Spin-orbit potentials for elastic scattering of polarized 6Li ions from 12C and 58Ni

Nuclear 0

Physics

North-Holland

A407 (1983) 2088220 Publishing

Company

SPIN-ORBIT POTENTIALS FOR ELASTIC SCATTERING OF POLARIZED 6Li IONS FROM l*C AND 58Ni + K. RUSEK Institute

and Z. MOROZ

ofNuclear Research, Warsaw, Poland

and Ma.r-Planck-Institut ,jiir Kernphysik,, Heidelberg, FRG R. CAPLAR*,

P. EGELHOF**,

K. -H. MOBIUS

and E. STEFFENS

Max-Planck-institut ffir Kernphysik, Heidelberg, FRG

I. KOENIG,

A. WELLER

and D. FICK

Philipps-Universitst, Fachbereich Physik, Marburg, FRG Received 2 November (Revised 6 December

.\h\trart

E

1982 1982)

: Angular distributions of the differential cross section u/uR, of the vector analyzing power iT,, and of the 2nd rank tensor analyzing power TT’,, have been measured for elastic scattering of ‘Li from “C and s8Ni at 19.2 and 20.0 MeV, respectively. The vector and tensor polarization data can be well described using in addition to the complex central potential a real spin-orbit potential. Best-fit potentials are compared with those from folding models. In addition, vector analyzing power data were measured for 6Li-‘zC elastic scattering at 9.0 MeV bombarding energy. They are compared to predictions derived from an analysis of previously measured tensor analyzing powers of the same system at the same energy.

NUCLEAR REACTIONS ‘2C(6Li, 6Li), E = 9.0 MeV, measured iTI,, E = 19.2 MeV, measured u/o,(O), iT, ,(fl), T&,(0). Optical model analysis. 58Ni(6Li, 6Li), E = 20.0 MeV, measured u/u,(0), iT, ,(0), T,,(e). Optical, diffraction model analyses.

’ Supported partly by the Bundesministerium fur Forschung und Technologie, Bonn. * Alexander von Humboldt fellow, Permanent address : RuderBoSkovic Institute, Zagreb, ** Present address : Physikalisches Institut der Universitlt Basel, Switzerland. 208

Yugoslavia.

K. Rusek et al. / Spin-orbit potentials

209

1. Introduction The first extended experiments with a polarized ‘Li beam ‘) were devoted to the investigation of the 6Li spin-orbit potential ‘). Angular distributions of the vector analyzing powers iT, 1 [ref. “)I for elastic 6Li scattering on several target nuclei (12C, 160, 28Si, ‘*Ni) at energies around 20 MeV displayed large effects. The gross features of these data were understood in terms of a “frozen density” folded mode1 2,4). Within thi s model 6Li was described as a d-cc cluster system in relative S-state. The folded spin-orbit potential was calculated using deuteron-target spinorbit potentials from the literature. Also double folding potentials deduced from an effective nucleon-nucleon interaction described the main features of the data 5). Nevertheless, both analyses fail to describe the correct magnitude of iT,, for the scattering of 6Li on 58i’4 . Optical mode1 analyses using both real and complex ‘jLi spin-orbit potentials 6,7) had been performed as well. Except for the 6Li-58Ni system, the authors claim ‘) a better agreement between data and fit for a complex spin-orbit interaction. The necessity of a complex spin-orbit interaction was also suggested in a diffraction mode1 analysis using a suitable parametrized S-matrix *). Altogether these analyses left a confusing picture for the 6Li spin-orbit interaction. However, very recently coupled channel calculations ‘) including projectile excitation and using d-a cluster folding potentials straightened out the picture, at least for the 58Ni target. Nevertheless, the limited accuracy of this data is still one of the largest drawbacks for a comparison with any kind of theoretical predictions. Since these early 6Li measurements the source for polarized 6Li has been improved considerably both concerning the available beam currents and the equipment to avoid systematic errors lo). Having in mind the above discussion it was therefore considered useful to reinvestigate it least partly the elastic scattering of vector polarized 6Li at energies around 20 MeV. The targets “C and 58Ni have been chosen for this purpose. At 9.0 MeV bombarding energy a TT20 [ref. ‘“)I elastic 6Li-12C angular distribution ’ ’ ) was previously analyzed under the assumptions that 6Li tensor analyzing powers are exclusively generated by the spin-orbit interaction 12). This is in contrast to ‘Li where the tensor interaction is the main origin of the tensor analyzing powers “). To test the above assumption an angular distribution of the vector analyzing power for elastic 6Li-‘2C scattering was measured at 9.0 MeV additionally. Around 20 MeV additional angular distributions of TT20 were measured for elastic scattering of 6Li on 12C and 58Ni to check the hypothesis made above. Notwithstanding, the main purpose of the present experiment is the investigation of vector analyzing powers and the determination of spin-orbit potentials. Some emphasis is put on the question of whether a complex 6Li spin-orbit potential is required by the 58Ni data or not. Experimental details and the data obtained are included in sect. 2. Sect. 3 contains a discussion on the 58Ni data in terms of an

210

K. Rusek et al. / Spin-orbit potentials

optical model analysis together with an analysis within the diffraction whereas sect. 4 is devoted to the optical model analysis of the 12C data.

model, Sect. 5

bears a few final remarks.

2. Experimental

methods and results

The source for polarized alkali ions at the Heidelberg EN-tandem lo) allows one to produce a 6Li beam which is both vector and tensor polarized with respect to the normal to the scattering plane. The averaged beam current of Li3+ was about 100 nA after acceleration. The difference in cross section to the right and to the left normalized to the cross section for an unpolarized beam determines the vector analyzing power iT,,. The difference between the sum of both cross sections and the cross section for an,unpolarized beam normalized to the cross section for an unpolarized beam determines the tensor analyzing power TT20 [refs. 13,16)]. Both quantities have to be normalized to the actual vector and tensor polarization of the beam, respectively. During the experiments the tensor polarization of the beam (typical value around Tt20 z 0.64) was determined absolutely and monitored with a deuterium gas polarimeter by the reaction 2H(6Li, 4He)4He [ref. “)I. The vector polarization of the beam (typical value around it, 1 z 0.37) was monitored by elastic 6Li-4He scattering ‘). Its value was determined absolutely by the previous reaction assuming equal depolarization for vector and tensor polarization of the beam. The accuracy of the determination of the beam polarization is about 10 ‘:<,. Artificially induced effects caused by long-time shifts of the beam intensity and beam polarization were suppressed using a routing system to switch the beam polarization either on and off or from plus to minus each one to two seconds by turning on and off different high frequency oscillators in the ion source ‘vl’). A logical pulse to the data-taking system marked the polarization state. The routing system was controlled by a charge integrator connected to the Farday cup assuring equal charge collected for each polarization state of the beam. During switching from one polarization to the other no data were taken. This “dead” interval was long enough to account also for the sticking time of ions on the surface ionizer which is by far the largest “recovery” time in the beam transport system lo). At the exit of the ion source a Wien filter served to align the spin axis along the normal to the scattering plane. The detector system consisted of four AE-E telescopes, two telescopes on either side of the beam separated by 15”. The angular defining slits were positioned at the distance of about 110 mm from the centre of the target, giving an angular resolution of about + 1.6“. The thickness of the AE detectors was roughly 15 pm and of the E-detectors about 300 pm. In order to minimize systematic errors the beam intensity and position was monitored by two counters placed at 0 = 25O on either side of the beam. Mass identification of the reaction products, in particular

K. Rusek et al. / Spin-orbit pofentials

211

‘Li and ‘Li, was made using two-dimensional (d.E, E) spectra. To reduce the data flow to the computer analogue mass identification units were used to perform a preliminary cut of unwanted light particles, mainly a-particles. The thickness of the targets between 90 and 150 pg/cm2 allowed an energy separation of elastic from inelastic scattering. The energies of the 6Li beam were chosen to obtain similar centre-of-mass energies for existing ‘Li scattering data on the same target 16). Figs. 1 and 2 display the data obtained for ‘jLi elastic scattering on “C and 58Ni, respectively. The angular distributions for o/oR and iT, , show features known from previous experiments ‘). The absolute values of the differential cross section for elastic scattering of 6Li on 58Ni were obtained normalizing the cross section to the Rutherford cross section at 0_,, = 33”. For ‘Li-“C scattering the product of target thickness and solid angle of each counter was determined using 21.1 MeV ‘Li ions for which energy absolute cross sections are published I’). With this normalization absolute cross sections for %i elastic scattering on “C at 19.2 MeV were determined using the very same experimental arrangement as for ‘Li. This normalization is believed to result in a common scaling error of about 10 “0 for both systems.

I

0

20

I 40

I

I 60

I

I 80

I

IT, 100

I I I I 1 120 140 160 %m.(deg)

Fig. 1. Angular distribution of u/uR, iT, 1 and TT20 for elastic scattering solid curves display results of calculations -with a complex central (table 1).

of 6Li on “C at 19.24 MeV. The and a real spin-orbit potential

K. Rusek et al. 1 Spin-orbit potentials

212

I

’

I

I

’

I

’

II

1

E,,= 20.0 MeV

0

20

40

60

80 100 %Jn. (deg.)

120

140

.

160

Fig. 2. Angular distributions of o/aR, iT,, and TTZO for elastic scattering of 6Li on 5sNi at 20.0 MeV. The solid curves display results of calculations with a complex central and a real spin-orbit potential (table 1). The dotted ones indicate the effect of complex spin-orbit potential (see text).

Fig. 3 displays angular distributions angular distributions of a/aR [ref. “)I

of iT,, together with previously determined and ‘Tzo [ref. ‘“)I for elastic scattering of 9.0

MeV 6Li on 12C.

3. Elastic ‘jLi-‘*Ni scattering The angular distribution of ~/a~ observed for elastic ‘jLi-‘sNi scattering at 20.0 MeV is of typical Fresnel type ‘*) indicating the interaction to be dominated by strong absorption and strong Coulomb forces. Thus, the region of sensitivity to any type of phenomenological interaction is located around the grazing distance (grazing angular momentum). The observed (vector and tensor) analyzing powers are smoothly varying with angle and have a positive sign. The sign is in accordance with expectations from folding models 2,4*5). The statistical accuracy of the vector analyzing power data has been improved considerably when compared to the earlier data ‘). The new data rule out any kind of strong oscillations in angle which - despite a smooth angular dependence ~/a~ - have been believed to be recognized in the vector analyzing powers *).

213

K. Rusek et al. / Spin-orbit potentials

I

0

%n.

%n.(deg)

Fig. 3. Angular distributions of u/aR [ref. I’)]. TT,, [ref. ‘“)I and iT,, for elastic scattering of 9.0 MeV the data points presented as open circles were polarized 6Li on “C In the iT,, angular distribution measured previously 14). The solid curves represent curves with a complex central and spin-orbit potential (table 2) derived previously I’).

3.1. DIFFRACTION

MODEL

ANALYSIS

Heavy ion scattering data in the regime of Fresnel scattering are suitable for an analysis within the diffraction model using a simple parametrization of the nuclear S-matrix in I-space. Restricting the analysis to the vector analyzing power data the method of Hill and Frahn 8, can be followed very closely. In their approximation the S-matrix elements for spin-l particles are given by G(n) = SLN’(A)exp {2ia(A)+ 2it6,(1)},

(1)

where ;i = I + i and z = 1, 0, - 1. The Coulomb phase shifts are denoted by @(A) and SLN)(n) denotes that part of the S-matrix originating from the central nuclear interaction. It is characterized by a “grazing” angular momentum A, a diffuseness A and a real phase shift a reflecting refractive effects in the nuclear interaction: SkN’(L) = { 1 + exp {(A -2)/A The effect of the spin-orbit interaction which is parametrized according to

is entirely

-ice}] - ‘. included

a 6,(A) = 2rcAs - S’N’(I A,, A ) ant’ s.

(2) into

the phase

s,(n)

(3)

K. Rusek et al. / Spin-orbit potentials

214

A, and A, have obvious

meanings.

The strength K

=

constant,

/c,+iri.

(4)

I)

can be chosen to be complex since the spin-orbit coupling may modify the absorptive as well as the refractive part of the central interaction. Phenomenologically a complex value of rc corresponds to a complex spin-orbit interaction. The best fit to the data displayed as solid curves in fig. 4 was obtained with the following parameters A = 11.30, A, = 11.0,

A = 0.65,

cr = 0.00,

A, = 0.65,

K, = 0.25,

The values of the parameters located in the same region

Ki = 0.00.

(5)

show that the central and spin-orbit interaction are of angular momentum space around I z 11. The

20

40

60

80

100

120 6’~.

140

160

m.(deg)

Fig. 4. The solid curve displays an analysis of the data of fig. 2 (6Li-58Ni, 20.0 MeV) within the diffraction model assuming a real spin-orbit coupling. The dashed curve indicates the influence of a complex spin-orbit coupling. For details see text.

K. Rusek Ed al. / Spin-orbit potentials

analysis

requires

no

refractive

part

in

the

215

S-matrix:

IX= 0.

Moreover,

in

contradiction to the results of an anlysis within the diffraction model 8), but in agreement with an optical model analysis 7, of the old data 2), there is no need for a complex 6Li-58Ni spin-orbit interaction (Q = 0). In order to demonstrate the influence of a complex spin-orbit interaction the dashed curve in fig. 4 was calculated with ~~ = 0.05 instead of 0.00. It affects mainly the most backward angles where the statistical accuracy of the data is limited.

3.2. OPTICAL

MODEL

ANALYSIS

The optical model analysis was performed with the spin-l code DDTP 19). Except for the radius of the potential which was parametrized according to R = r,(Ai+Ai*), A, and Ai being the mass numbers of projectile and target, respectively; the potentials are defined as given in the reference above. It should not be concealed that the tits to the data were performed without an automatic search routine. The fits were extracted from a large number of individual calculations. Optical model parameters describing the elastic scattering of 6Li on 58Ni at Eii = 22.8 MeV [ref. ‘)I served as starting parameters. At first the central part of the potential was adjusted to describe the angular distribution of g/gR. Then an overall tit including the vector analyzing power data has been performed, assuming the spin-orbit potential to be real. This restriction is justified by the results of the previous subsection. The solid curves in fig. 2 in the diagrams for o/o, and iT,, display the tit to the data obtained with the parameter set of table 1. The data are described very well. No significant improvement of the description of the data could be%obtained by adding an imaginary part to the spin-orbit potential. In order to demonstrate its influence, the dashed curves for a/aR and i7’,, were obtained adding an imaginary Is potential of gaussian form (W = -0.10 MeV, r = 1.27 fm, a = 0.20 fm). TABLE

Optical

model

parameters

1

used in the analysis of elastic scattering of vector 19.2 MeV and on “‘Ni at 20.0 MeV 6Li-12C, ELi = 19.2 MeV

real central imag. central imag. central (deriv.) real Is, Thomas real Is, Gauss Coulomb

V (MeV)

r (fm)

a (fm)

144.2 1.00

0.808 0.634

0.674 0.870

10.30

0.634

0.870

0.990 1.300

1.452

0.540

polarized

‘Li-‘*Ni,

“Li on “C

E,, = 20.0 MeV

V (MeV)

r (fm)

a (fm)

126.8 15.24

1.052 1.036

0.520 1.156

0.460

1.350

0.400

1.443

at

216

K. Rusek et al. / Spin-orbit

potentials

t

_,,oo[~;~,[“:‘:““~ , ] 3

5

7

9

11 r

(fm)

Fig. 5. Comparison of the radial dependences of various spin-orbit potentials for 6Li-58Ni elastic scattering. The dashed curve results from a single folding model *.4) whereas the dashed dotted curve is obtained in a double folding model calculation ‘). The solid line represents the potential of table 1.

The two existing folding potentials 2,4,5) do not result into an equal good description of the data as the best lit potentials do. The single folding potential 2,4) yields almost zero analyzing powers whereas the double folding potential “) reproduces the correct sign but not the magnitude of the observed vector analyzing powers. One may ask whether the drawback of folding potentials is the question of their strength and/or of their radial dependence. The radial dependence of the best lit potential and of the folding potentials are displayed in fig. 5. in the region of interest (R 2 8 fm) the radial dependences differ not very much, but their strength does. One really wonders why even the tail of a potential of such a weakly bound system like 6Li cannot be described properly by these models. However, very recently projectile excitation of 6Li was identified as the main process generating a large spin-orbit interaction which strongly alters the predictions for vector analyzing powers obtained from frozen density folding model spin-orbit potentials 9). The vector analyzing power data of fig. 2 are described by this means equally well 20) as the earlier data obtained at somewhat higher bombarding energy. Previously it was suggested 12) that - in contrast to ‘Li [refs. ‘“pi”)] - 6Li tensor analyzing powers are exclusively generated by the spin-orbit force. In the TT20 part of fig. 2 the solid curve displays the result of a calculation with the spin-orbit potential of table 1 as the only spin-dependent potential. The dashed curve is spin-orbit potential. The obtained by adding, as for iTi,, a small imaginary calculations describe a great deal of the observed small effect.

K. Rusek et al. / Spin-orbit potentials

4. Elastic ‘Li-‘*C

217

scattering

The angular distribution obtained for the ‘Li elastic scattering on “C display large oscillations contrary to the scattering of 6Li on 58Ni. These are caused mainly by a reduced Coulomb interaction. At the present energy the grazing angular momentum is smaller than 10h and hence the system does not belong to the diffractive scattering regime 18). It cannot be treated by a diffraction scattering analysis as it was done for 58Ni. The optical model analysis was performed as outlined for 58Ni. The central potential parameters obtained in a previous global analysis “) served as starting parameters. Firstly, vector analyzing powers were calculated with the folding model those spin-orbit potentials from the literature 2*4,5) using for the central interaction parameters fitting the differential elastic cross section. In contrast to 58Ni both folding spin-orbit potentials yield, the same results, despite some minor details. They reproduce the gross structure in the magnitude of iT, 1 for backward angles, buth both fail to describe even the gross structure observed for forward angles. However, when fitting the data using a real spin-orbit potential a parameter set (table 1) can be found which describes reasonably well the observed vector analyzing powers including the forward angles (fig. 1, solid line). The spin-orbit potential is parametrized with a gaussian form factor which diffuseness turns out to be rather large +. Fig. 6 displays this potential together with the folded ones. Whereas the two folded potentials are similar in the tail region (R 2 4 fm) the phenomenological potential differs quite a bit from them. In order to investigate the properties of this potential in more detail the corresponding S-matrix (S, = IS,1 exp2i8,) shall’be discussed and compared to the one obtained for the 58Ni target (fig. 7 ). The S-matrix elements were calculated with the, potential parameter sets of table 1. For 58Ni the S-matrix indicates the strong sensitivity of the interaction to the region around the grazing angular momentum (/,, z 11) defined by IS,1 = 0.5. For smaller I-values S, approaches zero. Around the grazing angular momentum the phase 6, is almost negligible which reflects the vanishing contribution of refractive effects (diffraction model analysis : c( = 0.0, subsect. 3.1). The plots for ’ 2C read quite differently : for I,, z 9 the phase 6, does not vanish nor does ISi1 for angular momentum much smaller than the grazing angular momentum. This means that in contrast to “Ni for the 6Li scattering on “C scattering p recesses from both the surface and the interior contribute to the cross section. Since vector analyzing powers are very sensitive to any kind of interference effects the difficulties in fitting the 12C data are not surprising.

’ Other spin-orbit potentials which describe the data almost as well as the gaussian potential were found too: Thomas shape, V = 2.1 MeV, r = 1.08 fm, a = 0.59 fm, or Woods-Saxon derivative shape, V = 0.52 MeV, r = 1.01 fm, a = 0.59 fm.

K. Rusek et al. 1 Spin-orbit potentials

218

+-_-AL-x

/’

6Li + 12C -10.0 0

Fig.

6. Comparison

2

4

6

8 r (fm)

of the radial dependences of various spin-orbit potentials for 6Li-‘zC scattering. The meaning of the curves is the same as in fig. 5.

elastic

This is in agreement with similar conclusions drawn from an analysis of other ‘jLi-r2C scattering data 21). In this analysis the region of sensitivity was visualized in r-space. A similar method was used in the present work to show the sensitivity of the spin-orbit potential on the vector analyzing power iT,,. A dip with a width of 0.1 fm was formed in the potential at a radius r = R by multiplying the potential in the region from R - 0.05 fm to R + 0.05 fm artificially with a factor of 0.8. Then the dip was moved across the potential and the relative change of x2 was

10

Fig. 7. Angular

momentum 6Li-s8Ni

e

20

dependence of the S-matrix S, = (S,(exp (2iS,), for elastic 6Li-1zC (right) scattering, calculated from the potential of table 1.

(left) and

219

K. Rusek et al. / Spin-orbit potentials

a c t

200

;

100

z e k 5 x

0

-100

0

2

4

6

3

6

5

7

R (fm)

9

11

R(fm)

potential at radius r = R Fig. 8. Relative change (sensitivity) of x2 for iT,, to a dip in the spin-orbit (reduction of the potential to 0.8 of this original value) with a width of 0.1 fm for ‘Li-“C (left) and ‘Li“Ni (right) scattering.

plotted as a function of R. The results are displayed in fig. 8. The right part includes the results for the 6Li-58Ni scattering. As to be expected from the diffraction model analysis and from the S-matrix elements of fig. 6 the range of sensitivity is localized around R z 8.5 fm, far outside the surface of both nuclei. The results for 12C (left part of fig. 8 ) look quite different. The region of sensitivity is spread over a wide region ranging from 7 fm, outside the surfaces of the nuclei, to around 3 fm, inside the nuclei. Similar to the central potential 21) the inner part of the spin-orbit potential also contributes to the ‘jLi-“C interaction. The original idea that 6Li tensor analyzing powers are generated by the spinorbit force was developed in an analysis of 9.0 MeV 6Li-12C scattering data for T7’2, [ref. “)I. Fig. 3 displays these results (parameter set table 2) together with the predictions for the presently measured data for iTI,. Undoubtedly this assumption describes the main features of both, the TT2,, and iT,, data. The same assumption was now made for the description of the T7”0 data at 20 MeV. Fig. 1 displays in the lower part the results of a calculation in which the 6Li spin-orbit potential (table 1) was assumed to be the only spin-dependent potential. At this energy, as TABLE 2 Optical

model parameters

derived

previously scattering

“) which are used in the description of 9.0 MeV bLi on r2C hLi-‘*C, V (MeV)

real central imag. central real Is, Thomas imag. Is, Thomas Coulomb

158.8 2.9 1 7.29 0.865

of the data for elastic

Et = 9.0 MeV

r (fm)

a (fm)

0.763 1.075 0.955 1.217 0.808

0.708 0.808 0.110 0.155

220

K. Rusek et al. / Spin-orbit potentials

for 58Ni, also for the 12C target the 6Li spin-orbit potential seems to account for most of the observed effect in TT20. 5. Final remarks The investigation shows that even for such a simple projectile as 6Li the spinorbit potential is still apart from being understood completely, yet. However, qualitative features of the interaction become transparent now. For a “Ni target there is no strong need for an imaginary spin-orbit potential. Since 6Li has an almost vanishing spectroscopic quadrupole moment - in contrast to ‘Li - the tensor analyzing power data are mainly a result of the 6Li spin-orbit potential. However, the strength of the spin-orbit potential cannot be reproduced by a folding model calculation. As shown recently, projectile excitation 9, and target excitation (“C) [ref. “)I are essential mechanisms to understand the 6Li spinorbit interaction in detail. The authors thank Dr. W. Dreves, unpublished data for this presentation.

Marburg

for the permission

to

use

References 1) E. St&fens, W. Dreves, H. Ebinghaus, M. Kiihne,F. Fiedler, P. Egelhof, G. Engelhardt, D. Kassen, R. Schafer, W. Weiss and D. Fick, Nucl. Instr. 143 (1977) 409 2) W. Weiss, P. Egelhof, K. -D. Hildenbrand,D. Kassen, M. Makowska-Rzeszutko, D. Fick, H. Ebinghaus, E. Steffens, A. Amakawa and K. -I. Kubo, Phys. Lett. 6lB (1976) 237 3) M. Simon& in Lecture Notes in Physics, vol. 30, ed. D. Fick (Berlin-Springer, 1974) p. 38 4) H. Amakawa and K. -1. Kubo, Nucl. Phys. A266 (1976) 521 5) F. Petrovich, D. Stanley, L. A. Parks and P. Nagel, Phys. Rev. Cl7 (1978) 1642 6) J. Meyer, R. S. Nahabetian and E. Elbaz, Lett. Nuovo Cim. 22 (1978) 355 7) J. Meyer and E. Elbaz, Proc. Sth ht. Symp. on polarization phenomena in nuclear physics, Santa Fe 1980, ed. G. G. Ohlsen et al. (AIP, 1981) p. 1091 8) T. F. Hill and W. Frahn, Ann. of Phys. 124 (1980) I 9) H. Nishioka, R. C. Johnson, J. A. Tostevin and K. -1. Kubo, Phys. Rev. Lett. 48 (1982) 1795 10) E. Steffens, Nucl. Instr. 184 (1981) 173, and references therein I I) W.Dreves,thesisUniversityHeidelberg(l978),andAnnualReportMPIKernphysik,Heidel~rg(I978), unpubljshed 12) J. Meyer and E. Elbaz, see ref. ‘), p. 1083 13) D. Fick, Ann. Rev. Nucl. Part. Sci. 31 (1981) 53, and references therein 14) W. Haeberfi, see ref. 3), p. 229 15) P. Zupranski, W. Dreves, P. Egelhof, E. Steffens, D. Fick and F. RoseI, Nucl. Instr. 167 (1979) 193 16) Z. Moroz, P. Zupranski, R. Biittger, P. Egelhof, K. -H. Mobius, G. Tungate, E. Steffens. W. Dreves, 1. Koenig and D. Fick, Nucl. Phys. A381 (1982) 294, and to be published 17) I. E. Poling, E. Norbeck and R. R. Carlson, Phys. Rev. Cl3 (1976) 648 18) W. Frahn, Ann. of Fhys. 72 (1972) 524 19) R. P. Goddard, Deuteron optical model program DDTP, University of Wisconsin 1977, unpublished; private Communication 20) R. C. Johnson, private communication 21) E. Norbeck, M. D. Strathman and D. A. Fox, Phys. Rev. Cl8 (1978) 1275 22) K. Rusek, to be published