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Excitation of 6Li by 16O at Ecm = 18.7 MeV
Volume 142B, number 4
PHYSICS LETTERS
26 July 1984
EXCITATION OF 6Li BY 160 A T E c m = 18.7 MeV ¢~ M.F. VINEYARD 1, K.W. KEMPER and J. COOK Department o f Physics, Florida State University, Tallahassee, FL 32306, USA Received 17 January 1984
Angular distributions have been measured at Ecm = 18.7 MeV tbr the elastic scattering of 6 Li + 160 and the excitation of the 3+ (2.18) MeV state in 6Li. The sequential breakup cross section is about a factor of 30 smaller than the direct breakup cross section. Coupled-channels effects due to the 3+ state of 6Li are found to have an important role in the scattering process.
Recently, considerable success has been achieved in obtaining optical potentials for nuclear scattering beginning with a microscopic n u c l e o n - n u c l e o n interaction [ 1 ]. However, success in describing the scattering o f 6Li, 7Li and 9Be projectiles has been possible only with a significant reduction in the strength of the potential. Recent attempts to understand this have focussed on coupling to the breakup channels (e.g. ref. [2]). In this Letter, inelastic scattering data for the excitation o f 6Li are presented. These are the first measurements o f the predominantly nuclear excitation o f the unbound 3 + (2.18 MeV) state o f 6Li in a heavy-ion collision. The effect o f coupling to this state is found to be very important in understanding the scattering process. Since the excited states o f 6 Li are unbound, the usual technique used to measure the projectile excitation o f 6Li has been to detect the a and deuteron breakup products in a coincidence experiment and then kinematically reconstruct the cross sections. In order to obtain absolute cross sections from these measurements, certain assumptions must be made about the dissociation probability o f the resonant 6Li* nucleus, since the c~ and d cannot be emitted in a relative S state. Earlier studies [3] have been perWork supported in part by the National Science Foundation. 1 Present address: Argonne National Laboratory, Argonne, IL 60439, USA.
0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Divison)
formed at energies close to the Coulomb barrier in which the dissociation probabilities o f the 2.18 MeV state in 6Li were calculated assuming a pure E2 interaction in the first step o f the reaction and subsequent decay with relative angular momentum L = 2 between the cz and d. Although reasonable agreement between the results o f these calculations and the experimental dissociation probabilities (determined by piecemeal transformation o f a position spectrum into the CM system o f the 6Li*) was obtained at forward angles, the calculations overpredicted the magnitude o f the dissociation probabilities at the larger angles even at energies close to the Coulomb barrier. Due to the problem o f reconstructing the cross sections, there have previously been no angular distribution measurements for the excitation o f specific states in 6Li in a predominantly nuclear heavy-ion collision. The cross sections reported here for the excitation o f the 3 + (2.18 MeV) state in 6Li were measured with the Florida State University super FN tandem Van de Graaff accelerator by scattering 160 from 6Li at ELA B = 68.6 MeV (EcM = 18.7 MeV) to avoid the dificulties previously discussed. The forward-angle elastic scattering data were measured by scattering 6Li from 160 at ELA B = 25.7 MeV (ECM 18.7 MeV). Silicon surface-barrier counter telescopes were used throughout these measurements to achieve particle identification and, during the 160 + 6Li experiments, to obtain sorted linear energy spectra for the recoil
249
Volume 142B, number 4
PHYSICS LETTERS
6Li particle group in addition to the 160 particle group. The recoil 6Li spectra were taken to obtain the back-angle elastic data. From the 160 spectra, it was possible to obtain an angular distribution for the excitation o f the 3 + (2.18 MeV) state o f 6Li together with an estimate o f the 2 + (4.31 MeV) and continuum breakup cross sections. Absolute normalization of the datawasdetermined using two different techniques. The absolute cross sections for the 6Li scattering data were established by measuring the elastic scattering o f 20 MeV 160 ions from SiO 2 targets at 0LA B = 15--20 ° , where the scattering was found to be Mort. The Mort cross sections and elastic scattering yields were used to determine the product o f the target thickness and detector solid angle which was then used to calculate the absolute cross sections for the 6 Li scattering. The absolute cross sections for the 160 + 6Li reaction were determined by scattering 6.868 MeV protons from the 6 Li targets and comparing to the previously measured cross sections of Bingham et al. [4]. The difference between the forward-angle 6Li scattering cross sections and those for the back-angle 160 + 6Li recoil data was found to be -+6%. A typical 160 spectrum from the 160 + 6Li reaction is shown in fig. la. Spectra were also taken on a I2C target at each angle so that the location in the spectra and the yields from peaks due to this contaminant could be determined. A typical spectrum taken on the 12C target is shown in fig. lb. It can be seen in the spectrum from the 6Li target (fig. la) that there is a broad structureless continuum yield at low ejectile energy while the spectrum from the 12C target (fig. lb) indicates a small yield in this region. By summing this continuum yield, an estimate o f the continuum, or direct, breakup cross section was obtained at each angle. A total continuum cross section estimate o f > 1000 nab was obtained by summing the cross sections obtained at each angle. At several angles it was possible to extract a yield for the 2 + (4.31 MeV) state o f 6Li. An estimate o f the total cross section for this state is 15 rob. From fig. la it is evident that at this energy the direct breakup contribution is much greater than the contribution from the sequential breakup proceeding through the 3 + state. This is in sharp contrast to the findings of an earlier study [5] in which the breakup o f 70 MeV 7Li from 12C was found to be dominated by the sequential process 250
I .!
26 July 1984
Ejob--68.6 MeV
• 1 12Co.o tli
e,ab: 13 °
~
× 3~i
. ~11~,i~,,,. ,. ,.j i
6
°Lio.o'XJ i i '} t/2a ~t Sid t ~ o.oi
1
h~'i 7 o ~S
8;"~5~J~oo" ~);':'!" s~,; '' --~6Too/'J
teO*lzC
IZCo./o b
Elab= 68.6 MeV elob = 15o
6
( i2
x
2 '4
16
C4.44
06.13)Mut
\i
,
60
180
300
q20 Chonnel
5'40
'6 0
Fig. 1. Energy spectra at Elab = 68.6 MeV and 01ab = 13° for (a) 160 + 6Li and (b) ]60 + 12C.
proceeding through the unbound second excited ( 7 / 2 - , 4.63 MeV) state of 7Li. The elastic scattering data were analyzed with the optical model (OM) using a potential consisting of double-folded real and Woods-Saxon imaginary parts. The real double-folded potential was generated by folding the microscopic M3Y interaction [6] (supplemented by a single nucleon exchange term) with the 6Li and 160 ground state densities. The 6Li density was obtained from the electron scattering work of Suelzle et al. [7] and a harmonic oscillator density was assumed for 160. In addition to this optical potential, a Coulomb potential for a point charge interacting with a uniformly charged sphere of radius R = 1.25 (61/3 + 161/3) fm was included. Initially, the normalization factor of the real double-folded poten-
Volume 142B, number 4
PHYSICS LETTERS
b"<.,~ \
I
/
Ec m=18.7MeV
6Li +160
Eloslic •
..•.
. • • •.t;,
• •/•
C
) /
;~*
> io-
'\,% )\,I +\ ~'
E
,/1
"
¢~.
°'/OR [ O I
It
+
~'/'x
i O. /
•'// -
6Li 3 (2.18MeV)
V
O.01
0
i ~
30
,
~
60
i
90 ec.m(.de g. )
i
r
120
150
180
Fig. 2. Data for the elastic scattering of 6Li + 160 at Ecru = 18.7 MeV and the inelastic excitation of the 3+ (2.18 MeV) state in 6 Li. The curves show the results of the optical model (OM) and coupled-channels (CC) calculations discussed in the text. tial was fixed at N = 1.0 and the imaginary potential parameters were extensively searched upon to fit the data. A good fit to the data could not be obtained with this procedure. The normalization factor was then searched upon along with the imaginary potential parameters and a good fit to the data was obtained over the entire angular range with a normalization factor of 0.61. The resulting fit to the elastic scattering data is shown as the dashed line in fig. 2 and the potential parameters are given in table 1. Coupled-channels (CC) calculations were then performed with the computer code CHUCK3 [8] to investigate the effect of coupling the 3 + state in 6Li to the elastic channel. A rotational model was assumed for 6Li, with the 1+ ground state and 3 + (2.18 MeV)
Table 1 Optical model parameters and deformation lengths• The potential consists of a double-folded real part, with a normalization factor N, and a Woods-Saxon imaginary part. Calculation N
W0 ria) (MeV) (fro)
aI 8 °1 (fm) (fm)
8211 (fm)
OM CC
6•62 10.5
0•80 0.90
-0.78
0.61 0.75
a) Rx = rx(A~/a +A.~/3).
1.35 1.05
-1.54
26 July 1984
state belonging to a K = 1 rotational band. The L = 2 transition between the two states and the L = 2 reorientation term for the 3 + state were included in the calculations. The real double-folded form factor was obtained by folding the M3Y interaction with a derivative transition density pO'(r) = 60"ld Po(r)/drl for 6Li and the 160 ground state density. Here PO(r) is the 6Li ground-state density, and 80. is the quadrupole deformation length for the transition from state i to state/'. For the 1+ 4 3 + transition, 801 was fixed by normalizing the transition density to the experimental B(E2; 1+ ~ 3 +) value [9] of 25.6e 2 fm 4. In the rigidrotor model 611 = fi 01 , but we have assumed here 811 = ½8 01 since 6-01 is large. The imaginary part of the" form factor was obtained from a Legendre expansion of a Woods-Saxon potential with the same deformation length as the real part. Coulomb excitation was included with the same 8 01 and was found to only be important for the 3 + channel for 0cm < 20 °. The parameters N, W0, r I and a I were optimised to describe the data, resulting in the final parameters of table 1 and the fits shown as the full lines of fig. 2. The description of the elastic scattering data is reasonable over the whole angular range. The part from 0cm = 60 ° to 90 ° is very sensitive to reorientation effects in the 3 + state and requires a negative 8 2 to be described correctly• Thus the sign of the deformation length is unambiguously determined from the coupled channels calculations. The 3 + prediction has the correct forward angle magnitude if8 01 is reduced by about 15%. This reduction is consistent with the results of Yen et al. [I0] and Petrovich et at. [11] in which their obtained B(E2) values were 10-20% lower than that of ref. [9]. The 3 - (6.13 MeV) state in 160 was only weakly excited, and the inclusion of this state in the CC calculations made little difference to the results. The only effect of including coupling to the 3 - state was a reduction of about 15% in the depth W0 of the imaginary potential. In conclusion, coupled-channels effects due to the 3 + state of 6Li are very important in the scattering of 6Li projectiles. When coupling to this low-lying, strongly excited state was taken into account, two important results were observed. The first being that the normalization of the real double-folded potential, necessary to fit the elastic scattering data, changed from 0.61 to 0.75 thus reducing the discrepancy be251
Volume 142B, number 4
PHYSICS LETTERS
tween 6Li and other heavy-ion projectiles. Secondly, a comparison o f the imaginary potentials obtained from the OM and CC fits shows that when the coupling is included the imaginary potential becomes weaker in the surface region. This provides evidence that at least part o f the large phenomenological imaginary potential which often dominates 6Li scattering arises from coupling to excited states o f 6 Li. From the present 160 + 6Li experiment, it was determined that the total continuum breakup cross section is > 1000 rob. This is very much larger than the total inelastic cross section for the 3 + state (OTOT(3 +) ~ 23 mb) obtained from the CC calculations, and it is possible t h a t , i f the continuum breakup could be included in CC calculations, the renormalization o f the real double-folded potential might be removed. The theoretical work o f ref. [2] is concerned with this, and the data presented here should be valuable in the context o f understanding breakup effects in elastic scattering.
252
26 July 1984
References [1] G.R. Satchler and W.G. Love, Phys. Rep. 55C (1979) 183. [ 1 ] I.J. Thompson and M.A. Nagarajan, Phys. Lett. 106B (1981) 163; Y. SakUragi, M. Yahiro and M. Kamimura, Prog. Theor. Phys. 68 (1982) 322; Y. Sakuragi, M. Yahiro and M. Kamimura, Prog. Theor. Phys. 70 (1983) 1047. [3 ] D. Scholz, H. Gemmeke, L. Lassen, R. Ost and K. Bethge, Nucl. Phys. A288 (1977) 351; H. Gemmeke, B. Deluigi, L. Lassen and D. Scholz, 7. Phys. A286 (1978) 73. [4] H.G. Bingham, A.R. Zander, K.W. Kemper and N.R. Fletcher, Nucl. Phys. A173 (1971) 265. [5 ] A.C. Shorter, A.N. Bice, J.M. Wonters, W.D. Rae, and J. Cerny, Phys. Rev. Lett.46 (1981) 12. [6] G. Bertsch, J. Borysowicz, J. McManus and W.G. Love, Nucl. Phys. A284 (1977) 399. [7 ] L.R. Suelzle, M.R. Yearian and H. Crannel, Phys. Rev. 162 (1967) 992. [8] P.D. Kunz, University of Colorado, unpublished (with modifications by J .R. Comfort). [9] F. Eigenbrod, Z. Phys. 228 (1969) 337. [10] R. Yen, L.S. Cardman, D. Kalivisky, J.R. Legg and C.K. Bockelman, Nucl. Phys. A235 (1974) 135. [11] F. Petrovich, R.H. Howell, C.H. Poppe, S.M. Austin and G.M. Crawley, Nucl. Phys. A383 (1982) 355.
PHYSICS LETTERS
26 July 1984
EXCITATION OF 6Li BY 160 A T E c m = 18.7 MeV ¢~ M.F. VINEYARD 1, K.W. KEMPER and J. COOK Department o f Physics, Florida State University, Tallahassee, FL 32306, USA Received 17 January 1984
Angular distributions have been measured at Ecm = 18.7 MeV tbr the elastic scattering of 6 Li + 160 and the excitation of the 3+ (2.18) MeV state in 6Li. The sequential breakup cross section is about a factor of 30 smaller than the direct breakup cross section. Coupled-channels effects due to the 3+ state of 6Li are found to have an important role in the scattering process.
Recently, considerable success has been achieved in obtaining optical potentials for nuclear scattering beginning with a microscopic n u c l e o n - n u c l e o n interaction [ 1 ]. However, success in describing the scattering o f 6Li, 7Li and 9Be projectiles has been possible only with a significant reduction in the strength of the potential. Recent attempts to understand this have focussed on coupling to the breakup channels (e.g. ref. [2]). In this Letter, inelastic scattering data for the excitation o f 6Li are presented. These are the first measurements o f the predominantly nuclear excitation o f the unbound 3 + (2.18 MeV) state o f 6Li in a heavy-ion collision. The effect o f coupling to this state is found to be very important in understanding the scattering process. Since the excited states o f 6 Li are unbound, the usual technique used to measure the projectile excitation o f 6Li has been to detect the a and deuteron breakup products in a coincidence experiment and then kinematically reconstruct the cross sections. In order to obtain absolute cross sections from these measurements, certain assumptions must be made about the dissociation probability o f the resonant 6Li* nucleus, since the c~ and d cannot be emitted in a relative S state. Earlier studies [3] have been perWork supported in part by the National Science Foundation. 1 Present address: Argonne National Laboratory, Argonne, IL 60439, USA.
0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Divison)
formed at energies close to the Coulomb barrier in which the dissociation probabilities o f the 2.18 MeV state in 6Li were calculated assuming a pure E2 interaction in the first step o f the reaction and subsequent decay with relative angular momentum L = 2 between the cz and d. Although reasonable agreement between the results o f these calculations and the experimental dissociation probabilities (determined by piecemeal transformation o f a position spectrum into the CM system o f the 6Li*) was obtained at forward angles, the calculations overpredicted the magnitude o f the dissociation probabilities at the larger angles even at energies close to the Coulomb barrier. Due to the problem o f reconstructing the cross sections, there have previously been no angular distribution measurements for the excitation o f specific states in 6Li in a predominantly nuclear heavy-ion collision. The cross sections reported here for the excitation o f the 3 + (2.18 MeV) state in 6Li were measured with the Florida State University super FN tandem Van de Graaff accelerator by scattering 160 from 6Li at ELA B = 68.6 MeV (EcM = 18.7 MeV) to avoid the dificulties previously discussed. The forward-angle elastic scattering data were measured by scattering 6Li from 160 at ELA B = 25.7 MeV (ECM 18.7 MeV). Silicon surface-barrier counter telescopes were used throughout these measurements to achieve particle identification and, during the 160 + 6Li experiments, to obtain sorted linear energy spectra for the recoil
249
Volume 142B, number 4
PHYSICS LETTERS
6Li particle group in addition to the 160 particle group. The recoil 6Li spectra were taken to obtain the back-angle elastic data. From the 160 spectra, it was possible to obtain an angular distribution for the excitation o f the 3 + (2.18 MeV) state o f 6Li together with an estimate o f the 2 + (4.31 MeV) and continuum breakup cross sections. Absolute normalization of the datawasdetermined using two different techniques. The absolute cross sections for the 6Li scattering data were established by measuring the elastic scattering o f 20 MeV 160 ions from SiO 2 targets at 0LA B = 15--20 ° , where the scattering was found to be Mort. The Mort cross sections and elastic scattering yields were used to determine the product o f the target thickness and detector solid angle which was then used to calculate the absolute cross sections for the 6 Li scattering. The absolute cross sections for the 160 + 6Li reaction were determined by scattering 6.868 MeV protons from the 6 Li targets and comparing to the previously measured cross sections of Bingham et al. [4]. The difference between the forward-angle 6Li scattering cross sections and those for the back-angle 160 + 6Li recoil data was found to be -+6%. A typical 160 spectrum from the 160 + 6Li reaction is shown in fig. la. Spectra were also taken on a I2C target at each angle so that the location in the spectra and the yields from peaks due to this contaminant could be determined. A typical spectrum taken on the 12C target is shown in fig. lb. It can be seen in the spectrum from the 6Li target (fig. la) that there is a broad structureless continuum yield at low ejectile energy while the spectrum from the 12C target (fig. lb) indicates a small yield in this region. By summing this continuum yield, an estimate o f the continuum, or direct, breakup cross section was obtained at each angle. A total continuum cross section estimate o f > 1000 nab was obtained by summing the cross sections obtained at each angle. At several angles it was possible to extract a yield for the 2 + (4.31 MeV) state o f 6Li. An estimate o f the total cross section for this state is 15 rob. From fig. la it is evident that at this energy the direct breakup contribution is much greater than the contribution from the sequential breakup proceeding through the 3 + state. This is in sharp contrast to the findings of an earlier study [5] in which the breakup o f 70 MeV 7Li from 12C was found to be dominated by the sequential process 250
I .!
26 July 1984
Ejob--68.6 MeV
• 1 12Co.o tli
e,ab: 13 °
~
× 3~i
. ~11~,i~,,,. ,. ,.j i
6
°Lio.o'XJ i i '} t/2a ~t Sid t ~ o.oi
1
h~'i 7 o ~S
8;"~5~J~oo" ~);':'!" s~,; '' --~6Too/'J
teO*lzC
IZCo./o b
Elab= 68.6 MeV elob = 15o
6
( i2
x
2 '4
16
C4.44
06.13)Mut
\i
,
60
180
300
q20 Chonnel
5'40
'6 0
Fig. 1. Energy spectra at Elab = 68.6 MeV and 01ab = 13° for (a) 160 + 6Li and (b) ]60 + 12C.
proceeding through the unbound second excited ( 7 / 2 - , 4.63 MeV) state of 7Li. The elastic scattering data were analyzed with the optical model (OM) using a potential consisting of double-folded real and Woods-Saxon imaginary parts. The real double-folded potential was generated by folding the microscopic M3Y interaction [6] (supplemented by a single nucleon exchange term) with the 6Li and 160 ground state densities. The 6Li density was obtained from the electron scattering work of Suelzle et al. [7] and a harmonic oscillator density was assumed for 160. In addition to this optical potential, a Coulomb potential for a point charge interacting with a uniformly charged sphere of radius R = 1.25 (61/3 + 161/3) fm was included. Initially, the normalization factor of the real double-folded poten-
Volume 142B, number 4
PHYSICS LETTERS
b"<.,~ \
I
/
Ec m=18.7MeV
6Li +160
Eloslic •
..•.
. • • •.t;,
• •/•
C
) /
;~*
> io-
'\,% )\,I +\ ~'
E
,/1
"
¢~.
°'/OR [ O I
It
+
~'/'x
i O. /
•'// -
6Li 3 (2.18MeV)
V
O.01
0
i ~
30
,
~
60
i
90 ec.m(.de g. )
i
r
120
150
180
Fig. 2. Data for the elastic scattering of 6Li + 160 at Ecru = 18.7 MeV and the inelastic excitation of the 3+ (2.18 MeV) state in 6 Li. The curves show the results of the optical model (OM) and coupled-channels (CC) calculations discussed in the text. tial was fixed at N = 1.0 and the imaginary potential parameters were extensively searched upon to fit the data. A good fit to the data could not be obtained with this procedure. The normalization factor was then searched upon along with the imaginary potential parameters and a good fit to the data was obtained over the entire angular range with a normalization factor of 0.61. The resulting fit to the elastic scattering data is shown as the dashed line in fig. 2 and the potential parameters are given in table 1. Coupled-channels (CC) calculations were then performed with the computer code CHUCK3 [8] to investigate the effect of coupling the 3 + state in 6Li to the elastic channel. A rotational model was assumed for 6Li, with the 1+ ground state and 3 + (2.18 MeV)
Table 1 Optical model parameters and deformation lengths• The potential consists of a double-folded real part, with a normalization factor N, and a Woods-Saxon imaginary part. Calculation N
W0 ria) (MeV) (fro)
aI 8 °1 (fm) (fm)
8211 (fm)
OM CC
6•62 10.5
0•80 0.90
-0.78
0.61 0.75
a) Rx = rx(A~/a +A.~/3).
1.35 1.05
-1.54
26 July 1984
state belonging to a K = 1 rotational band. The L = 2 transition between the two states and the L = 2 reorientation term for the 3 + state were included in the calculations. The real double-folded form factor was obtained by folding the M3Y interaction with a derivative transition density pO'(r) = 60"ld Po(r)/drl for 6Li and the 160 ground state density. Here PO(r) is the 6Li ground-state density, and 80. is the quadrupole deformation length for the transition from state i to state/'. For the 1+ 4 3 + transition, 801 was fixed by normalizing the transition density to the experimental B(E2; 1+ ~ 3 +) value [9] of 25.6e 2 fm 4. In the rigidrotor model 611 = fi 01 , but we have assumed here 811 = ½8 01 since 6-01 is large. The imaginary part of the" form factor was obtained from a Legendre expansion of a Woods-Saxon potential with the same deformation length as the real part. Coulomb excitation was included with the same 8 01 and was found to only be important for the 3 + channel for 0cm < 20 °. The parameters N, W0, r I and a I were optimised to describe the data, resulting in the final parameters of table 1 and the fits shown as the full lines of fig. 2. The description of the elastic scattering data is reasonable over the whole angular range. The part from 0cm = 60 ° to 90 ° is very sensitive to reorientation effects in the 3 + state and requires a negative 8 2 to be described correctly• Thus the sign of the deformation length is unambiguously determined from the coupled channels calculations. The 3 + prediction has the correct forward angle magnitude if8 01 is reduced by about 15%. This reduction is consistent with the results of Yen et al. [I0] and Petrovich et at. [11] in which their obtained B(E2) values were 10-20% lower than that of ref. [9]. The 3 - (6.13 MeV) state in 160 was only weakly excited, and the inclusion of this state in the CC calculations made little difference to the results. The only effect of including coupling to the 3 - state was a reduction of about 15% in the depth W0 of the imaginary potential. In conclusion, coupled-channels effects due to the 3 + state of 6Li are very important in the scattering of 6Li projectiles. When coupling to this low-lying, strongly excited state was taken into account, two important results were observed. The first being that the normalization of the real double-folded potential, necessary to fit the elastic scattering data, changed from 0.61 to 0.75 thus reducing the discrepancy be251
Volume 142B, number 4
PHYSICS LETTERS
tween 6Li and other heavy-ion projectiles. Secondly, a comparison o f the imaginary potentials obtained from the OM and CC fits shows that when the coupling is included the imaginary potential becomes weaker in the surface region. This provides evidence that at least part o f the large phenomenological imaginary potential which often dominates 6Li scattering arises from coupling to excited states o f 6 Li. From the present 160 + 6Li experiment, it was determined that the total continuum breakup cross section is > 1000 rob. This is very much larger than the total inelastic cross section for the 3 + state (OTOT(3 +) ~ 23 mb) obtained from the CC calculations, and it is possible t h a t , i f the continuum breakup could be included in CC calculations, the renormalization o f the real double-folded potential might be removed. The theoretical work o f ref. [2] is concerned with this, and the data presented here should be valuable in the context o f understanding breakup effects in elastic scattering.
252
26 July 1984
References [1] G.R. Satchler and W.G. Love, Phys. Rep. 55C (1979) 183. [ 1 ] I.J. Thompson and M.A. Nagarajan, Phys. Lett. 106B (1981) 163; Y. SakUragi, M. Yahiro and M. Kamimura, Prog. Theor. Phys. 68 (1982) 322; Y. Sakuragi, M. Yahiro and M. Kamimura, Prog. Theor. Phys. 70 (1983) 1047. [3 ] D. Scholz, H. Gemmeke, L. Lassen, R. Ost and K. Bethge, Nucl. Phys. A288 (1977) 351; H. Gemmeke, B. Deluigi, L. Lassen and D. Scholz, 7. Phys. A286 (1978) 73. [4] H.G. Bingham, A.R. Zander, K.W. Kemper and N.R. Fletcher, Nucl. Phys. A173 (1971) 265. [5 ] A.C. Shorter, A.N. Bice, J.M. Wonters, W.D. Rae, and J. Cerny, Phys. Rev. Lett.46 (1981) 12. [6] G. Bertsch, J. Borysowicz, J. McManus and W.G. Love, Nucl. Phys. A284 (1977) 399. [7 ] L.R. Suelzle, M.R. Yearian and H. Crannel, Phys. Rev. 162 (1967) 992. [8] P.D. Kunz, University of Colorado, unpublished (with modifications by J .R. Comfort). [9] F. Eigenbrod, Z. Phys. 228 (1969) 337. [10] R. Yen, L.S. Cardman, D. Kalivisky, J.R. Legg and C.K. Bockelman, Nucl. Phys. A235 (1974) 135. [11] F. Petrovich, R.H. Howell, C.H. Poppe, S.M. Austin and G.M. Crawley, Nucl. Phys. A383 (1982) 355.