Nuclear Physics A368 (1981) 173-188

0 North-Holland Publishing Company

FUSION AND DIRECT REACTIONS

FOR STRONGLY AND WEAKLY BOUND PROJECTILES

M. HUGI, J. LANG, R. MILLER and E. UNGRICHT

Lahoratorium fiir Kernphysik, Eidg. Technische Hochschule, 8093 Ziirich. Swifzwlund

and

K. BODEK, L. JARCZYK. B. KAMYS, A. MAGIERA. A. STRZALKOWSKI and G. WILLIM

Institute qf Ph?sics, Jagrlloniun Uniwrsit~, 30059 Cracon. Poland

Received 12 March 1981

Abstract: The interaction of “Li. 9Be and “C projectiles with a “Si target was investigated by

measuring the angular distributions of the elastically scattered projectiles and of the emitted protons, deuterons and cc-particles. The experiment was performed in order to deduce direct

and compound nucleus process contributions to the total reaction cross section and to study the influence of the projectile structure on the relative importance of these two mechanisms. Optical mode1 parameters and therefore the total reaction cross section are strongly influenced by the binding energy of the projectile. The parameters of the Glas-Mosel model describing the fusion reaction vary smoothly with the atomic number. In the system ‘Be+‘sSi around 50 “” of all reactions are direct processes even at energies near the Coulomb barrier. whereas in the other systems the direct part amounts to 15 on (“C) and 30 O0 (‘Li) only

NUCLEAR REACTIONS ‘8Si(bLi. p), (hLi, d). (6Li, G(). (6Li. 6Li). E(c.m.) = 10.7, 16.5,

20.6 MeV, 28Si(9Be, p). (9Be. d). (9Be. c(). (9Be, ‘Be), (9Be, 9Be). E(c.m.) = 9.1, 10.6, 12.9, E 15.1. 17.4, 19.7. 22.7 MeV; 28Si(‘2C, p). (“C. d), (“C, c(). E(c.m.) = 15.4, 18.9, 25.2 MeV;

measured a(B); deduced a(fusion). o(direct). a(reaction). Optical model and statistical model analysis.

1. Introduction

For some heavy-ion systems the total fusion cross section does not exhaust the

total reaction cross section even at low energies ’ - 3). Especially large differences

were observed for 9Be projectiles4* 5 ). The 9Be ions differ from other heavy

projectiles by their low neutron binding energy and in consequence by their rather

loose structure. It was then concluded that the direct cross sections rather than the

fusion cross sections might be strongly influenced by the binding energy of the

projectile ‘). Also elastic scattering was shown to be dependent on the projectile

binding energy 6, ‘). The present work investigates to what extent differences in the binding energy

173

174 M. Huyi et (11. / Fusion and direct reactions

and the structure of the projectile influence the contribution of fusion and other

reaction processes. Experiments were performed for the weakly bound projectiles

‘jLi and 9Be and for the strongly bound nucleus 12C interacting with a 28Si target.

In the discussion the results for the 160 + 28Si system published by other authors

were also used 8, 9).

The reaction cross section oR was deduced from an optical model analysis

of the elastic scattering data. The fusion cross section cfus was determined from

a statistical model analysis of the evaporation spectra of light charged particles.

The contributions from direct reactions odir were estimated from observed forward-

backward asymmetries in the emission of charged particles and from measurements

of the inelastic scattering cross section. The reliability of the determination of the

different contributions was checked by calculating the reaction balance

gR = cfus + Odir.

2. The experiment

The measurements were performed at the tandem Van de Graaff accelerator of

the ETH Ziirich. Beams of 6Li. 9Be and 12C ions with intensities between 50 and

200 nA were focussed on self-supporting natural silicon targets with thicknesses

from 50 to 100 pg/cm’. The targets showed a slight contamination of oxygen and a

considerable build-up of the carbon content during the measurement. The beam

energies were 13, 20 and 25 MeV (lab) for 6Li ions, 12, 14, 17, 20, 23, 26 and

30 MeV for 9Be ions and 22, 27 and 36 MeV for “C ions. Some of the results

for 9Be + 28Si have been published earlier ‘).

Usually the fusion cross section is determined by a measurement of the

evaporation residues, For light heavy-ion systems and in the presence of strong direct

reactions this procedure leads to difficulties, since the evaporation of several

charged particles gives the same residual nuclei as the direct reactions. Therefore

in this work the fusion cross sections were determined by another method, namely,

from a statistical model analysis of the spectra of the evaporated light particles.

A measurement of the angular distributions of these reaction products allows a

separation of direct and compound reactions under two assumptions : (i) the direct cross sections are strongly forward peaked and negligible in the

backward hemisphere,

(ii) the compound products are evaporated symmetrically around 90° in the c.m.s.

The spectra of the emitted protons, deuterons and cc-particles were measured with

AE-E counter telescopes in steps of 5” between 5’ and 40” (lab) and in 20” intervals

from 40” to 160”. The telescopes consisted, for most of the measurements, of a

thin surface barrier silicon detector and a thick Li-drifted silicon detector. At

angles below 40” the high counting rate caused by elastically scattered ions would

destroy the transmission detectors within a short time. Here, the spectra were

M. Huyi et al. 1 Fusion and direct reactions 175

obtained in two separate measurements: the low-energy part with an ionisation

chamber to) as AE detector and a surface barrier E-detector at a reduced beam

current, and the much less intense high-energy part with solid state telescopes

protected by absorber foils in front of them. The angular resolution of the counters

was + 1”. The detector telescopes accepted protons with energies between 3 and

30 MeV and a-particles with energies from 2.5 to 50 MeV.

The corrections for the target contaminations were determined from separate

measurements using Si. SiOz and C targets. The cross sections were normalised

to the elastic scattering yields monitored at a fixed angle. The relative errors of the

double differential cross sections are estimated to be 6 9: at higher and up to 15 y0

at lower beam energies. The error of the absolute normalisation is of the order of

8 ‘, The spectra exhibit a continuous character typical for evaporation processes. / 0 . No peaks corresponding to transitions to discrete states were observed. The

double differential cross sections were evaluated by splitting the spectra into

1 MeV intervals and averaging over energy inside the intervals. Fig. 1 shows

100 28Si(6Li.D) I

f 0 50 100 150 100

$ \

2 IO

g .- I t

C?

% 0 50 100 150

0 50 100 150

-- 0 50 100 I50 0 50 100 150

0 50 100 I50 0 50 100 150

CM-angle [deg]

Fig. 1. Typical angular distributions d20/dS2dE for protons. deuterons and cc-particles emitted from the

reactions 6Li + *sSi. 9Be + ‘sSi and “C + 28Si. The curves show statistical model predictions for the first evaporation step. (Outgoing c.m. energies 0 6 MeV. A 8 MeV, + 10 MeV, x 12 MeV, 0 14 MeV

and * 16 MeV.)

176 M. Hugi et al. / Fusion atzd direct reactions

representative examples of the obtained angular distributions. A marked increase of the cross sections at forward angles is observed for all ejectiles in the system ‘Li+‘*Si and for the a-particles in the two other systems, indicating important contributions from direct processes in these cases. The proton angular distributions are symmetric around 90” (c.m.) for the two systems ‘Be+ “Si and “C+‘%Gi. The deuteron channel is very weak in these systems.

Angle integrated spectra are obtained from these double differential cross sections by integration over the backward hemisphere and multiplication by a factor of 2 ‘(cf. fig. 5). In this way contributions from direct reactions could be reduced substantially.

The direct contributions to the light charged particle emission were estimated from the differences in the spectra measured in the forward and backward hemisphere (cf. fig. 6). In some cases, cross sections can be obtained directly from these differences. There are, however, direct reactions in which two light charged particles are emitted in one reaction process. They will contribute twice to the direct reaction cross section. Problems connected with taking into account such processes are discussed in sect. 5. One important example is the production of two cc-particles by the decay of ‘Be emitted in the interaction of 9Be with 18Si. This reaction was studied in a separate experiment. Angular distributions of the (unstable) ‘Be nuclei were measured by detecting the two cr-particles in coincidence using the experimental arrangement described in ref. ii). From the measured cc-particle energies the *Be energy can be calculated. The energy resolution was sufficient to separate the transitions to the first six excited states while at higher excitation energies up to 8.5 MeV transitions to eight strongly populated states were observed. The angular distributions for one of the most intense lines are shown in fig. 2.

Furthermore inelastic scattering will contribute to the direct cross section. Some information on inelastic scattering to the first excited state of the target nucleus and, in the case of r2C, also to the first excited state of the projectile, could be obtained together with the measurement of elastic scattering described below.

For the calculation of the total reaction cross section and the transmission coefficients used in the Hauser-Feshbach analysis of the fusion process, elastic scattering data are required. The existing experimental material was supplemented by additional measurements. The scattered ions were detected in single semi- conductor detectors or in counter telescopes depending on the energy and the angle so that the full angular range from IO0 to 160” (c.m.) could be covered. The angular resolution of the detecting systems was 0.5*-0.7”. The absolute values of the cross sections were determined by normalisation to the simultaneously measured Rutherford scattering on a thin gold layer evaporated on the Si target. The relative errors were estimated to be 3-5 %, the error of the overall no~alisation was around 8 %. The angular distributions used in the analyses are shown in fig. 3. For 6Li + 28Si the data obtained in the present work agree very well with results from refs. “‘i3). For i2C+ **Si, the elastic scattering cross sections published in ref. i4) were used.

177

0 50 IO0 1500 50

CM -angle [deg] 100 150

Fig. 2. Neutron transfer reaction and DWBA calculation If) for PBe+ZsSi.

3. Optical model analysis and total reaction cross section

For a comparison of the different systems it is important that the experimental data are analyzed in a consistent way. Thus the measured angular distributions were reanalyzed although extensive studies exist in the literature 6. ‘. I*, 14). A standard four-parameter energy-independent optical model potential with a Woods- Saxon form factor was used in all cases. Due to a continuous ambiguity in the potential determination, one of the parameters (e.g. the depth of the real potential V,) could be chosen arbitrarily. The vafues obtained for the parameters are listed in table 1 and the quality of the tits is illustrated in fig. 3.

The elastic scattering probes the potential in a limited region near the strong absorption radius R,, a lS(At+At) fm only. For the system 9Be+28Si this region covers e.g. distances from 6 to 11 fm [ref. “)I. It is wprthwhile to compare in this region of sensitivity the potentials for 6Li+ *‘Si, ‘Be+ ‘*Si, ‘*C f **Si and 160+ **Si [for the last reaction the potential El8 of ref. ’ *) was used]. The potentials for the weakly bound projectiles ‘Li and 9Be have a rather large

I-78 M. Huyi et al. / Fusion and direct reactions

TAKE I

Optical-model parameters for ‘Li + 28Si, yBe+ ‘*Si and “C+ “‘Si

Reaction 2’ (MeV) W (MeV) R (fm) a (fm)

bLi + *“Si 62 63 4.81 0.75 ‘Be +%i 60 104.9 4.48 0.83

‘ZCf’RSi 60 7.1 6.69 0.45

Coulomb radius R, = 1.2A: I3 fm for all three reactions. Volume absorption with standard Woods- Saxon form factor.

diffuseness a and also a large ratio of imaginary to real potential W/V (calculated at the radius of strong absorption). For the strongly bound 12C and 160 both

0 50 lob 150

CM - ongie [deg]

0 50 loo 150

CM-ongle [deg]

Fig. 3. Elastic scattering of 6Li+28Si, 9Be+tsSi and *zC+zsSi together with optical model fits. [O present work, + Poling et af. I’), &, Bethge et al. 13), x Cheng et al. ‘3.1

M. Hugi et ai. j Firsion and direct reactions 179

lO-2

lO-3

0 I 2 3 0 I 2 3

Reduced Distance [f m]

%e+'*Si I

IO-’

IO-2

lO-3

Fig. 4. Elastic cross sections as a function of the classical distance D of closest approach. Reduced distance = D/(A:!3+AA’3). [The data for ‘60+*sSi are from refs. 15.27).]

values are distinctly smaller. Therefore one can conclude that a clear effect of the projectile binding energy is seen in the optical potential. In fig. 4 the elastic scattering cross sections are plotted as a function of the semiclassical distance of closest approach. One again has the impression that there is a larger absorption in the surface region (- 1.7-2.0 fm) due to direct reactions for the loosely bound projectiles 6Li and ‘Be.

From the fitted optical potentials the total reaction cross sections and the transmission coefficients are calculated. Both vary not more than 10 % for different potential families provided that the elastic scattering data are reasonably reproduced.

4. Statistical model analysis of evaporation spectra and fusion reaction cross sections

A statistical model analysis based on the Hauser-Feshbach theory was performed to deduce fusion cross sections from the angular integrated energy spectra of the emitted protons, deuterons and cr-particles. Because of the strong absorbing nature of heavy-ion potentials a good separation of fusion and other reaction

180 M. Hugi et ul. / Fusion and direct reactions

processes in the angular momentum space can be expected 16); it is then reasonable to assume a sharp cut-off of the transmission coefficients T, at some cut-off angular momentum Zr,, in the formula of the fusion cross section

cJfus = ; rg< (2f+ l)T,, f-0

where k is the asymptotic wave number in the entrance channel. IfUs is an adjustable parameter 5). The transmission coefficients T, in the entrance channel were calculated from the optical model discussed in sect. 3.

The program GROGI- used in the present analysis allowed to follow the evaporation process of neutrons, protons, a-particles and y-rays through all steps of the cascade I’. ‘a). Since the program GROGI- was not designed to calculate the deuteron emission, another program, EVAN, was written. This program was working similarly as GROGI- and included deuteron emission, but calculated the first step of evaporation only (which is sufficient in the deuteron case).

The evaporation probabilities are dependent on the level densities of the intermediate and tinal nuclei and the transmission coefficients of the light ejectiles. These transmission coefficients were calculated from potentials given in the Perey and Perey compilation 19) whereas the level densities were obtained from the formula of Lang “) :

p(E, J) = o(E, .I)--w(E, J+ l),

04 E, J) = -l _._-- exp (2aU), 12 $izw

J2 _ u = E- 2s -b‘= at2_$t,

where E is the excitation energy, 6 the pairing correction, J the nuclear spin, t9 the effective nuclear moment of inertia, a the level density parameter of the excited nuclei and 2 the thermodynamical temperature with t 2 1, = 0.2 MeV.

The influence of a variation of different parameters was studied in detail for the “Be + 28Si system 4). It was found that the level density parameters a affect the shape of the spectra rather than the absolute magnitude. Changes of the fusion cut-off angular momentum I,,, influence only the absolute values of the a-particle

spectra and, to a much smaller extent, of the proton spectra. The moments of inertia are of little importance. Different sets of optical model parameters give similar results as long as they tit the elastic scattering data equally well. Table 2 shows that the level density parameters obtained for the residual nuclei of the most important first stage of the evaporation cascade are compatible with the values recommended by Gilbert and Cameron 21).

Fig. 5 shows a comparison of experiments and calculations. The excellent

M. Huyi et al. / Fusion und direct ~e~~tio~s 181

TABIX 2

Comparison of level density parameters used in the statistical model analysis with those of Gilbert and Cameron ’ ‘)

Residue Gilbert + Cameron

a [MeV-$1

‘Li + **Si “Be+%i ‘?C+28Si

39ca 4.15-5.01 5.10 W 4.68 - 5.54 4.60 3hAr 4.03-4.82 4.20 4.40 3”cl 4.49-5.28 4.25 =c1 -4.07 4.20 33s 3.90 4.36 3oP 3.18-3.84 3.55

0 IO 20 0 IO 20

ECM [MeV]

Fig. 5. Angular integrated energy spectra and statistical model fits for the evaporation products from the reactions 6Li + “‘Si, ‘Be f *%i and “C + 28Si, The complete set of data from the reaction 9Be+ “Si

can be found in ref. ‘).

182 M. Hugi et al. / Fusion and direcf reactions

TABLE 3

Results of statistical model analysis, direct reaction analysis and reaction balance (the symbols are

explained in the text)

Vfus D&r (mbf (mb)

OM

(nz)

13 I rf:l

agreement in the proton spectra indicates a reasonable choice of all relevant parameters besides if,,. The a-spectra determine reliably the cut-off angular momenta, which in turn give the fusion cross sections. The values for !,,, and crfus obtained in the present analysis or given in the literature can be found in table 3.

5. Direct reaction contribution

From a comparison of fusion and totai reaction cross sections {table 3) it is evident that, especially for weakly bound projectiles, large contributions must be ascribed to some direct reaction processes. At the energies under investigation, three types of reactions are of chief importance for the observed differences between o, and cfUs, namely inelastic scattering, particle transfer reactions and breakup processes. In this section estimates of the different contributions based on experimental data will be given.

In transfer and breakup processes the charged particles are emitted mainly in Ihe forward direction, so that the number of particles belonging to direct reactions is equal to the difference between the counts in the forward and backward hemi- spheres. In order to find the total direct reaction cross section, one should know the fraction of cases, in which two iight charged particles per event are produced. Coincidence experiments would be necessary to determine this fraction in a rigorous way, but such experiments were performed onfy for the (9Be, ‘Be) reaction on ‘*Si. In some cases considerations on Q-values and spectroscopic factors allow one to exclude certain reactions either completely or in certain parts of the spectra. The remaining uncertainty in the total direct reaction cross section is rather small and is included in the error quoted in table 3.

The particular procedure was dependent on the project&. As an example, the case of ‘Be (at 20 MeV) will be discussed. Here, mainly a-particles are produced in direct reactions. The other direct processes are inelastic scattering and ‘Be transfer leading to the emission of a neutron. As this last reaction was not measured its cross section is not included in the total reaction cross section for direct processes. In breakup and neutron transfer processes two cw-particles are formed. These reactions are clearly seen as a bump in the a-spectra at low energies, if they proceed via the ground state- of sBe (fig. 6). Alpha particles with higher energies originate in a- and ‘He-transfer reactions or in neutron transfer processes via excited states of *Be. In the Jatter case, the second or-particle has a very low energy and will not be measured because of the energy threshold of the detecting system. Thus a rather simple separation between events belgnging to processes with one and with two a-particles in the final state is possible. The main uncertainty comes from the extrapolation of the part of the spectra corresponding to the emission of one cc-particle to lower energies. A further differentiation of the various direct reactions is not necessary if one is interested in the tota reaction

184 M. Huyi et al. / Fusion and direct reactions

6Li + ‘?3i Direct Contribution

Y 0 IO 20 30 0 IO 20

%‘0°

9 IO l c.

8 l s

i

5 .- ‘.

8’ . l t

E

.

LA- O IO 20

.*-% . l

.

l .

~

.* .

.

.

3 -

‘“~~~1 0 IO 20 300 IO 20 30 0 IO 20 30

gBe + 2eSi Direct Contribution

IO 20 300 IO 20 30 0 IO 20 30

&.,I [MeVl

Fig. 6. Direct contributions For 9Be+Z8Si and “C+“Si only the cc-spectra

185

0 5 IO I5 20 25 30

ECM [Mevl

9Be + 28Si 20 MeV

Neutrontransfer (*Be, ‘Be)

Neutrontransfer (‘Se, ‘Be*)

Fig. 7. Separation into different reactions for the direct contribution in the a-spectra of the reaction

%e+ ‘%i at 20 MeV.

cross section only. It can be done in a rather reliable way on the basis of an experiment, in which 8Be nuclei were identified by recording two a-particles in coincidence. The DWBA analysis of the measured data (see solid line in fig. 2) allows one to determine cross sections for not only reactions with *Be in the ground state as an intermediate nucleus, but also for processes via excited states of ‘Be. Fig. 7 indicates how the different direct reaction processes contribute to the spectrum of a-particles.

As mentioned earlier some information on inelastic scattering could be obtained simultan~usly with the measurement of the eiastic scattering. Additional data, especially for “C projectiles, could be found in the literature. Very little is, however, known on cross sections to higher excited states. The inelastic scattering cross sections included in the direct reaction cross section in table 3 are only lower limits.

The result of the estimations for the direct reaction cross sections are listed in table 3. In the following paragraphs a few indications concerning the relative importance of different reactions will be given:

(a) 6Li+z8Si: The most im~rtant direct reaction is the neutron transfer which accounts for approximately half of the total direct cross section; the. rest is shared mainly between breakup into a deuteron and an a-particle [fragmentation into three parts is negligible 22)] and a-transfer processes. Inelastic scattering contributes only a few percent.

(b) 9Be+ 28Si: The contributions from alpha and ‘He transfer processes increase strongly from approximately zero at lower beam energies (below 14 MeV) to around half of the total direct cross section at the highest energy., Breakup and neutron transfer cross section are of the same order of magnitude and both

186 M. Hugi et ni. / Fusion ttnd direct reacrions

decrease with increasing energy from 40 “/i, to 20 >& Inelastic scattering is responsible for a few percent of all direct reactions also in this case.

(c) r2C+ 28Si: Inelastic scattering is in this case responsible for at least 3 of the total direct cross section. The proton and deuteron spectra have no contributions from direct reactions. The contribution to the cr-spectra shows a large number of cr’s emitted with rather high energies. Such M’S are produced either in an g-transfer reaction leaving the residual 8Be in a highly excited state, or by two a- and 8Be- transfer reactions. A clean separation of the two reactions was not possible.

6. Discussion

The determination of fusion, direct and total reaction cross sections is not free from model assumptions. A good test for the reliability of the results is to check the balance of the total reaction cross section against the sum of fusion and direct processes (fig. 8 and table 3). The data of the present work fulfill this balance within the quoted errors. Considering other fusion measurements for the same reactions, it seems extremely difficult to explain the large differences between total and fusion reaction cross sections reported by Eck 23) for 9Be+ 28Si at 30 MeV and by Jordan 8, for r2C+ 28Si at low energies. Therefore their results are disregarded in the further discussions. Discrepancies exist also between the optical model reaction cross sections of Jordan ‘) and Rascher ‘) for I ho + “Si, whereas their fusion cross sections are in agreement.

The fusion cross sections of the four systems 6Li+ ‘*Si, 9Be+28Si, “C+‘*Si and 160+28Si behave very similarly. This becomes quite obvious if we consider the parameters of the Glas-Mosel model of fusion 24). In this model. the fusion

‘& +*?$i ‘2C+28Si

Fig. 8. Fusion, direct and optical model reaction cross sections for the studied systems. Curves are to guide the eye.

hf. Htqi et al. 1 Fusion and direct reactions I87

cross section can be parametrised as

&Xl - v131~c.m.) low energies flfus =

nRf,U - ~cri&,.~ high energies

with R, = ~~(~~~~~~. The parameters fitted to the experiment (table 4) show a steady increase of the barrier height with the projectile mass, but no dependence on the projectile binding energy. Restricting the further discussion to low-energy data we note that the barrier radius ip, lies near to the strong absorption radius where the potential is well defined by elastic scattering. Therefore low-energy fusion experiments give no additional information on the nuclear potential. Similar ideas as in the Gas-Mosel model 26> can be used to calculate the fusion cut-off angular momentum and the fusion cross section if the nuclear potential is known (e.g. from an optical model analysis). It is worthwhile to note that the folding potentials determined by Satchler [with normalisation factors of 0.6 and 0.4 for 6Li and 9Be. respectively *‘)I give very good agreement not only with elastic scattering data, but also with the fusion cross sections.

TABLE 4

Fusion parameters in the Glas-Mosel model

Reaction v, (MeV) rB (fmf V,, (MeW r,, (fm) Ref.

bLi + ‘%i 6.0 1.48 9Be + *“Si 8.8 I .46

‘2C+28Si 12.9 1.39 15.0 1.39 0.0 1.09

*Y+‘% 16.6 1.45 0.0 0.99 :;

17.2 1.44 0.0 1.11 gI

R = r(,4;‘“+A”3). t

The contribution of the direct reactions depends quite strongly on the projectiles. At low energies it practically vanishes for the strongly bound i 2C and 160 while for the weakly bound ‘Be and 6Li it is of the same order of magnitude as the contri- bution of the fusion reactions. This behaviour is clearly seen in the optical poten- tials. For loosely bound particles the potentials are more diffuse and contain a higher imagina~ part.

We gratefully acknowledge the ~~ancial support of the Swiss National Science Foundation. Special thanks are due to Prof. K. Crotowski and the staff of the Nuclear Detector Laborato~ of the Jagellonian University for providing Li- drifted semiconductor detectors for the experiment, and to Dr. G. R. Satchfer for sending us numericat values of his potent~aIs.

188

References

1) J. R. Birkehmd, L. E. Tubbs, 5. R. Huizenga, J. N. De and D, Specber, Phys. Reports 56 (1979) 107 2) J. P. Wieleczko, S. Harar, M. Conjeaud and F. Saint-Laurent, Phys. Len. 93B (1980) 35 3) D. G. Kovar, D. F. Geesaman, T. H. Braid, Y. Eisen, W. Henning, T. R. Ophel, M. Paul, K. E.

Rehm, S. J. Sanders, P. Sperr, J. P. Schiffer, S. L. Tabor, S. Vigdor and 3. Zeidman, Phys, Rev. C20 (1979) 1305

4) L. Jarczyk, J. Okolowicz, A. Strzaikowski, H. Witala, W. Zipper. J. Lang. R, Mtiller, E, Ungricht and J. UntctnChrer, Phys. Rev. Cl7 (1978) 2106

5) K. Bodek, M. Hugi, J. Lang, R. Miiller, E. Ungr~~fit, K. Jankowskj, W. Zipper, L. Jarczyk, A. Strza~kowski, G. Willim and H. Witala, Nucl. Phys. A339 (1980) 353

6) R. Balzer, M. Hugi, B. Kamys, J. Lang, R. Mfiller, E. Ungricht, J. UnternLhrer, L. Jarczyk and A. Strzalkowski, Nucl. Phys. A293 (1977) 518

7) M. S. Zismann~ J. 6. Cramer, D. A. Goldberg, 3. W. Watson and R. M. DeVries, Pbys. Rev. C2f (1980) 2398

8) W. J. Jordan, J. V. Maher and J. C. Peng, Phys. Lett. 87B (1979) 38 9) R. Rascher, W. F. J. Miifler and K. P. Lieb, Phys. Rev. C20 (1979) 1028

10) E. Ungricht, Thesis ETH Ziiricb (1979 unpublished) 11) J. Lang, R. Miiller. J. Unternlhrer, L. Jarczyk, B. Kamysand A. Strzaikowski, Phys. Rev. Cl6(1977)

1448 12) J. E. Poling, E. Norbeck and R. R. Carlson, Phys. Rev. Cl3 (1976) 648 13) K. Bethge, C. M. Fou, and R. W. Zurmiihle, Nucl. Pbys. Al23 (1969) 521 14) C. M. Cheng J. V. Maher, W. Oelert and F. D. Snyder, Phys. Lett. 71B (1977) 304 15) 3.6. Cramer, R. M. DeVries, D. A. Goldberg, M. S. Zisman andC. F. Maguire, Phys. Rev. (X4(1976)

2158 16) D. Wilmore and P. E. Hodgson, Nucl. Phys. 32 (1962) 353 17) J. R. Grover and J. Gilat, Phys. Rev. 157 (1967) 802 18) J. Gilat, BNL Report No. BNL 50246 (T-580) 19) C. M. Perey and F. G. Percy, Atomic Data and Nucl. Data Tables 13 (1974) 293 20) D. W. Lang, Nucl. Phys. 77 (1966) 545 21) A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1446 22) H. Gemmecke, Habilitation Univ. Heidelberg (1978) unpublished 23) J. S. Eck, J. R.‘Leigh, T. R. Ophel and P. D. Clark, Phys. Rev. C21 (1980) 2352 24) D. Glas and U. Mosel, Nucl. Phys. A237 (1975) 429 25) C. R, Satchler, Phys. Lett. 833 (1979) 284 26) M. Hugi, L. Jarczyk, B. Kamys, J. Lang, R. Miiiler, A. Str~alkowski, E. Ungricht and W. Zipper,

J. of Phys. 66 (1980) 12.57 27) J. S. Eck, T. J. Gray and R. K. Gardner, Phys. Rev. Cl6 (1977) 1873