These structures do not necessarily a p p e a r in an analysis of the u n p o l a r i z e d cross section a l o n e (e.g. ref. 4)), which can be described with weakly e n e r g y - d e p e n d e n t o p t i c a l - m o d e l parameters. The gross features of the integrated parameters of this work agree with the c o r r e s p o n d i n g results of n e u t r o n scattering a n d with the predictions of the JLM m o d e l (see figs. 9 a n d 10). A d d i t i o n a l l y , they reveal the existence o f r e s o n a n c e structures which prevent us from a p p l y i n g the optical model in the usual way. This new i n f o r m a t i o n c o u l d be only o b t a i n e d by the i n c l u s i o n of the a n a l y z i n g power data.

References 1) J.N. Bahcall, W.F. Huebner, S.H. Lubow, P.D. Parker and R.K. Ulrich, Rev. Mod. Phys. 54 (1982)

2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

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