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Systematics of quasi-elastic neutron transfer cross sections for heavy-ion induced reactions
Volume 194, number 3
PHYSICS LETTERS B
13 August 1987
SYSTEMATICS OF QUASI-ELASTIC NEUTRON TRANSFER CROSS SECTIONS FOR H E A V Y - I O N I N D U C E D R E A C T I O N S A.M. VAN D E N B E R G 1, K.E. R E H M , D.G. KOVAR, W. K U T S C H E R A a n d G.S.F. S T E P H A N S 2 Argonne National Laboratory, Argonne, IL 60439, USA
Received 20 March 1987
Quasi-elastic neutron transfer reactions on samarium isotopes using a 58Nibeam at a center of mass energy of 245 MeV have been studied. Angle-integrated cross sections for one-neutron pickup reactions show an increase as a function of the target mass number A. Together with data from other systems covering a large range in mass and Q-value it is observed that the quasi-elastic one-neutron-transfer cross sections follow a simple systematic behaviour.
Recently much attention has been p a i d to the study o f quasi-elastic reactions i n d u c e d by very heavy ions ( A > 4 0 ) . It was f o u n d [1,2] that at energies in the vicinity o f the C o u l o m b b a r r i e r quasi-elastic transfer reactions are the d o m i n a n t reaction channels. Results o f a systematic study [ 3] o f SSNi a n d 64Ni i n d u c e d reactions on even-A tin isotopes show a strong increase o f the angle-integrated cross section for oneneutron transfer reactions as a function o f the groundstate Q-value Qgg. This b e h a v i o u r (Qgg systematics) which is similar to the results o b t a i n e d from light heavy-ion i n d u c e d reactions [4] indicates that the yields for the quasi-elastic neutron transfer reactions are d e t e r m i n e d by the available phase-space. The objective o f the present study was to see to what extent other effects are i m p o r t a n t also. So far all m e a s u r e m e n t s o f quasi-elastic transfer cross sections for reactions i n d u c e d by m e d i u m weight ions were p e r f o r m e d on targets with a closed p r o t o n shell (i.e. on Pb [1], N i [2] a n d Sn [3] isotopes). N o systematic m e a s u r e m e n t s have been done on strongly d e f o r m e d nuclei a n d therefore we chose the Ni + Sm system to investigate the b e h a v i o u r o f the transfer cross section in a transitional region. The nuclear :~ This research was supported by the US Department of Energy, Nuclear Physics Division, under Contract W-31-109-Eng-38. t Present address: Fysisch Laboratorium, Rijks Universiteit Utrecht, 3508 TA Utrecht, The Netherlands. 2 Present address: 26-415, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 334
structure o f the Sm isotopes changes d r a m a t i c a l l y in going from 144Sm which has a closed neutron shell to 154Sm which is a well d e f o r m e d nucleus. A SSNi b e a m from the Argonne t a n d e m - l i n a c comb i n a t i o n was used to b o m b a r d 144,149'1545m isotopes at a center o f mass energy o f 245 M e V which is roughly 30% above the C o u l o m b barrier. Targets b a c k e d with a' thin carbon foil were m a d e from enriched material ( e n r i c h m e n t > 9 7 % ) a n d had a typical thickness o f 200 I.tg/c)n2. The reaction products were m o m e n t u m analyzed in a split-pole magnetic spectrograph a n d detected in a focal-plane gas counter from which an u n a m b i g u o u s mass and Z identification was obtained. The typical energy resolution ( m a i n l y due to the target thickness) was 1.5 M e V a n d absolute cross sections are e s t i m a t e d to be accurate to within 10%. Results for the elastic scattering angular distribution (this includes inelastic excitation to states up to 10 MeV excitation energy) for the collision o f 58Ni with 144Sm a n d l S4Sm are shown in fig. 1 together with results from CCBA calculations [5] using a s t a n d a r d heavy-ion potential ( V= 100 MeV, W = 40 MeV, ro= 1.25 fro, a = 0.5 fm) and coupling strengths taken from the literature ~. The coupling scheme used in the calculations is i n d i c a t e d in fig. 1. Coupling to m o r e channels had to be restricted because o f c o m p u t a t i o n a l limits and no a t t e m p t has been For footnote see next page. 0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
Volume 194, number 3
oL i
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13 August 1987
PHYSICS LETTERS B ,
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144
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149
154
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Fig. 1. Cross sections for the sum of elastic and inelastic scattering for 58Nion ~44Smand ~S4Sm,respectively.Curves are CCBA calculations performed with the code PTOLEMY [ 5] using the indicated coupling scheme (see text). Dashed lines indicate the total cross sectionfor inelasticexcitation,dot-dashed that for pure elastic scattering, and the solid that for the sum of these two components, respectively. made to try different potential parameters for 144Sm and 154Sm. F r o m these CCBA calculations we found for the total reaction cross section values of 1320 m b and 1472 m b for the S8Ni on 144Sm and on 'S4Sm reactions, respectively. These values compare rather well with those obtained from the simple quarterpoint angle recipe [6] which yielded 1 3 0 0 + 5 0 m b and 1460+ 50 mb, respectively. Although the total reaction cross sections differ by only 10% for these two cases, the calculated total yields for inelastic excitation are very much different: 1.5 b for 58Ni+ 144Sm and 12 b for 58Ni+ 154Sm. This difference arises m a i n l y from"the large probability for C o u l o m b excitation predicted for the heavier target. The angular distributions for the quasi-elastic
,t The coupling parameters for the SSNi+~Sm reaction are given as (nuclear and Coulombdeformationswere taken to be equal): SSNi: BE(2)=0.25 e2b 2, BE(3)=0.01 e-~b3, fl2=0.079,
f13=0.10, laasm: BE(2)=0.07 e2b 2, BE(3)=0.19 e2b 3, fl2=0.17, fl3=0.14, ~54Sm: BE(2; 0+~2+)=4.26 e2b 2, BE(2; 2+-,4+)=2.13 e2b z, B E ( 2 ; 4+--.6+)=1.99 e2b 2, BE(4; 0+-,4+)=0.23 e2b4, BE(6; 0+~6-)=0.07 e2b 6, f12=0.72, fl4=0.06, Q= - 1.3 b.
Fig. 2. Angle-integratedcross sections for quasi-elastic neutron transfer reactions induced by SSNion ASm isotopes (open bars). Solid bars are the cross sections calculated with the code PTOLEMY [ 5] and normalized to the measured cross sections for the 154Sm(58Ni,59Ni)153Smreaction (see text). The uncertainties of the experimental cross sections are 10%. transfer reactions (defined as processes with Q > - 30 MeV) are bell-shaped and peak at angles somewhat smaller than the quarter point angle for elastic scattering (see refs. [ 1 - 3 ] ) . The angle-integrated cross sections for the three systems are shown in fig. 2. Similar to thd results obtained for SSNi+Sn one observes an increase of the one-neutron transfer cross section with increasing n e u t r o n n u m b e r N of the target nucleus. The large positive Q-value for the 149Sm(58Ni, S9Ni)148Sm reaction does not lead to a particular e n h a n c e m e n t of the cross section, in agreement with the fact that the level density for oneparticle transfer is constant as function of the excitation energy. In order to estimate the extent to which Q-matching effects influence these transfer processes we performed DWBA calculations with the code P T O L E M Y [5 ] assuming the pickup of a P3/2 neutron from the target nucleus and transfering it to the lowest P3/2 state in 59Ni. The calculations were done with bound-state parameters of ro=1.25 fm and a = 0 . 6 5 fm and the same (spherical) scattering potential as used for the CCBA calculations mentioned above. Normalizing the strength of the calculated cross sections to the data for the 58Ni + ~SnSm reaction we obtain the values shown as solid bars in fig. 2. The increase of the cross sections with increas335
Volume 194, number 3
PHYSICS LETTERS B
ing mass n u m b e r A is quite well r e p r o d u c e d in these calculations. These results indicate that the m a i n reason for this increase o f the neutron transfer cross section is due to the m o r e favorable k i n e m a t i c a l matching conditions in the heavier Sm isotopes. The strong excitation o f the rotational b a n d in 1545m due to Coulomb excitation does not appear to have a large influence on the strength o f the neutron transfer process. Together with previously published d a t a for neutron stripping a n d pickup cross sections [ 1-3,7,8] it is now possible to study the systematics o f these processes over a large range o f Q-values. Fig. 3 shows the cross sections for several one-neutron transfer reactions i n d u c e d by projectiles between mass n u m bers A = 28 a n d 64 on targets ranging from 58Ni to 2°Spb plotted as a function o f Qgg. The cross sections were not corrected for any energy dependence, because m e a s u r e m e n t s o n ' several systems [2,3,9] .... ~a
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Fig. 3. (a) Angle-integrated quasi-elastic reaction cross sections for heavy-ion induced one-neutron transfer reactions (stripping and pickup) for several systems as a function of the ground-state Q-value Qgg.(b) Angle and energy integrated cross sections multiplied by (&. Bf) ~"~(B~ and Bf are the binding energy of the transferred neutron in the entrance and exit channel, respectively) plotted as function of Qg, (see text for details). 336
indicate that the energy d e p e n d e n c e o f the neutron transfer cross sections is weak, if the incident energy is m o r e than 10% above the C o u l o m b barrier. In general one observes an exponential rise o f the cross section over almost two orders o f m a g n i t u d e with increasing Qgg-value. In a d d i t i o n there are large fluctuations, in particular at Qgg-values between - 3 and - 7 MeV. The exponential increase o f the cross sections is not due to differences in the spectroscopic factors, which vary only by a factor o f two for the systems studied here. F u r t h e r m o r e , the cross section for the reaction with the most positive Qgg-value (149Sm(58Ni, S9Ni)148Sm) which is also the only case involving a target with an o d d neutron n u m b e r is also somewhat lower than expected from the systematics given in fig. 3a. A detailed analysis o f the data reveals that for the same Qgg-value the cross sections for reactions i n d u c e d by projectiles with low neutron b i n d i n g energies (e.g. 64Ni or 5°Ti) are generally larger than for reactions involving projectiles with a larger neutron binding energy (e.g~ 58Ni, 28Si). This b e h a v i o r o f the angle-integrated cross sections is in q u a l i t a t i v e agreement with semiclassical calculations o f ref. [ 10 ]. The integrated cross section for neutron transfer reactions as calculated in ref. [ 10] has in a d d i t i o n to the spectroscopic factors a n d a function describing the Q-matching b e h a v i o u r (eq. (2.16) in ref. [ 10]) a term which d e p e n d s on the p r o d u c t o f the binding energy o f the transferred neutron in the entrance (Bi) and the exit channel (Bf), i.e.
-
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13 August 1987
o"~ (Bi .Bf) 3/2
(1)
(see also ref. [11]). D e t a i l e d calculations with the finite-range code P T O L E M Y [5] indicate that the exponent d e p e n d s slightly on the angular-moment u m transfer a n d is between 0.9 a n d 1.2. Multiplying the m e a s u r e d angle-integrated cross sections by (Bi'Bf) 1"1 reduces the large fluctuations in fig. 3a illustrated in fig. 3b where this " r e d u c e d " cross section is plotted versus Qgg. F o r simplicity ground state b i n d i n g energies have been used in fig. 3b. The use o f b i n d i n g energies for excited states results in a shift o f the whole distribution in fig. 3b upwards by less than 10% without effecting the overall shape. As can be seen in fig. 3b only the cross section for the 58Ni + 149Sm system (solid cross in fig. 3) still shows a large deviation from the general trend o f the data, possibly due to the neglect o f pairing corrections.
Volume 194, number 3
PHYSICS LETTERS B
The increase o f these r e d u c e d cross sections with increasing Q ~ can be u n d e r s t o o d from the Q-matching b e h a v i o u r which for neutron transfer reactions corresponds to an o p t i m u m Q-window centered a r o u n d Q = 0 . A p p r o x i m a t i n g this Q-window by a gaussian we obtain for the energy and angle-integrated cross section Q~
ared(agg) = N
j
exp(-O2/272) dO,
(2)
where N is a n o r m a l i z a t i o n constant, containing all the i n f o r m a t i o n o f the spectroscopic factors, a n d 7 is the variance o f the Q-window. The solid line in fig. 3b is the result o f a leastsquares fit to the d a t a using eq. ( 2 ) with N a n d y as the two free p a r a m e t e r s (7 = 5.9 M e V ) . Taking into account the fact that there are still differences in the sum o f the spectroscopic factors for the i n d i v i d u a l reactions, the general b e h a v i o u r o f these excitationenergy- and angle-integrated cross sections is quite remarkable. It should be m e n t i o n e d that the lightest system used in these systematics was 58Ni+58Ni. Reactions i n d u c e d by lighter projectiles a n d / o r targets (e.g. 160+2°8pb (ref. [9]) or 28Si+58Ni (ref. [ 12])) have cross sections which are somewhat lower than p r e d i c t e d by the systematics. This correlation can now be used to predict cross sections for even heavier systems which are experimentally m o r e difficult to measure. F o r the reaction 2°8pb(S6Kr, 87Kr)2°7pb (ref. [ 13]) a cross section o f cr = 189 m b is o b t a i n e d from the systematics, which compares well with the e x p e r i m e n t a l value o f a = 205_+ 20 mb. F o r even heavier systems neutron transfer reactions are m e a s u r e d using m a i n l y chemical [14] or y - r a y techniques [15]. Both m e t h o d s have some inherent difficulties in obtaining total transfer cross sections. In a d d i t i o n for very fissile nuclei some part o f the reaction strength might r e m a i n u n d e t e c t e d due to transfer-induced fission processes. A detailed c o m p a r i s o n with the systematics presented a b o v e is therefore difficult. F o r the reaction 232Th(2°6pb, 2°7pb)231Th [15] a transfer cross section o f a = 2 9 0 m b is predicted, in reasonable agreement with the e x p e r i m e n t a l Value o f 369_+40 mb. F o r 238U(238U,237U)239Uthe systematics predict 300 mb. So far no transfer d a t a at sufficiently high b o m b a r d i n g energies have been m e a s u r e d for this system. In ref. [14] a value o f
13 August 1987
a = 1 1 0 m b was obtained, which due to the low b o m barding energy and the problem with transfer induced fission, however, can only be regarded as a l o w e r limit. Summarizing, we have studied SSNi induced quasielastic reactions on three Sm isotopes. Total reaction cross sections d e t e r m i n e d from the s u m m e d angular distribution for elastic and inelastic scattering ranged from 1300 m b for the 58Ni on 1445m reaction to 1460 m b for the 58Ni+ lS4Sm system. C o u p l e d channels calculations indicate that the increase in deformation mostly affects the inelastic excitation, which is predominantly due to the Coulomb interaction. Total angle-integrated cross sections for the quasi-elastic neutron transfer reactions are o f the order o f 150-200 mb, being roughly 12% o f the total reaction cross section. D W B A calculations indicate that the yield for these quasi-elastic transfer reactions are governed by Q-value matching and angular m o m e n t u m matching conditions. The strong inelastic excitation in the system SSNi+ 1545m does not seem to influence strongly the magnitude o f the transfer processes. F r o m the systematics o f the angle-integrated cross sections o b t a i n e d in a variety o f heavy-ion i n d u c e d reactions (Ap> 28) it is possible to predict neutron transfer cross sections at b o m b a r d i n g energies o f ( 1 0 - 8 0 ) % above the C o u l o m b barrier. We wish to thank S.C. Pieper for helpful suggestions regarding the CCBA calculations. [ 1] K.E. Rehm et al., Phys. Rev. Lett. 51 (1983) 1426. [2] K.E. Rehm et al., Phys. Rev. Lett. 55 (1985) 280. [3] A.M. van den Berg et al., Phys. Rev. Lett. 56 (1986) 572; and to be submitted to Phys. Rev. C. [4] A.G. Artukh et al., Nucl. Phys. A 160 (1971) 511. [5] M.H. Macfarlane and S.C. Pieper, code PTOLEMY, Argonne National Laboratory Report ANL76-11 (Rev. 1) (1978). [6] W.E. Frahn, Nucl. Phys. A 302 (1978) 267. [7] J.J. Kolata et al., Phys. Rev. C30 (1984) 125. [8] K.E. Rehm et al., J. Phys. Soc. Japan Suppl. 54 (1985) 410. [9] S.C. Pieper et al., Phys. Rev. C 18 (1978) 180. [ 10 ] P.J.A. Buttle and L.J.B. Goldfarb, Nucl. Phys. A 176 ( 1971 ) 299. [ 11 ] R. Bass, Nuclear reactions with heavy ions (Springer, Berlin, 1980). [12] Y. Sugiyama et al., Phys. Len. B 176 (1986) 302. [ 13] A.J. Baltz et al., Phys. Rev. C 29 (1984) 2392. [14] G. Wirth et al., Phys, Lett. B 177 (1986) 282. [ 15 ] F.W.N. de Boer et al., Z. Phys. A 325 (1986) 457. 337
PHYSICS LETTERS B
13 August 1987
SYSTEMATICS OF QUASI-ELASTIC NEUTRON TRANSFER CROSS SECTIONS FOR H E A V Y - I O N I N D U C E D R E A C T I O N S A.M. VAN D E N B E R G 1, K.E. R E H M , D.G. KOVAR, W. K U T S C H E R A a n d G.S.F. S T E P H A N S 2 Argonne National Laboratory, Argonne, IL 60439, USA
Received 20 March 1987
Quasi-elastic neutron transfer reactions on samarium isotopes using a 58Nibeam at a center of mass energy of 245 MeV have been studied. Angle-integrated cross sections for one-neutron pickup reactions show an increase as a function of the target mass number A. Together with data from other systems covering a large range in mass and Q-value it is observed that the quasi-elastic one-neutron-transfer cross sections follow a simple systematic behaviour.
Recently much attention has been p a i d to the study o f quasi-elastic reactions i n d u c e d by very heavy ions ( A > 4 0 ) . It was f o u n d [1,2] that at energies in the vicinity o f the C o u l o m b b a r r i e r quasi-elastic transfer reactions are the d o m i n a n t reaction channels. Results o f a systematic study [ 3] o f SSNi a n d 64Ni i n d u c e d reactions on even-A tin isotopes show a strong increase o f the angle-integrated cross section for oneneutron transfer reactions as a function o f the groundstate Q-value Qgg. This b e h a v i o u r (Qgg systematics) which is similar to the results o b t a i n e d from light heavy-ion i n d u c e d reactions [4] indicates that the yields for the quasi-elastic neutron transfer reactions are d e t e r m i n e d by the available phase-space. The objective o f the present study was to see to what extent other effects are i m p o r t a n t also. So far all m e a s u r e m e n t s o f quasi-elastic transfer cross sections for reactions i n d u c e d by m e d i u m weight ions were p e r f o r m e d on targets with a closed p r o t o n shell (i.e. on Pb [1], N i [2] a n d Sn [3] isotopes). N o systematic m e a s u r e m e n t s have been done on strongly d e f o r m e d nuclei a n d therefore we chose the Ni + Sm system to investigate the b e h a v i o u r o f the transfer cross section in a transitional region. The nuclear :~ This research was supported by the US Department of Energy, Nuclear Physics Division, under Contract W-31-109-Eng-38. t Present address: Fysisch Laboratorium, Rijks Universiteit Utrecht, 3508 TA Utrecht, The Netherlands. 2 Present address: 26-415, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 334
structure o f the Sm isotopes changes d r a m a t i c a l l y in going from 144Sm which has a closed neutron shell to 154Sm which is a well d e f o r m e d nucleus. A SSNi b e a m from the Argonne t a n d e m - l i n a c comb i n a t i o n was used to b o m b a r d 144,149'1545m isotopes at a center o f mass energy o f 245 M e V which is roughly 30% above the C o u l o m b barrier. Targets b a c k e d with a' thin carbon foil were m a d e from enriched material ( e n r i c h m e n t > 9 7 % ) a n d had a typical thickness o f 200 I.tg/c)n2. The reaction products were m o m e n t u m analyzed in a split-pole magnetic spectrograph a n d detected in a focal-plane gas counter from which an u n a m b i g u o u s mass and Z identification was obtained. The typical energy resolution ( m a i n l y due to the target thickness) was 1.5 M e V a n d absolute cross sections are e s t i m a t e d to be accurate to within 10%. Results for the elastic scattering angular distribution (this includes inelastic excitation to states up to 10 MeV excitation energy) for the collision o f 58Ni with 144Sm a n d l S4Sm are shown in fig. 1 together with results from CCBA calculations [5] using a s t a n d a r d heavy-ion potential ( V= 100 MeV, W = 40 MeV, ro= 1.25 fro, a = 0.5 fm) and coupling strengths taken from the literature ~. The coupling scheme used in the calculations is i n d i c a t e d in fig. 1. Coupling to m o r e channels had to be restricted because o f c o m p u t a t i o n a l limits and no a t t e m p t has been For footnote see next page. 0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )
Volume 194, number 3
oL i
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13 August 1987
PHYSICS LETTERS B ,
i
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MUTUAL 144Sm
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154
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Fig. 1. Cross sections for the sum of elastic and inelastic scattering for 58Nion ~44Smand ~S4Sm,respectively.Curves are CCBA calculations performed with the code PTOLEMY [ 5] using the indicated coupling scheme (see text). Dashed lines indicate the total cross sectionfor inelasticexcitation,dot-dashed that for pure elastic scattering, and the solid that for the sum of these two components, respectively. made to try different potential parameters for 144Sm and 154Sm. F r o m these CCBA calculations we found for the total reaction cross section values of 1320 m b and 1472 m b for the S8Ni on 144Sm and on 'S4Sm reactions, respectively. These values compare rather well with those obtained from the simple quarterpoint angle recipe [6] which yielded 1 3 0 0 + 5 0 m b and 1460+ 50 mb, respectively. Although the total reaction cross sections differ by only 10% for these two cases, the calculated total yields for inelastic excitation are very much different: 1.5 b for 58Ni+ 144Sm and 12 b for 58Ni+ 154Sm. This difference arises m a i n l y from"the large probability for C o u l o m b excitation predicted for the heavier target. The angular distributions for the quasi-elastic
,t The coupling parameters for the SSNi+~Sm reaction are given as (nuclear and Coulombdeformationswere taken to be equal): SSNi: BE(2)=0.25 e2b 2, BE(3)=0.01 e-~b3, fl2=0.079,
f13=0.10, laasm: BE(2)=0.07 e2b 2, BE(3)=0.19 e2b 3, fl2=0.17, fl3=0.14, ~54Sm: BE(2; 0+~2+)=4.26 e2b 2, BE(2; 2+-,4+)=2.13 e2b z, B E ( 2 ; 4+--.6+)=1.99 e2b 2, BE(4; 0+-,4+)=0.23 e2b4, BE(6; 0+~6-)=0.07 e2b 6, f12=0.72, fl4=0.06, Q= - 1.3 b.
Fig. 2. Angle-integratedcross sections for quasi-elastic neutron transfer reactions induced by SSNion ASm isotopes (open bars). Solid bars are the cross sections calculated with the code PTOLEMY [ 5] and normalized to the measured cross sections for the 154Sm(58Ni,59Ni)153Smreaction (see text). The uncertainties of the experimental cross sections are 10%. transfer reactions (defined as processes with Q > - 30 MeV) are bell-shaped and peak at angles somewhat smaller than the quarter point angle for elastic scattering (see refs. [ 1 - 3 ] ) . The angle-integrated cross sections for the three systems are shown in fig. 2. Similar to thd results obtained for SSNi+Sn one observes an increase of the one-neutron transfer cross section with increasing n e u t r o n n u m b e r N of the target nucleus. The large positive Q-value for the 149Sm(58Ni, S9Ni)148Sm reaction does not lead to a particular e n h a n c e m e n t of the cross section, in agreement with the fact that the level density for oneparticle transfer is constant as function of the excitation energy. In order to estimate the extent to which Q-matching effects influence these transfer processes we performed DWBA calculations with the code P T O L E M Y [5 ] assuming the pickup of a P3/2 neutron from the target nucleus and transfering it to the lowest P3/2 state in 59Ni. The calculations were done with bound-state parameters of ro=1.25 fm and a = 0 . 6 5 fm and the same (spherical) scattering potential as used for the CCBA calculations mentioned above. Normalizing the strength of the calculated cross sections to the data for the 58Ni + ~SnSm reaction we obtain the values shown as solid bars in fig. 2. The increase of the cross sections with increas335
Volume 194, number 3
PHYSICS LETTERS B
ing mass n u m b e r A is quite well r e p r o d u c e d in these calculations. These results indicate that the m a i n reason for this increase o f the neutron transfer cross section is due to the m o r e favorable k i n e m a t i c a l matching conditions in the heavier Sm isotopes. The strong excitation o f the rotational b a n d in 1545m due to Coulomb excitation does not appear to have a large influence on the strength o f the neutron transfer process. Together with previously published d a t a for neutron stripping a n d pickup cross sections [ 1-3,7,8] it is now possible to study the systematics o f these processes over a large range o f Q-values. Fig. 3 shows the cross sections for several one-neutron transfer reactions i n d u c e d by projectiles between mass n u m bers A = 28 a n d 64 on targets ranging from 58Ni to 2°Spb plotted as a function o f Qgg. The cross sections were not corrected for any energy dependence, because m e a s u r e m e n t s o n ' several systems [2,3,9] .... ~a
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I,,
2.5
Fig. 3. (a) Angle-integrated quasi-elastic reaction cross sections for heavy-ion induced one-neutron transfer reactions (stripping and pickup) for several systems as a function of the ground-state Q-value Qgg.(b) Angle and energy integrated cross sections multiplied by (&. Bf) ~"~(B~ and Bf are the binding energy of the transferred neutron in the entrance and exit channel, respectively) plotted as function of Qg, (see text for details). 336
indicate that the energy d e p e n d e n c e o f the neutron transfer cross sections is weak, if the incident energy is m o r e than 10% above the C o u l o m b barrier. In general one observes an exponential rise o f the cross section over almost two orders o f m a g n i t u d e with increasing Qgg-value. In a d d i t i o n there are large fluctuations, in particular at Qgg-values between - 3 and - 7 MeV. The exponential increase o f the cross sections is not due to differences in the spectroscopic factors, which vary only by a factor o f two for the systems studied here. F u r t h e r m o r e , the cross section for the reaction with the most positive Qgg-value (149Sm(58Ni, S9Ni)148Sm) which is also the only case involving a target with an o d d neutron n u m b e r is also somewhat lower than expected from the systematics given in fig. 3a. A detailed analysis o f the data reveals that for the same Qgg-value the cross sections for reactions i n d u c e d by projectiles with low neutron b i n d i n g energies (e.g. 64Ni or 5°Ti) are generally larger than for reactions involving projectiles with a larger neutron binding energy (e.g~ 58Ni, 28Si). This b e h a v i o r o f the angle-integrated cross sections is in q u a l i t a t i v e agreement with semiclassical calculations o f ref. [ 10 ]. The integrated cross section for neutron transfer reactions as calculated in ref. [ 10] has in a d d i t i o n to the spectroscopic factors a n d a function describing the Q-matching b e h a v i o u r (eq. (2.16) in ref. [ 10]) a term which d e p e n d s on the p r o d u c t o f the binding energy o f the transferred neutron in the entrance (Bi) and the exit channel (Bf), i.e.
-
,4 104
-I0.0
13 August 1987
o"~ (Bi .Bf) 3/2
(1)
(see also ref. [11]). D e t a i l e d calculations with the finite-range code P T O L E M Y [5] indicate that the exponent d e p e n d s slightly on the angular-moment u m transfer a n d is between 0.9 a n d 1.2. Multiplying the m e a s u r e d angle-integrated cross sections by (Bi'Bf) 1"1 reduces the large fluctuations in fig. 3a illustrated in fig. 3b where this " r e d u c e d " cross section is plotted versus Qgg. F o r simplicity ground state b i n d i n g energies have been used in fig. 3b. The use o f b i n d i n g energies for excited states results in a shift o f the whole distribution in fig. 3b upwards by less than 10% without effecting the overall shape. As can be seen in fig. 3b only the cross section for the 58Ni + 149Sm system (solid cross in fig. 3) still shows a large deviation from the general trend o f the data, possibly due to the neglect o f pairing corrections.
Volume 194, number 3
PHYSICS LETTERS B
The increase o f these r e d u c e d cross sections with increasing Q ~ can be u n d e r s t o o d from the Q-matching b e h a v i o u r which for neutron transfer reactions corresponds to an o p t i m u m Q-window centered a r o u n d Q = 0 . A p p r o x i m a t i n g this Q-window by a gaussian we obtain for the energy and angle-integrated cross section Q~
ared(agg) = N
j
exp(-O2/272) dO,
(2)
where N is a n o r m a l i z a t i o n constant, containing all the i n f o r m a t i o n o f the spectroscopic factors, a n d 7 is the variance o f the Q-window. The solid line in fig. 3b is the result o f a leastsquares fit to the d a t a using eq. ( 2 ) with N a n d y as the two free p a r a m e t e r s (7 = 5.9 M e V ) . Taking into account the fact that there are still differences in the sum o f the spectroscopic factors for the i n d i v i d u a l reactions, the general b e h a v i o u r o f these excitationenergy- and angle-integrated cross sections is quite remarkable. It should be m e n t i o n e d that the lightest system used in these systematics was 58Ni+58Ni. Reactions i n d u c e d by lighter projectiles a n d / o r targets (e.g. 160+2°8pb (ref. [9]) or 28Si+58Ni (ref. [ 12])) have cross sections which are somewhat lower than p r e d i c t e d by the systematics. This correlation can now be used to predict cross sections for even heavier systems which are experimentally m o r e difficult to measure. F o r the reaction 2°8pb(S6Kr, 87Kr)2°7pb (ref. [ 13]) a cross section o f cr = 189 m b is o b t a i n e d from the systematics, which compares well with the e x p e r i m e n t a l value o f a = 205_+ 20 mb. F o r even heavier systems neutron transfer reactions are m e a s u r e d using m a i n l y chemical [14] or y - r a y techniques [15]. Both m e t h o d s have some inherent difficulties in obtaining total transfer cross sections. In a d d i t i o n for very fissile nuclei some part o f the reaction strength might r e m a i n u n d e t e c t e d due to transfer-induced fission processes. A detailed c o m p a r i s o n with the systematics presented a b o v e is therefore difficult. F o r the reaction 232Th(2°6pb, 2°7pb)231Th [15] a transfer cross section o f a = 2 9 0 m b is predicted, in reasonable agreement with the e x p e r i m e n t a l Value o f 369_+40 mb. F o r 238U(238U,237U)239Uthe systematics predict 300 mb. So far no transfer d a t a at sufficiently high b o m b a r d i n g energies have been m e a s u r e d for this system. In ref. [14] a value o f
13 August 1987
a = 1 1 0 m b was obtained, which due to the low b o m barding energy and the problem with transfer induced fission, however, can only be regarded as a l o w e r limit. Summarizing, we have studied SSNi induced quasielastic reactions on three Sm isotopes. Total reaction cross sections d e t e r m i n e d from the s u m m e d angular distribution for elastic and inelastic scattering ranged from 1300 m b for the 58Ni on 1445m reaction to 1460 m b for the 58Ni+ lS4Sm system. C o u p l e d channels calculations indicate that the increase in deformation mostly affects the inelastic excitation, which is predominantly due to the Coulomb interaction. Total angle-integrated cross sections for the quasi-elastic neutron transfer reactions are o f the order o f 150-200 mb, being roughly 12% o f the total reaction cross section. D W B A calculations indicate that the yield for these quasi-elastic transfer reactions are governed by Q-value matching and angular m o m e n t u m matching conditions. The strong inelastic excitation in the system SSNi+ 1545m does not seem to influence strongly the magnitude o f the transfer processes. F r o m the systematics o f the angle-integrated cross sections o b t a i n e d in a variety o f heavy-ion i n d u c e d reactions (Ap> 28) it is possible to predict neutron transfer cross sections at b o m b a r d i n g energies o f ( 1 0 - 8 0 ) % above the C o u l o m b barrier. We wish to thank S.C. Pieper for helpful suggestions regarding the CCBA calculations. [ 1] K.E. Rehm et al., Phys. Rev. Lett. 51 (1983) 1426. [2] K.E. Rehm et al., Phys. Rev. Lett. 55 (1985) 280. [3] A.M. van den Berg et al., Phys. Rev. Lett. 56 (1986) 572; and to be submitted to Phys. Rev. C. [4] A.G. Artukh et al., Nucl. Phys. A 160 (1971) 511. [5] M.H. Macfarlane and S.C. Pieper, code PTOLEMY, Argonne National Laboratory Report ANL76-11 (Rev. 1) (1978). [6] W.E. Frahn, Nucl. Phys. A 302 (1978) 267. [7] J.J. Kolata et al., Phys. Rev. C30 (1984) 125. [8] K.E. Rehm et al., J. Phys. Soc. Japan Suppl. 54 (1985) 410. [9] S.C. Pieper et al., Phys. Rev. C 18 (1978) 180. [ 10 ] P.J.A. Buttle and L.J.B. Goldfarb, Nucl. Phys. A 176 ( 1971 ) 299. [ 11 ] R. Bass, Nuclear reactions with heavy ions (Springer, Berlin, 1980). [12] Y. Sugiyama et al., Phys. Len. B 176 (1986) 302. [ 13] A.J. Baltz et al., Phys. Rev. C 29 (1984) 2392. [14] G. Wirth et al., Phys, Lett. B 177 (1986) 282. [ 15 ] F.W.N. de Boer et al., Z. Phys. A 325 (1986) 457. 337