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Elastic scattering of polarized deuterons from 40Ca and 58Ni at intermediate energies
Volume 156B, n u m b e r 3,4
PHYSICS LETTERS
20 June 1985
ELASTIC SCATI'ERING OF POLARIZED D E U T E R O N S F R O M 4°Ca AND ~SNi AT INTERMEDIATE ENERGIES NGUYEN VAN SEN, J. ARVIEUX, YE YANLIN, G. GAILLARD 1 Instltut des Sciences Nuclbalres, F-38026 Grenoble, France
B. BONIN, A. B O U D A R D , G. BRUGE, J.C. L U G O L D - Ph N / M E , CEN- Saclay, F-91191 Gtf - sur- Yvette, France
R. BABINET, T. H A S E G A W A
2,
F. SOGA 2
Laboratotre Nattonal Saturne, F- 91191 Gzf - sur- Yvette, France
J.M. CAMERON, G.C. NEILSON and D.M. SHEPPARD Department of Physics, Unwerstty of Alberta, Edmonton T6G 2J1, Canada
Recewed 21 February 1985
Angular dlstnbut~ons of cross secuon, and Ay and Ayy analyzang powers were measured for polarized deuteron elastic scattenng from 58N~ at 200, 400 and 700 MeV, and 4°Ca at 700 MeV. Phenomenologmal potenttals were obtmned from an optical model analysis of the data The total reaction cross sections deduced were compared to predictions from the Glauber theory optical hrmt.
Polarization data have been widely measured [1 ] for the deuteron elastic scattering at energies up to 80 MeV. In contrast, at intermediate energies there are until now only a few pioneering data obtained 25 years ago by means of double-scattering techniques, with a rather limited accuracy [2]. This lack of data prevents a reliable theoretical investigation of nuclear reactions involving the d-nucleus interaction [3,4]. For instance, it was recently demonstrated [3] in a (10, d) reaction study that the DWBA calculations at intermediate energies depend strongly on the distortion effects, with a greater sensitivity to deuteron optical potentials than to proton ones. Recent measurements [5] for the elastic scattering of 80 MeV polarized deuterons from 58Ni exhibited evidence for a nuclear rainbow phenomenon, characi Present address: T R I U M F , Vancouver, Canada 2 Present address. INS, Tokyo, Japan
0370-2693/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
terized by an exponential-like faUoff of the cross section at large scattering angles associated with rising values of the analyzing powers saturating close to unity. Description of such a refractive process has been proven to be useful towards an unambiguous determination of the interaction potential in the nuclear surface [6], while higher energy data should "probe further into the surface region" [7]. In the present work, angular distributions of o(0), and analyzing powers were measured for 58Ni targets at 200, 400, and 700 MeV and 40Ca at 700 MeV with polarized deuteron beams from the Saturne synchrotron. The measurements were performed with beam intensity up to 5 X 109 d/s and beam polarization of about 82% of the maximum value for the tensor part and nearly 100% for the vector part. The beam polarization was measured by a poladrneter described recently [8]. The scattered deuterons were detected with the energy-loss spectrometer SPES 1 185
PHYSICS LETTERS
Volume 156B, number 3A
Targets of 58Ni, 147 and 30 mg/cm 2 thick, of ~9]. °Ca, 200 mg/cm 2 thick, and of mtca, 24.3 mg/cm 2 thick, were used in the measurements, the thinner in those at small forward angles. Beam spots on the target were of about 8 mm in diameter. The energy resolution of the detected deuterons, presently better than 300 keV, stems essentially from the energy loss straggling in the target. In order to measure the vector Ay and tensor Ayy analyzing powers simultaneously with o(0), four beam polarization states, one state per beam burst, were produced through r.f. transitions. The relative normalization of the countings was made by means of either a secondary-emission detector placed upstream of the scattering chamber or a threescintillator telescope mounted in this chamber at 50 ° in the vertical plane for detecting particles produced in the target. Tensor asymmetries of a few percent were measured on that scintillator detector, so that relevant corrections were made. For the absolute normalization of the data, the incident number of deuterons was measured by means of an activation method [10]. A carbon disk is then bombarded during about five minutes with the incident beam, and the ll C production in the inclusive reaction C(d, l l c ) x subsequently measured through the 11Cpositron decay. The experimental results are displayed in fig. 1, where the error bars account only for the statistical uncertainties. The absolute normalization was made with overall errors of about 10% for o(O), including uncertainties on target thickness and projectile num-
7oo
F
•<
'
'-~-'-- l
'
40
20
70o
'
,
~J'.4
o50
(~ " 20
0
4'0
0
ec.m(deg-)
10 ' 20
0
1'0
20
Fig. 1. Angular distributions of Rutherford-reduced cross section and analyzing powers for deuteron elastic scattering from SgNi and 4°Ca, compared to optical model calculations with the parameters in table 1. 186
20 June 1985
ber, and 6% for the analyzing powers. The general pattern of o(0) and Ay at 700 MeV and particularly at 400 MeV is reminiscent of the proton data behavior in the transition energy region (200-500 MeV). The present data were analyzed in terms of the optical model using a complex central potential of the Woods-Saxon shape, a spin orbit term of the Thomas form, and a Coulomb term given by a potential for a uniformly charged sphere of radius R c = 1.3 A~/3 fm. From now on, the notations are the same as in Daehnick et al. [1]. These authors have performed a systematic analysis of deuteron elastic scattering from 12 to 90 MeV. Their DCV-F global potential is able to provide the main features of the 200 MeV data, particularly the refractive behavior related to the rainbow phenomenon, so that its parameters were used as starting values for the fitting procedure. The calculations were performed with the ECIS code [11 ]. Various approximate methods of taking the relativistic kinematics into account in the Schrbdinger equation have been proposed [12]. In ECIS, the reduced mass is calculated with the CM total energies of the projectile and target instead of the rest masses, and the wave number is deduced from the CM projectile momentum, while the optical potential is unchanged. The polarization data allow one to put severe constraints upon the determination of the parameters. Although a rainbow phenomenon is clearly observed at 200 MeV, ambiguities still remain when only o(0) and Ayy are fitted. But when Ay is taken into account the ambiguities are eliminated and a single family of optical model parameters is, heretofore, obtained. Similar ambiguities occur at 400 MeV but the roles of Ay andAyy are permuted. These features point out the usefulness of a simultaneous measurement of o(0) and both the vector and tensor components. At 700 MeV the coupling of Ay andAyy are stronger; a good fit of o(0) and one of them provides generally an acceptable description of the other. The data for 4°Ca at 700 MeV compared to those for 58Ni do not reveal a strong mass dependence. The o~tical potential for 40Ca is very close to that for 50' Ni. An 8% reduction of the real potential strenp-~th for 5 8 Ni leads to a fit of comparable quality for ~ u , Ca. Without such a reduction the X2 would be worsened by about 15%. The calculations, in fig. 1, reproduce fairly well
Volume 156B, number 3,4
PHYSICS LETTERS
e~
o
=22
~
oo
O
¢'q
O
I
,---t
c5~c5
c5
~
o. o . o .
¢'1
~e,i
eq
c5oc5
c5
t~
t'-I (',1
,--I
~c5~
~N O
o.
ed
c5 c5 c5 c5
20 June 1985
the experimental data except at angles smaller than 5 ° where the calculations underestimate noticeably o(0) for 200 and 700 MeV. A careful investigation of measurements and calculations does not allow one to presume until now the origin of this discrepancy, which may be due to shortcomings of the theoretical model although an experimental overestimate cannot be def'mitely ruled out. The best-fit parameters, in table 1, do not allow a straightforward interpretation of the energy dependence of the potential. Attempts to put boundary conditions for a smooth energy dependence of the parameters lead to fits with appreciably lower quality. A more significant comparison with the calculations at lower energies can be made through the volume integrals (J/2A) and the rms radii. The imaginary J/2A and rms radius, in fig. 2, follow fairly well the trends predicted by the DLW-F global potential [ 1], which is able to anticipate their slope change near 200 MeV. The real J/2A decreases with the energy up to 400 MeV then increases slightly at 700 MeV. The real rms radius agrees with the predicted value at 200 MeV but decreases with energy above 400 MeV reflecting the progressive transparency of the target. Such a transparency has been pointed out by DeVries and Peng [13] in a study of nucleus-nucleus total reaction cross sections (OR). Since the composite projectiles are strongly absorbed at low energies, o R is expected to level off at the geometrical limit and stays at that value at intermediate and high ener-
400 ,
JR/2A
JI/2A
200
+
\ ~-'~+ ~
;
I
+~ ~
~
I
i
i
~-+_
_+_
I
_ .+_
+
rrns RR
' 4;0 '8~o
Fins
RI
400
800
Tlob(MeV) Fig. 2. Volume integrals (in MeV fm 3) and rms radii (in fm) for the real (RR) and imaginary (RI) parts of the optical potential: (+) present work; (e) previous works at lower energies [1 ]. The dashed line represents the predictions from the DCV-F global potential [1 ].
187
Volume 156B, number 3,4
PHYSICS LETTERS
1.6
0.8 Ii,,ll
,
10
,
.I,.,.t
i
,
,I.ii
100 Tc.m/n (HEY)
Fig. 3. Reaction czoss sections from the present (+) and previous (e) analyses [1 ], and direct measurements (X) compared to Glauber theory predictions (full line) and the geometrical limit [13] calculated with R = 7.4 fm (dasdhed line). gies. In fact, there is a striking similarity between the behavior o f o R and the total nucleon-nucleon cross section (oNN), which decreases with increasing energy up to the pion production threshold, then increases [14,15]. Using the Glauber theory optical limit [16], DeVries and Peng [13] were able to describe the energy dependence o f o R for various systems. In fig. 3, the o R obtained for the d + 58Ni system from the present optical model analysis are plotted together with those deduced at lower energies [1 ]. At intermediate energies, o R is conspicuously lower than the geometrical value. The microscopic calculations shown use the same theoretical approach as in ref. [13]. The o NN is taken to be the isotopic average [17] of the n - p and p - p values, which are deduced from a smooth fit o f the experimental data [14,15] for laboratory energy above 20 MeV, and calculated at lower energies from N - N phase-shifts [18], since the p - p cross section is not accurately known at such low energies. The nuclear density distribution is assumed to be the charge distribution provided by electron scattering data [19]: p(r) = P0(1 + wr2[c2)[1
+ exp((r - c)/z)]-1,
with c = 4.3092 fm, z = 0.5169 fm, and w = -0.1308. The microscopic calculations are able to reproduce the phenomenological results within 10%, emphasizing the strong correlation o f the d-nucleus and N - N interactions. In summary, simultaneous measurements of o(0), and vector and tensor analyzing powers for deuteron elastic scattering from 58Ni at 200, 400 and 700 MeV 188
20 June 1985
allow one to obtain almost without ambiguities optical potentials for the d + 58Ni interaction. The potentials at 700 MeV for 58Ni and 40Ca are very similar and can then be considered to be a good representation of the optical potential for medinm-mass targets at that energy. The imaginary volume integral and rms radius of the 58Ni potential, plotted as function o f energy, follow the trends predicted from a global analysis of low-energy data [1 ]. The real rms radius together with the o R deduced from the calculations reflect the transparency of the nucleus at intermediate energies and emphasize the importance o f the knowledge of the nuclear wavefunction inner part in studies of nuclear reactions involving the d-nucleus interaction. The present analysis may be subject to shortcomings due to the non-relativistic approach. The data available are, however, expected to stimulate investigations of the relativistic effects in the deuteron scattering [20] in light of the successful description of the proton scattering by relativistic theories.
References [1] W.W. Daehnick et al., Phys. Rev. C21 (1980) 2253, and references therein. [2] J. Button and R. Mermod, Phys. Rev. 118 (1960) 1333, and references therein. [3] G.R. Smith et al., Phys. Rev. C30 (1984) 593. [4] H. Ohnuma et al., Phys. Lett. 147B (1984) 253. [5] E.J. Stephenson et al., Nucl. Phys. A359 (1981) 316. [6] D.A. Goldberg et al., Phys. Rev. C10 (1974) 1362. [7] J.G. Kramer and R.M. DeVries, Phys. Rev. C22 (1980) 91. [8] J. Arvieux et al., Nucl. Phys. A431 (1984) 613 [9 ] A. Boudazd, Ensembles de d6teetion magn6tique du Laboratoire National Saturne, LNS Report (1980). [10] H. Qu6chon, Thesis (Orsay, 1980); Phys. Rev. C26 (1982) 2565. [11] J. Raynal, ECIS code, CEA-R2511 Report (1965). [12] A. Ingemarsson, Phys. Scr. 9 (1974) 156, [13] R.M. DeVries and J.C. Peng, Phys. Rev. C22 (1980) 1055. [14] W.N. Hess, Rev Mod. Phys. 30 (1958) 368. [15] D. Saloner and C. Teopffer, Nucl. Phys. A283 (1977) 108. [16] W. Czyz and L.C. MaMmon, Ann. Phys. (NY)52 (1969) 59. [17] P.J. Karol, Phys. Rev. Cll (1975) 1203. [18] M.H MacGregor et al., Phys. Rev. 182 (1969) 1714. [19] C.W. DeJager et al., At. Data Nucl. Data Tables 14 (1974) 479. [20] J.R. Shepard et al., Phys. Rev. Lett. 49 (1982) 14.
PHYSICS LETTERS
20 June 1985
ELASTIC SCATI'ERING OF POLARIZED D E U T E R O N S F R O M 4°Ca AND ~SNi AT INTERMEDIATE ENERGIES NGUYEN VAN SEN, J. ARVIEUX, YE YANLIN, G. GAILLARD 1 Instltut des Sciences Nuclbalres, F-38026 Grenoble, France
B. BONIN, A. B O U D A R D , G. BRUGE, J.C. L U G O L D - Ph N / M E , CEN- Saclay, F-91191 Gtf - sur- Yvette, France
R. BABINET, T. H A S E G A W A
2,
F. SOGA 2
Laboratotre Nattonal Saturne, F- 91191 Gzf - sur- Yvette, France
J.M. CAMERON, G.C. NEILSON and D.M. SHEPPARD Department of Physics, Unwerstty of Alberta, Edmonton T6G 2J1, Canada
Recewed 21 February 1985
Angular dlstnbut~ons of cross secuon, and Ay and Ayy analyzang powers were measured for polarized deuteron elastic scattenng from 58N~ at 200, 400 and 700 MeV, and 4°Ca at 700 MeV. Phenomenologmal potenttals were obtmned from an optical model analysis of the data The total reaction cross sections deduced were compared to predictions from the Glauber theory optical hrmt.
Polarization data have been widely measured [1 ] for the deuteron elastic scattering at energies up to 80 MeV. In contrast, at intermediate energies there are until now only a few pioneering data obtained 25 years ago by means of double-scattering techniques, with a rather limited accuracy [2]. This lack of data prevents a reliable theoretical investigation of nuclear reactions involving the d-nucleus interaction [3,4]. For instance, it was recently demonstrated [3] in a (10, d) reaction study that the DWBA calculations at intermediate energies depend strongly on the distortion effects, with a greater sensitivity to deuteron optical potentials than to proton ones. Recent measurements [5] for the elastic scattering of 80 MeV polarized deuterons from 58Ni exhibited evidence for a nuclear rainbow phenomenon, characi Present address: T R I U M F , Vancouver, Canada 2 Present address. INS, Tokyo, Japan
0370-2693/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
terized by an exponential-like faUoff of the cross section at large scattering angles associated with rising values of the analyzing powers saturating close to unity. Description of such a refractive process has been proven to be useful towards an unambiguous determination of the interaction potential in the nuclear surface [6], while higher energy data should "probe further into the surface region" [7]. In the present work, angular distributions of o(0), and analyzing powers were measured for 58Ni targets at 200, 400, and 700 MeV and 40Ca at 700 MeV with polarized deuteron beams from the Saturne synchrotron. The measurements were performed with beam intensity up to 5 X 109 d/s and beam polarization of about 82% of the maximum value for the tensor part and nearly 100% for the vector part. The beam polarization was measured by a poladrneter described recently [8]. The scattered deuterons were detected with the energy-loss spectrometer SPES 1 185
PHYSICS LETTERS
Volume 156B, number 3A
Targets of 58Ni, 147 and 30 mg/cm 2 thick, of ~9]. °Ca, 200 mg/cm 2 thick, and of mtca, 24.3 mg/cm 2 thick, were used in the measurements, the thinner in those at small forward angles. Beam spots on the target were of about 8 mm in diameter. The energy resolution of the detected deuterons, presently better than 300 keV, stems essentially from the energy loss straggling in the target. In order to measure the vector Ay and tensor Ayy analyzing powers simultaneously with o(0), four beam polarization states, one state per beam burst, were produced through r.f. transitions. The relative normalization of the countings was made by means of either a secondary-emission detector placed upstream of the scattering chamber or a threescintillator telescope mounted in this chamber at 50 ° in the vertical plane for detecting particles produced in the target. Tensor asymmetries of a few percent were measured on that scintillator detector, so that relevant corrections were made. For the absolute normalization of the data, the incident number of deuterons was measured by means of an activation method [10]. A carbon disk is then bombarded during about five minutes with the incident beam, and the ll C production in the inclusive reaction C(d, l l c ) x subsequently measured through the 11Cpositron decay. The experimental results are displayed in fig. 1, where the error bars account only for the statistical uncertainties. The absolute normalization was made with overall errors of about 10% for o(O), including uncertainties on target thickness and projectile num-
7oo
F
•<
'
'-~-'-- l
'
40
20
70o
'
,
~J'.4
o50
(~ " 20
0
4'0
0
ec.m(deg-)
10 ' 20
0
1'0
20
Fig. 1. Angular distributions of Rutherford-reduced cross section and analyzing powers for deuteron elastic scattering from SgNi and 4°Ca, compared to optical model calculations with the parameters in table 1. 186
20 June 1985
ber, and 6% for the analyzing powers. The general pattern of o(0) and Ay at 700 MeV and particularly at 400 MeV is reminiscent of the proton data behavior in the transition energy region (200-500 MeV). The present data were analyzed in terms of the optical model using a complex central potential of the Woods-Saxon shape, a spin orbit term of the Thomas form, and a Coulomb term given by a potential for a uniformly charged sphere of radius R c = 1.3 A~/3 fm. From now on, the notations are the same as in Daehnick et al. [1]. These authors have performed a systematic analysis of deuteron elastic scattering from 12 to 90 MeV. Their DCV-F global potential is able to provide the main features of the 200 MeV data, particularly the refractive behavior related to the rainbow phenomenon, so that its parameters were used as starting values for the fitting procedure. The calculations were performed with the ECIS code [11 ]. Various approximate methods of taking the relativistic kinematics into account in the Schrbdinger equation have been proposed [12]. In ECIS, the reduced mass is calculated with the CM total energies of the projectile and target instead of the rest masses, and the wave number is deduced from the CM projectile momentum, while the optical potential is unchanged. The polarization data allow one to put severe constraints upon the determination of the parameters. Although a rainbow phenomenon is clearly observed at 200 MeV, ambiguities still remain when only o(0) and Ayy are fitted. But when Ay is taken into account the ambiguities are eliminated and a single family of optical model parameters is, heretofore, obtained. Similar ambiguities occur at 400 MeV but the roles of Ay andAyy are permuted. These features point out the usefulness of a simultaneous measurement of o(0) and both the vector and tensor components. At 700 MeV the coupling of Ay andAyy are stronger; a good fit of o(0) and one of them provides generally an acceptable description of the other. The data for 4°Ca at 700 MeV compared to those for 58Ni do not reveal a strong mass dependence. The o~tical potential for 40Ca is very close to that for 50' Ni. An 8% reduction of the real potential strenp-~th for 5 8 Ni leads to a fit of comparable quality for ~ u , Ca. Without such a reduction the X2 would be worsened by about 15%. The calculations, in fig. 1, reproduce fairly well
Volume 156B, number 3,4
PHYSICS LETTERS
e~
o
=22
~
oo
O
¢'q
O
I
,---t
c5~c5
c5
~
o. o . o .
¢'1
~e,i
eq
c5oc5
c5
t~
t'-I (',1
,--I
~c5~
~N O
o.
ed
c5 c5 c5 c5
20 June 1985
the experimental data except at angles smaller than 5 ° where the calculations underestimate noticeably o(0) for 200 and 700 MeV. A careful investigation of measurements and calculations does not allow one to presume until now the origin of this discrepancy, which may be due to shortcomings of the theoretical model although an experimental overestimate cannot be def'mitely ruled out. The best-fit parameters, in table 1, do not allow a straightforward interpretation of the energy dependence of the potential. Attempts to put boundary conditions for a smooth energy dependence of the parameters lead to fits with appreciably lower quality. A more significant comparison with the calculations at lower energies can be made through the volume integrals (J/2A) and the rms radii. The imaginary J/2A and rms radius, in fig. 2, follow fairly well the trends predicted by the DLW-F global potential [ 1], which is able to anticipate their slope change near 200 MeV. The real J/2A decreases with the energy up to 400 MeV then increases slightly at 700 MeV. The real rms radius agrees with the predicted value at 200 MeV but decreases with energy above 400 MeV reflecting the progressive transparency of the target. Such a transparency has been pointed out by DeVries and Peng [13] in a study of nucleus-nucleus total reaction cross sections (OR). Since the composite projectiles are strongly absorbed at low energies, o R is expected to level off at the geometrical limit and stays at that value at intermediate and high ener-
400 ,
JR/2A
JI/2A
200
+
\ ~-'~+ ~
;
I
+~ ~
~
I
i
i
~-+_
_+_
I
_ .+_
+
rrns RR
' 4;0 '8~o
Fins
RI
400
800
Tlob(MeV) Fig. 2. Volume integrals (in MeV fm 3) and rms radii (in fm) for the real (RR) and imaginary (RI) parts of the optical potential: (+) present work; (e) previous works at lower energies [1 ]. The dashed line represents the predictions from the DCV-F global potential [1 ].
187
Volume 156B, number 3,4
PHYSICS LETTERS
1.6
0.8 Ii,,ll
,
10
,
.I,.,.t
i
,
,I.ii
100 Tc.m/n (HEY)
Fig. 3. Reaction czoss sections from the present (+) and previous (e) analyses [1 ], and direct measurements (X) compared to Glauber theory predictions (full line) and the geometrical limit [13] calculated with R = 7.4 fm (dasdhed line). gies. In fact, there is a striking similarity between the behavior o f o R and the total nucleon-nucleon cross section (oNN), which decreases with increasing energy up to the pion production threshold, then increases [14,15]. Using the Glauber theory optical limit [16], DeVries and Peng [13] were able to describe the energy dependence o f o R for various systems. In fig. 3, the o R obtained for the d + 58Ni system from the present optical model analysis are plotted together with those deduced at lower energies [1 ]. At intermediate energies, o R is conspicuously lower than the geometrical value. The microscopic calculations shown use the same theoretical approach as in ref. [13]. The o NN is taken to be the isotopic average [17] of the n - p and p - p values, which are deduced from a smooth fit o f the experimental data [14,15] for laboratory energy above 20 MeV, and calculated at lower energies from N - N phase-shifts [18], since the p - p cross section is not accurately known at such low energies. The nuclear density distribution is assumed to be the charge distribution provided by electron scattering data [19]: p(r) = P0(1 + wr2[c2)[1
+ exp((r - c)/z)]-1,
with c = 4.3092 fm, z = 0.5169 fm, and w = -0.1308. The microscopic calculations are able to reproduce the phenomenological results within 10%, emphasizing the strong correlation o f the d-nucleus and N - N interactions. In summary, simultaneous measurements of o(0), and vector and tensor analyzing powers for deuteron elastic scattering from 58Ni at 200, 400 and 700 MeV 188
20 June 1985
allow one to obtain almost without ambiguities optical potentials for the d + 58Ni interaction. The potentials at 700 MeV for 58Ni and 40Ca are very similar and can then be considered to be a good representation of the optical potential for medinm-mass targets at that energy. The imaginary volume integral and rms radius of the 58Ni potential, plotted as function o f energy, follow the trends predicted from a global analysis of low-energy data [1 ]. The real rms radius together with the o R deduced from the calculations reflect the transparency of the nucleus at intermediate energies and emphasize the importance o f the knowledge of the nuclear wavefunction inner part in studies of nuclear reactions involving the d-nucleus interaction. The present analysis may be subject to shortcomings due to the non-relativistic approach. The data available are, however, expected to stimulate investigations of the relativistic effects in the deuteron scattering [20] in light of the successful description of the proton scattering by relativistic theories.
References [1] W.W. Daehnick et al., Phys. Rev. C21 (1980) 2253, and references therein. [2] J. Button and R. Mermod, Phys. Rev. 118 (1960) 1333, and references therein. [3] G.R. Smith et al., Phys. Rev. C30 (1984) 593. [4] H. Ohnuma et al., Phys. Lett. 147B (1984) 253. [5] E.J. Stephenson et al., Nucl. Phys. A359 (1981) 316. [6] D.A. Goldberg et al., Phys. Rev. C10 (1974) 1362. [7] J.G. Kramer and R.M. DeVries, Phys. Rev. C22 (1980) 91. [8] J. Arvieux et al., Nucl. Phys. A431 (1984) 613 [9 ] A. Boudazd, Ensembles de d6teetion magn6tique du Laboratoire National Saturne, LNS Report (1980). [10] H. Qu6chon, Thesis (Orsay, 1980); Phys. Rev. C26 (1982) 2565. [11] J. Raynal, ECIS code, CEA-R2511 Report (1965). [12] A. Ingemarsson, Phys. Scr. 9 (1974) 156, [13] R.M. DeVries and J.C. Peng, Phys. Rev. C22 (1980) 1055. [14] W.N. Hess, Rev Mod. Phys. 30 (1958) 368. [15] D. Saloner and C. Teopffer, Nucl. Phys. A283 (1977) 108. [16] W. Czyz and L.C. MaMmon, Ann. Phys. (NY)52 (1969) 59. [17] P.J. Karol, Phys. Rev. Cll (1975) 1203. [18] M.H MacGregor et al., Phys. Rev. 182 (1969) 1714. [19] C.W. DeJager et al., At. Data Nucl. Data Tables 14 (1974) 479. [20] J.R. Shepard et al., Phys. Rev. Lett. 49 (1982) 14.