Marked inconsistencies in earlier data for two-neutron transfer strengths in the samarium isotopes make comparison with model predictions difficult. We compare here the results of a careful high-resolution (p, t) reaction study on 148,150,152,154Sm at Ep=40 MeV with IBA model predictions

Fortune, HT

Hageman, DCJM

Saha, A

Scholten, O

Physics Letters B

University of Groningen

   University of GroningenTwo neutron transfer in samarium isotopes and IBA model predictionsSaha, A; Scholten, O; Hageman, DCJM; Fortune, HTPublished in:Physics Letters BDOI:10.1016/0370-2693(79)90582-3IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1979Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Saha, A., Scholten, O., Hageman, DCJM., & Fortune, HT. (1979). Two neutron transfer in samariumisotopes and IBA model predictions. Physics Letters B, 85(2-3), 215-218. https://doi.org/10.1016/0370-2693(79)90582-3CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 12-11-2019Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 TWO NEUTRON TRANSFER IN SAMARIUM ISOTOPES AND IBA MODEL PREDICTIONS A. SAHA 1, O. SCHOLTEN, D.C.J.M. HAGEMAN and H.T. FORTUNE 2 Kernfysisch Versneller Instituut, Groningen, The Netherlands Received 1 June 1979 Marked inconsistencies in earlier data for two-neutron transfer strengths in the samarium isotopes make comparison with model predictions difficult. We compare here the results of a careful high-resolution (p, t) reaction study on 148,150,1s2,154 Sm at Ep = 40 MeV with IBA model predictions. The stable samarium isotopes ranging from N = 84 to N = 90 encompass the region in which nuclei under- go a shape transition from vibrational to rotational. The interacting boson model (IBA) [1] predicts this change in the samarium isotopes in a natural and consistent way, and also explains rather well the en- ergy levels and electromagnetic transition rates. As two-neutron transfer eactions are rather sensitive to the overlap of the wave functions of the target and residual nuclei, it seemed natural to test the predic- tions of the IBA model for two-neutron transfer eac- tions with those obtained from experiments. Several investigations of (p, t) reactions and one study of (t, p) on the samarium isotopes have been re- ported [2 -5] ,  all at bombarding energies below 26 MeV. However, inconsistencies among the data make comparison with theory difficult. Even for g.s. -+ g.s. transitions, discrepancies in the existing data are larger than the A-dependent effects predicted. Thus, we have performed a careful high-resolution study of the (p, t) reaction on the samarium isotopes in order to compare the results obtained with IBA model pre- dictions. Isotopically enriched targets of 148,150,152,154Sm were bombarded with 40 MeV protons from the KVI AVF cyclotron and the outgoing tritons were momen- 1 Present address: University of Pittsburgh, Pittsburgh, PA 15260, USA. 2 Present address: University of Pennsylvania, Philadelphia, PA 19104, USA. turn analyzed and detected in the focal plane detec- tion system of the QMG/2 magnetic spectrograph [6]. The total target hickness for each target was obtained by normalizing the measured elastic count rate in the l o  angular ange 20 ° to 35 ° (in steps of 2 ~- ) to the cross sections obtained from the optical model parameters of Becchetti and Greenlees [7] for 40 MeV protons. This method of estimating the target hickness intro- duced an absolute uncertainty of about 10%, but since the elastic data for all the targets were taken at the same time under identical conditions, the relative un- certainty is better than +5%. Since the main source of error in the determination of the absolute differential cross section is the uncertainty in the measurement ofthe target hickness, we estimate the uncertainty for the absolute differential cross section for all the iso- topes to be less than 10% and relative values to be within 5%. The g.s. cross sections we quote are for 01a b = 14 °. The (p, t) spectra t 01a b = 6 ° are displayed in fig. 1. The experimental energy resolution varied between 15 and 18 keV FWHM. Excitation energies listed on the (p, t) spectra were obtained from calibrations made by a least-squares polynomial fit to peaks having well- known energies. The results for each excitation energy were then averaged over at least six to eight angles. Standard eviations for the excitation energies are less than 5 keV for the strongly excited peaks. The angular distributions to the 0 + states are shown in fig. 2. The curves through the data points are re- suits of L = 0 DWBA calculations using a cluster form 215 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 I00  50  I00  l u J50  z Z I n," Ld  0.. CO ~-60 0 (.,) 4O 20 60  40  20  0 0 ~ o ] m~o o Xl /2  # Xl /2  t54Sm (p,t)IS2Sm Ep= 40  MeV ~LAB. = 6 deg. o -o , . . -~  ~ ~ o ~ ~. { o~ o £ 'SZSm (p,t) IS°sin t.- X l /2  - -  15°Sm (p,t) ~48Sm o - o ~ o r-- 200 400 148Sin (p,t) 146Sm 600 800 CHANNEL NUMBER * - - -X  f /2  (z - -X l /2  Fig. 1. Spectra of (p, t) reactions on various isotopes of Sm. 216 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 103~ I I° o ~/ /~+ io ° Lo A÷2Sm (p , t )Asrn  Ep=4OMeV O÷stcltes i i 146Sm g.s. 146Sm 2341 146 Sm 2958 146 Sm 3059 146 Sm 375t  Possible L=O 101 / ,~  ,o I'0 20 30 40 50 150 Sm 3045 x2 150 Sm 5219 150 Sm 5357 150 Sm 3721 ' I 8 cm (decj.) I J 148Sin ~s x2 148 Sm 1427 148 Sm 2373 150Srn gs 150Sm 735 150Sin 1251 x5 152Sm gs x2 152 Sm 687 152 Sm 1736 I I I I I I0 20 30 40 50 Fig. 2. Selected 0 ÷ angular distributions labeled by final nu- cleus and excitation energy (in keV). factor for the transferred dineutron. Shapes with mi- croscopic form factors are virtually identical. The opti- cal model parameters used and given in table 1 are not very much different from those listed in ref. [8], It should be emphasized that the DWBA calculations have been done primarily to take into account the Q- value effects before comparing with any model predic- tions. One of the main reasons for doing this experi- ment at Ep = 40 MeV is that the Q-value effects are rather small (+10%) over the range of isotopes and ex- citation energies tudies and are also independent of the choice of optical model parameters [9]. The L = 0 shapes are rather unique and easily dis- tinguishable from the other L-transfers. Several new 0 + states have thus been identified at E x = 2341, 2958, 3059 and 3751 keV in 146Sm, Ex = 2373 keV in 148Sm andE x = 1736 keV in 152Sm. Tentative 0 + spin assignments are made to the states at E x = 3045, 3219, 3357 and 3721 keV in 148Sm and 1670 keV in 152Sm. We observe no L = 0 strengths to states at E x = 2611 keV in 146Sm andE x = 1923 keV in 148Sm, which have previously been assigned 0 ÷ from other (p, t) [2 -4]  and (t, p) [5] experiments. The relative strengths of transitions to the ground states and the first excited 0 + states obtained in previ- ous (p, t) experiments [2-4]  and in this experiment are shown, in fig. 3, as functions of A. The strengths are normalized to 100 for the 148Sm(p, t)146Sm(g.s.). We immediately see that there are large discrepancies (over 50%) even in the g.s. strengths, especially for transitions to the 148,152Sm g.s. The Q-value effects have generally not been con- sidered for the earlier experiments, but they are not large enough to explain the discrepancies. Our results agree with those of Oelert etal. [4] within experimen- tal uncertainties for all except 152Sm g.s. where we dif. Table 1 Optical model parameters, (potentials in MeV, lengths in fro). V ro ao W v W' = 4 W D r d a d r e p 51.0 1.18 0.7 52.0 1.25 0.7 1.25 t 173.1 1.20 0.72 20.6 1.5 0.82 1.40 "2n" 1.25 0.65 cluster 217 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 ~J E u) Z W Z 150 t.d > d 100  W 60 f 40 [] 40 144 146 148 150 152 154 144 146 148 150 t52 154 A< A~ 50 I~  19.0 MeV 0 206 MeV g .s .~ g,S. (P J )  Z5.5 MeV IBA [[340.0 MeV (t,p) • 120MeV normalized here 144Sm 146Sm 148Sr n 150Sin 152Sm 154Sm A< Fig. 3. (a) Experimental (dots) and calculated (line) (p, t) and (t, p) relative g.s. to g.s. cross sections. The (p, t) data are nor- malized to 100 for 148Sm (p, t) 146Sm. The (t, p) data are normalized to the (p, t) results for A = 150. (b) Experimental (dots) and calculated (lines) (p, t) and (t, p) relative cross sec- tions for excited 0+ states. The same scale is used as in fig. 3a. Note that A denotes the final nucleus for (p, t), but the target nucleus for (t, p). fer by about 30%. Marked variations occur for the data of Debenham and Hintz [2] and McLatchie et al. [3] for 150,152Sm even though they did their experiments at practically the same incident proton energy. Causes of these discrepancies are not apparent, but we believe our results reflect the true cross sections as practically all possible sources of uncertainties have been carefully monitored and accounted for. Only one investigation of the (t, p) reaction on the Sm isotopes has been re- ported - at E t = 12 MeV by Bjerregaard et al. [5]. These relative strengths have also been plotted in fig. 3. In the IBA model the (p, t) and (t, p) strengths can be calculated by assuming that the two-neutron trans- fer is a collective process. Tile two-nucleon pickup op- erator, T(p, t) for 0 ÷ states can be written as T+(0) = AoSv(Y2  v - 2(rv)l/2 ' where 2~2 v is the size of the major shell (in this case 2~2 v = 44), and P/v is the boson number operator. For the two-nucleon stripping (t, p) reaction one has to take the hermitian conjugate of the above operator. The IBA parameters describing the Sm nuclei were taken from ref. [1 ] ,  in which excitation energies and B(E2) values are reproduced very well. The calculated ground-state cross sections are shown in fig. 3a. The parameter A 0 was determined by normalizing to an overall best fit. As was stated before there is a big dis- crepancy between the different measurements. The clear minimum in cross section observed for A = 150 is predicted by the IBA calculation, but the predicted increase in cross section when going from A = 146 to A = 148 is in contradiction with the present experi- ment. In the calculation for the (p, t) and (t, p) strengths to excited 0 + states there is no additional parameters For (t, p) the 05 strengths are reasonably well repro- duced with the exception of 148Sm where the calcu- lated value is much too low. For (p, t) the strengths are underpredicted for all nuclei but the behavior with A, especially the maximum for 15°Sm, is reproduced very well. In summary, new results for the (p, t) reaction on Sm isotopes remove many of the discrepancies present in earlier data. Calculations of the IBA type reproduce many of the observed features, but detailed agreement with 2n transfer strengths i  only fair. References  [1] A. Arima and F. Iachello, Phys. Rev. C16 (1977) 2085; O. Scholten, F. Iachello and A. Arima, Ann. Phys. (NY) 115 (1978) 321, and references therein. [2] P. Debenham and N.M. Hintz, Nucl. Phys. A195 (1972) 385. [3] W. McLatchie, W. Darcey and J.E. Kitching, Nucl. Phys. A159 (1970) 615. [4] W. Oelert, G. Lindstrom and V. Reich, Nucl. Phys. A233 (1974) 237. [5] J.H. Bjerregaard, O. Hansen and O. Nathan, Nucl. Phys. 86 (1966) 145. [6] J. van der Plicht and J.C. Vermeulen, Nucl. Instrum. Methods 156 (1978) 103. [7] F.D. Becchetti and G.W. Greenless, Phys. Rev. 182 (1969) 1190. [8] H. Nann and B.H. Wildenthal, Phys. Rev. C13 (1976) 1009. [9] A. Saha and H T. Fortune, Phys. Rev. C, to be published. 218 

Two neutron transfer in samarium isotopes and IBA model predictions

   University of GroningenTwo neutron transfer in samarium isotopes and IBA model predictionsSaha, A; Scholten, O; Hageman, DCJM; Fortune, HTPublished in:Physics Letters BDOI:10.1016/0370-2693(79)90582-3IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1979Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Saha, A., Scholten, O., Hageman, DCJM., & Fortune, HT. (1979). Two neutron transfer in samariumisotopes and IBA model predictions. Physics Letters B, 85(2-3), 215-218. https://doi.org/10.1016/0370-2693(79)90582-3CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 27-04-2023Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 TWO NEUTRON TRANSFER IN SAMARIUM ISOTOPES AND IBA MODEL PREDICTIONS A. SAHA 1, O. SCHOLTEN, D.C.J.M. HAGEMAN and H.T. FORTUNE 2 Kernfysisch Versneller Instituut, Groningen, The Netherlands Received 1 June 1979 Marked inconsistencies in earlier data for two-neutron transfer strengths in the samarium isotopes make comparison with model predictions difficult. We compare here the results of  a careful high-resolution (p, t) reaction study on 148,150,1s2,154 Sm at Ep = 40 MeV with IBA model predictions. The stable samarium isotopes ranging from N = 84 to N = 90 encompass the region in which nuclei under- go a shape transition from vibrational to rotational. The interacting boson model (IBA) [1] predicts this change in the samarium isotopes in a natural and consistent way, and also explains rather well the en- ergy levels and electromagnetic transition rates. As two-neutron transfer reactions are rather sensitive to the overlap of the wave functions of  the target and residual nuclei, it seemed natural to test the predic- tions of the IBA model for two-neutron transfer reac- tions with those obtained from experiments. Several investigations of (p, t) reactions and one study of  (t, p) on the samarium isotopes have been re- ported [ 2 - 5 ] ,  all at bombarding energies below 26 MeV. However, inconsistencies among the data make comparison with theory difficult. Even for g.s. -+ g.s. transitions, discrepancies in the existing data are larger than the A-dependent effects predicted. Thus, we have performed a careful high-resolution study of  the (p, t) reaction on the samarium isotopes in order to compare the results obtained with IBA model pre- dictions. Isotopically enriched targets of  148,150,152,154Sm were bombarded with 40 MeV protons from the KVI AVF cyclotron and the outgoing tritons were momen- 1 Present address: University of  Pittsburgh, Pittsburgh, PA 15260, USA. 2 Present address: University of  Pennsylvania, Philadelphia, PA 19104, USA. turn analyzed and detected in the focal plane detec- tion system of the QMG/2 magnetic spectrograph [6]. The total target thickness for each target was obtained by normalizing the measured elastic count rate in the l o  angular range 20 ° to 35 ° (in steps of 2 ~- ) to the cross sections obtained from the optical model parameters of Becchetti and Greenlees [7] for 40 MeV protons. This method of estimating the target thickness intro- duced an absolute uncertainty of  about 10%, but since the elastic data for all the targets were taken at the same time under identical conditions, the relative un- certainty is better than +5%. Since the main source of error in the determination of  the absolute differential cross section is the uncertainty in the measurement of the target thickness, we estimate the uncertainty for the absolute differential cross section for all the iso- topes to be less than 10% and relative values to be within 5%. The g.s. cross sections we quote are for 01a b = 14 °. The (p, t) spectra at 01a b = 6 ° are displayed in fig. 1. The experimental energy resolution varied between 15 and 18 keV FWHM. Excitation energies listed on the (p, t) spectra were obtained from calibrations made by a least-squares polynomial fit to peaks having well- known energies. The results for each excitation energy were then averaged over at least six to eight angles. Standard deviations for the excitation energies are less than 5 keV for the strongly excited peaks. The angular distributions to the 0 + states are shown in fig. 2. The curves through the data points are re- suits of L = 0 DWBA calculations using a cluster form 215 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 I 0 0  5 0  I 0 0  l u J50 z Z I n," Ld  0.. CO ~ - 6 0  0 (.,) 4O 2 0  6 0  4 0  2 0  0 0 ~ o ] m ~ o  o X l / 2  # X l / 2  t54Sm (p,t)IS2Sm Ep= 4 0  MeV ~LAB. = 6 deg. o - o , . . - ~  ~ ~ o ~ ~. { o~ o £ 'SZSm (p,t) IS°sin t.- X l / 2  - -  15°Sm (p,t) ~48Sm o - o ~ o r-- 200 4 0 0  148Sin (p,t) 146Sm 6 0 0  8 0 0  C H A N N E L  N U M B E R  * - - - X  f / 2  (z - - X l / 2  Fig. 1. Spectra of (p, t) reactions on various isotopes of Sm. 2 1 6  Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 103~ I I° o ~ / / ~ +  io ° Lo A ÷ 2 S m  ( p , t ) A s r n  E p = 4 O M e V  O÷stcltes i i 146Sm g.s. 146Sm 2341 146 Sm 2958 146 Sm 3 0 5 9  146 Sm 3 7 5 t  Possible L=O 101 / , ~  ,o I'0 20 30 40 50 150 Sm 3045 x2 150 Sm 5219 150 Sm 5357 150 Sm 3721 ' I 8 cm (decj.) I J 148Sin ~s x2 148 Sm 1427 148 Sm 2373 150Srn gs 150Sm 735 150Sin 1251 x5 152Sm gs x2 152 Sm 687 152 Sm 1736 I I I I I I0 20 30 40 50 Fig. 2. Selected 0 ÷ angular distributions labeled by final nu- cleus and excitation energy (in keV). factor for the transferred dineutron. Shapes with mi- croscopic form factors are virtually identical. The opti- cal model parameters used and given in table 1 are not very much different from those listed in ref. [8],  It should be emphasized that the DWBA calculations have been done primarily to take into account the Q- value effects before comparing with any model predic- tions. One of  the main reasons for doing this experi- ment at Ep = 40 MeV is that the Q-value effects are rather small (+10%) over the range of  isotopes and ex- citation energies studies and are also independent of  the choice of  optical model parameters [9] .  The L = 0 shapes are rather unique and easily dis- tinguishable from the other L-transfers. Several new 0 + states have thus been identified at E x = 2341, 2958, 3059 and 3751 keV in 146Sm, Ex = 2373 keV in 148Sm andE x = 1736 keV in 152Sm. Tentative 0 + spin assignments are made to the states at E x = 3045, 3219, 3357 and 3721 keV in 148Sm and 1670 keV in 152Sm. We observe no L = 0 strengths to states at E x = 2611 keV in 146Sm andE x = 1923 keV in 148Sm, which have previously been assigned 0 ÷ from other (p, t) [ 2 - 4 ]  and (t, p) [5] experiments. The relative strengths of  transitions to the ground states and the first excited 0 + states obtained in previ- ous (p, t) experiments [ 2 - 4 ]  and in this experiment are shown, in fig. 3, as functions of  A. The strengths are normalized to 100 for the 148Sm(p, t)146Sm(g.s.). We immediately see that there are large discrepancies (over 50%) even in the g.s. strengths, especially for transitions to the 148,152Sm g.s. The Q-value effects have generally not been con- sidered for the earlier experiments, but they are not large enough to explain the discrepancies. Our results agree with those of  Oelert etal .  [4] within experimen- tal uncertainties for all except 152Sm g.s. where we dif. Table 1 Optical model parameters, (potentials in MeV, lengths in fro). V ro ao W v W' = 4 W D r d a d r e p 51.0 1.18 0.7 52.0 1.25 0.7 1.25 t 173.1 1.20 0.72 20.6 1.5 0.82 1.40 "2n" 1.25 0.65 cluster 217 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 ~J E u) Z W Z 150 t.d > d 1 0 0  W 60 f40 [] 40 144 146 148 150 152 154 144 146 148 150 t52 154 A< A~ 5 0  I ~  19.0 MeV 0 206 MeV g . s . ~  g,S. (P J)  Z5.5 MeV IBA [[340.0 MeV (t,p) • 120MeV normalized here 144Sm 146Sm 148Sr n 150Sin 152Sm 154Sm A< Fig. 3. (a) Experimental (dots) and calculated (line) (p, t) and (t, p) relative g.s. to g.s. cross sections. The (p, t) data are nor- malized to 100 for 148Sm (p, t) 146Sm. The (t, p) data are normalized to the (p, t) results for A = 150. (b) Experimental (dots) and calculated (lines) (p, t) and (t, p) relative cross sec- tions for excited 0 + states. The same scale is used as in fig. 3a. Note that A denotes the final nucleus for (p, t), but the target nucleus for (t, p). fer by about 30%. Marked variations occur for the data of  Debenham and Hintz [2] and McLatchie et al. [3] for 150,152Sm even though they did their experiments at practically the same incident proton energy. Causes of  these discrepancies are not  apparent,  but  we believe our results reflect the true cross sections as practically all possible sources of uncertainties have been carefully monitored and accounted for. Only one investigation of  the (t, p) reaction on the Sm isotopes has been re- ported - at E t = 12 MeV by Bjerregaard et al. [5]. These relative strengths have also been plot ted in fig. 3. In the IBA model the (p, t) and (t,  p) strengths can be calculated by assuming that the two-neutron trans- fer is a collective process. Tile two-nucleon pickup op- erator, T(p, t) for 0 ÷ states can be written as T+(0) = A o S v ( Y 2  v - 2(rv)l/2 ' where 2~2 v is the size of the major shell (in this case 2~2 v = 44), and P/v is the boson number operator.  For the two-nucleon stripping (t,  p) reaction one has to take the hermitian conjugate of the above operator.  The IBA parameters describing the Sm nuclei were taken from ref. [1 ] ,  in which excitation energies and B(E2) values are reproduced very well. The calculated ground-state cross sections are shown in fig. 3a. The parameter A 0 was determined by normalizing to an overall best fit. As was stated before there is a big dis- crepancy between the different measurements. The clear minimum in cross section observed for A = 150 is predicted by the IBA calculation, but  the predicted increase in cross section when going from A = 146 to A = 148 is in contradiction with the present experi- ment. In the calculation for the (p, t) and (t, p) strengths to excited 0 + states there is no additional parameters For (t,  p) the 05 strengths are reasonably well repro- duced with the exception of  148Sm where the calcu- lated value is much too low. For (p, t)  the strengths are underpredicted for all nuclei but the behavior with A,  especially the maximum for 15°Sm, is reproduced very well. In summary, new results for the (p, t) reaction on Sm isotopes remove many of  the discrepancies present in earlier data. Calculations of the IBA type reproduce many of the observed features, but  detailed agreement with 2n transfer strengths is only fair. R e f e r e n c e s  [1] A. Arima and F. Iachello, Phys. Rev. C16 (1977) 2085; O. Scholten, F. Iachello and A. Arima, Ann. Phys. (NY) 115 (1978) 321, and references therein. [2] P. Debenham and N.M. Hintz, Nucl. Phys. A195 (1972) 385. [3] W. McLatchie, W. Darcey and J.E. Kitching, Nucl. Phys. A159 (1970) 615. [4] W. Oelert, G. Lindstrom and V. Reich, Nucl. Phys. A233 (1974) 237. [5] J.H. Bjerregaard, O. Hansen and O. Nathan, Nucl. Phys. 86 (1966) 145. [6] J. van der Plicht and J.C. Vermeulen, Nucl. Instrum. Methods 156 (1978) 103. [7] F.D. Becchetti and G.W. Greenless, Phys. Rev. 182 (1969) 1190. [8] H. Nann and B.H. Wildenthal, Phys. Rev. C13 (1976) 1009. [9] A. Saha and H T. Fortune, Phys. Rev. C, to be published. 218 

English

ARTS repository - University of Groningen

   University of GroningenTwo neutron transfer in samarium isotopes and IBA model predictionsSaha, A; Scholten, O; Hageman, DCJM; Fortune, HTPublished in:Physics Letters BDOI:10.1016/0370-2693(79)90582-3IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1979Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Saha, A., Scholten, O., Hageman, DCJM., & Fortune, HT. (1979). Two neutron transfer in samariumisotopes and IBA model predictions. Physics Letters B, 85(2-3), 215-218. https://doi.org/10.1016/0370-2693(79)90582-3CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 17-07-2023Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 TWO NEUTRON TRANSFER IN SAMARIUM ISOTOPES AND IBA MODEL PREDICTIONS A. SAHA 1, O. SCHOLTEN, D.C.J.M. HAGEMAN and H.T. FORTUNE 2 Kernfysisch Versneller Instituut, Groningen, The Netherlands Received 1 June 1979 Marked inconsistencies in earlier data for two-neutron transfer strengths in the samarium isotopes make comparison with model predictions difficult. We compare here the results of  a careful high-resolution (p, t) reaction study on 148,150,1s2,154 Sm at Ep = 40 MeV with IBA model predictions. The stable samarium isotopes ranging from N = 84 to N = 90 encompass the region in which nuclei under- go a shape transition from vibrational to rotational. The interacting boson model (IBA) [1] predicts this change in the samarium isotopes in a natural and consistent way, and also explains rather well the en- ergy levels and electromagnetic transition rates. As two-neutron transfer reactions are rather sensitive to the overlap of the wave functions of  the target and residual nuclei, it seemed natural to test the predic- tions of the IBA model for two-neutron transfer reac- tions with those obtained from experiments. Several investigations of (p, t) reactions and one study of  (t, p) on the samarium isotopes have been re- ported [ 2 - 5 ] ,  all at bombarding energies below 26 MeV. However, inconsistencies among the data make comparison with theory difficult. Even for g.s. -+ g.s. transitions, discrepancies in the existing data are larger than the A-dependent effects predicted. Thus, we have performed a careful high-resolution study of  the (p, t) reaction on the samarium isotopes in order to compare the results obtained with IBA model pre- dictions. Isotopically enriched targets of  148,150,152,154Sm were bombarded with 40 MeV protons from the KVI AVF cyclotron and the outgoing tritons were momen- 1 Present address: University of  Pittsburgh, Pittsburgh, PA 15260, USA. 2 Present address: University of  Pennsylvania, Philadelphia, PA 19104, USA. turn analyzed and detected in the focal plane detec- tion system of the QMG/2 magnetic spectrograph [6]. The total target thickness for each target was obtained by normalizing the measured elastic count rate in the l o  angular range 20 ° to 35 ° (in steps of 2 ~- ) to the cross sections obtained from the optical model parameters of Becchetti and Greenlees [7] for 40 MeV protons. This method of estimating the target thickness intro- duced an absolute uncertainty of  about 10%, but since the elastic data for all the targets were taken at the same time under identical conditions, the relative un- certainty is better than +5%. Since the main source of error in the determination of  the absolute differential cross section is the uncertainty in the measurement of the target thickness, we estimate the uncertainty for the absolute differential cross section for all the iso- topes to be less than 10% and relative values to be within 5%. The g.s. cross sections we quote are for 01a b = 14 °. The (p, t) spectra at 01a b = 6 ° are displayed in fig. 1. The experimental energy resolution varied between 15 and 18 keV FWHM. Excitation energies listed on the (p, t) spectra were obtained from calibrations made by a least-squares polynomial fit to peaks having well- known energies. The results for each excitation energy were then averaged over at least six to eight angles. Standard deviations for the excitation energies are less than 5 keV for the strongly excited peaks. The angular distributions to the 0 + states are shown in fig. 2. The curves through the data points are re- suits of L = 0 DWBA calculations using a cluster form 215 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 I 0 0  5 0  I 0 0  l u J50 z Z I n," Ld  0.. CO ~ - 6 0  0 (.,) 4O 2 0  6 0  4 0  2 0  0 0 ~ o ] m ~ o  o X l / 2  # X l / 2  t54Sm (p,t)IS2Sm Ep= 4 0  MeV ~LAB. = 6 deg. o - o , . . - ~  ~ ~ o ~ ~. { o~ o £ 'SZSm (p,t) IS°sin t.- X l / 2  - -  15°Sm (p,t) ~48Sm o - o ~ o r-- 200 4 0 0  148Sin (p,t) 146Sm 6 0 0  8 0 0  C H A N N E L  N U M B E R  * - - - X  f / 2  (z - - X l / 2  Fig. 1. Spectra of (p, t) reactions on various isotopes of Sm. 2 1 6  Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 103~ I I° o ~ / / ~ +  io ° Lo A ÷ 2 S m  ( p , t ) A s r n  E p = 4 O M e V  O÷stcltes i i 146Sm g.s. 146Sm 2341 146 Sm 2958 146 Sm 3 0 5 9  146 Sm 3 7 5 t  Possible L=O 101 / , ~  ,o I'0 20 30 40 50 150 Sm 3045 x2 150 Sm 5219 150 Sm 5357 150 Sm 3721 ' I 8 cm (decj.) I J 148Sin ~s x2 148 Sm 1427 148 Sm 2373 150Srn gs 150Sm 735 150Sin 1251 x5 152Sm gs x2 152 Sm 687 152 Sm 1736 I I I I I I0 20 30 40 50 Fig. 2. Selected 0 ÷ angular distributions labeled by final nu- cleus and excitation energy (in keV). factor for the transferred dineutron. Shapes with mi- croscopic form factors are virtually identical. The opti- cal model parameters used and given in table 1 are not very much different from those listed in ref. [8],  It should be emphasized that the DWBA calculations have been done primarily to take into account the Q- value effects before comparing with any model predic- tions. One of  the main reasons for doing this experi- ment at Ep = 40 MeV is that the Q-value effects are rather small (+10%) over the range of  isotopes and ex- citation energies studies and are also independent of  the choice of  optical model parameters [9] .  The L = 0 shapes are rather unique and easily dis- tinguishable from the other L-transfers. Several new 0 + states have thus been identified at E x = 2341, 2958, 3059 and 3751 keV in 146Sm, Ex = 2373 keV in 148Sm andE x = 1736 keV in 152Sm. Tentative 0 + spin assignments are made to the states at E x = 3045, 3219, 3357 and 3721 keV in 148Sm and 1670 keV in 152Sm. We observe no L = 0 strengths to states at E x = 2611 keV in 146Sm andE x = 1923 keV in 148Sm, which have previously been assigned 0 ÷ from other (p, t) [ 2 - 4 ]  and (t, p) [5] experiments. The relative strengths of  transitions to the ground states and the first excited 0 + states obtained in previ- ous (p, t) experiments [ 2 - 4 ]  and in this experiment are shown, in fig. 3, as functions of  A. The strengths are normalized to 100 for the 148Sm(p, t)146Sm(g.s.). We immediately see that there are large discrepancies (over 50%) even in the g.s. strengths, especially for transitions to the 148,152Sm g.s. The Q-value effects have generally not been con- sidered for the earlier experiments, but they are not large enough to explain the discrepancies. Our results agree with those of  Oelert etal .  [4] within experimen- tal uncertainties for all except 152Sm g.s. where we dif. Table 1 Optical model parameters, (potentials in MeV, lengths in fro). V ro ao W v W' = 4 W D r d a d r e p 51.0 1.18 0.7 52.0 1.25 0.7 1.25 t 173.1 1.20 0.72 20.6 1.5 0.82 1.40 "2n" 1.25 0.65 cluster 217 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 ~J E u) Z W Z 150 t.d > d 1 0 0  W 60 f40 [] 40 144 146 148 150 152 154 144 146 148 150 t52 154 A< A~ 5 0  I ~  19.0 MeV 0 206 MeV g . s . ~  g,S. (P J)  Z5.5 MeV IBA [[340.0 MeV (t,p) • 120MeV normalized here 144Sm 146Sm 148Sr n 150Sin 152Sm 154Sm A< Fig. 3. (a) Experimental (dots) and calculated (line) (p, t) and (t, p) relative g.s. to g.s. cross sections. The (p, t) data are nor- malized to 100 for 148Sm (p, t) 146Sm. The (t, p) data are normalized to the (p, t) results for A = 150. (b) Experimental (dots) and calculated (lines) (p, t) and (t, p) relative cross sec- tions for excited 0 + states. The same scale is used as in fig. 3a. Note that A denotes the final nucleus for (p, t), but the target nucleus for (t, p). fer by about 30%. Marked variations occur for the data of  Debenham and Hintz [2] and McLatchie et al. [3] for 150,152Sm even though they did their experiments at practically the same incident proton energy. Causes of  these discrepancies are not  apparent,  but  we believe our results reflect the true cross sections as practically all possible sources of uncertainties have been carefully monitored and accounted for. Only one investigation of  the (t, p) reaction on the Sm isotopes has been re- ported - at E t = 12 MeV by Bjerregaard et al. [5]. These relative strengths have also been plot ted in fig. 3. In the IBA model the (p, t) and (t,  p) strengths can be calculated by assuming that the two-neutron trans- fer is a collective process. Tile two-nucleon pickup op- erator, T(p, t) for 0 ÷ states can be written as T+(0) = A o S v ( Y 2  v - 2(rv)l/2 ' where 2~2 v is the size of the major shell (in this case 2~2 v = 44), and P/v is the boson number operator.  For the two-nucleon stripping (t,  p) reaction one has to take the hermitian conjugate of the above operator.  The IBA parameters describing the Sm nuclei were taken from ref. [1 ] ,  in which excitation energies and B(E2) values are reproduced very well. The calculated ground-state cross sections are shown in fig. 3a. The parameter A 0 was determined by normalizing to an overall best fit. As was stated before there is a big dis- crepancy between the different measurements. The clear minimum in cross section observed for A = 150 is predicted by the IBA calculation, but  the predicted increase in cross section when going from A = 146 to A = 148 is in contradiction with the present experi- ment. In the calculation for the (p, t) and (t, p) strengths to excited 0 + states there is no additional parameters For (t,  p) the 05 strengths are reasonably well repro- duced with the exception of  148Sm where the calcu- lated value is much too low. For (p, t)  the strengths are underpredicted for all nuclei but the behavior with A,  especially the maximum for 15°Sm, is reproduced very well. In summary, new results for the (p, t) reaction on Sm isotopes remove many of  the discrepancies present in earlier data. Calculations of the IBA type reproduce many of the observed features, but  detailed agreement with 2n transfer strengths is only fair. R e f e r e n c e s  [1] A. Arima and F. Iachello, Phys. Rev. C16 (1977) 2085; O. Scholten, F. Iachello and A. Arima, Ann. Phys. (NY) 115 (1978) 321, and references therein. [2] P. Debenham and N.M. Hintz, Nucl. Phys. A195 (1972) 385. [3] W. McLatchie, W. Darcey and J.E. Kitching, Nucl. Phys. A159 (1970) 615. [4] W. Oelert, G. Lindstrom and V. Reich, Nucl. Phys. A233 (1974) 237. [5] J.H. Bjerregaard, O. Hansen and O. Nathan, Nucl. Phys. 86 (1966) 145. [6] J. van der Plicht and J.C. Vermeulen, Nucl. Instrum. Methods 156 (1978) 103. [7] F.D. Becchetti and G.W. Greenless, Phys. Rev. 182 (1969) 1190. [8] H. Nann and B.H. Wildenthal, Phys. Rev. C13 (1976) 1009. [9] A. Saha and H T. Fortune, Phys. Rev. C, to be published. 218 

NARCIS 

   University of GroningenTwo neutron transfer in samarium isotopes and IBA model predictionsSaha, A; Scholten, O; Hageman, DCJM; Fortune, HTPublished in:Physics Letters BDOI:10.1016/0370-2693(79)90582-3IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1979Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Saha, A., Scholten, O., Hageman, DCJM., & Fortune, HT. (1979). Two neutron transfer in samariumisotopes and IBA model predictions. Physics Letters B, 85(2-3), 215-218. https://doi.org/10.1016/0370-2693(79)90582-3CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 16-07-2023Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 TWO NEUTRON TRANSFER IN SAMARIUM ISOTOPES AND IBA MODEL PREDICTIONS A. SAHA 1, O. SCHOLTEN, D.C.J.M. HAGEMAN and H.T. FORTUNE 2 Kernfysisch Versneller Instituut, Groningen, The Netherlands Received 1 June 1979 Marked inconsistencies in earlier data for two-neutron transfer strengths in the samarium isotopes make comparison with model predictions difficult. We compare here the results of  a careful high-resolution (p, t) reaction study on 148,150,1s2,154 Sm at Ep = 40 MeV with IBA model predictions. The stable samarium isotopes ranging from N = 84 to N = 90 encompass the region in which nuclei under- go a shape transition from vibrational to rotational. The interacting boson model (IBA) [1] predicts this change in the samarium isotopes in a natural and consistent way, and also explains rather well the en- ergy levels and electromagnetic transition rates. As two-neutron transfer reactions are rather sensitive to the overlap of the wave functions of  the target and residual nuclei, it seemed natural to test the predic- tions of the IBA model for two-neutron transfer reac- tions with those obtained from experiments. Several investigations of (p, t) reactions and one study of  (t, p) on the samarium isotopes have been re- ported [ 2 - 5 ] ,  all at bombarding energies below 26 MeV. However, inconsistencies among the data make comparison with theory difficult. Even for g.s. -+ g.s. transitions, discrepancies in the existing data are larger than the A-dependent effects predicted. Thus, we have performed a careful high-resolution study of  the (p, t) reaction on the samarium isotopes in order to compare the results obtained with IBA model pre- dictions. Isotopically enriched targets of  148,150,152,154Sm were bombarded with 40 MeV protons from the KVI AVF cyclotron and the outgoing tritons were momen- 1 Present address: University of  Pittsburgh, Pittsburgh, PA 15260, USA. 2 Present address: University of  Pennsylvania, Philadelphia, PA 19104, USA. turn analyzed and detected in the focal plane detec- tion system of the QMG/2 magnetic spectrograph [6]. The total target thickness for each target was obtained by normalizing the measured elastic count rate in the l o  angular range 20 ° to 35 ° (in steps of 2 ~- ) to the cross sections obtained from the optical model parameters of Becchetti and Greenlees [7] for 40 MeV protons. This method of estimating the target thickness intro- duced an absolute uncertainty of  about 10%, but since the elastic data for all the targets were taken at the same time under identical conditions, the relative un- certainty is better than +5%. Since the main source of error in the determination of  the absolute differential cross section is the uncertainty in the measurement of the target thickness, we estimate the uncertainty for the absolute differential cross section for all the iso- topes to be less than 10% and relative values to be within 5%. The g.s. cross sections we quote are for 01a b = 14 °. The (p, t) spectra at 01a b = 6 ° are displayed in fig. 1. The experimental energy resolution varied between 15 and 18 keV FWHM. Excitation energies listed on the (p, t) spectra were obtained from calibrations made by a least-squares polynomial fit to peaks having well- known energies. The results for each excitation energy were then averaged over at least six to eight angles. Standard deviations for the excitation energies are less than 5 keV for the strongly excited peaks. The angular distributions to the 0 + states are shown in fig. 2. The curves through the data points are re- suits of L = 0 DWBA calculations using a cluster form 215 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 I 0 0  5 0  I 0 0  l u J50 z Z I n," Ld  0.. CO ~ - 6 0  0 (.,) 4O 2 0  6 0  4 0  2 0  0 0 ~ o ] m ~ o  o X l / 2  # X l / 2  t54Sm (p,t)IS2Sm Ep= 4 0  MeV ~LAB. = 6 deg. o - o , . . - ~  ~ ~ o ~ ~. { o~ o £ 'SZSm (p,t) IS°sin t.- X l / 2  - -  15°Sm (p,t) ~48Sm o - o ~ o r-- 200 4 0 0  148Sin (p,t) 146Sm 6 0 0  8 0 0  C H A N N E L  N U M B E R  * - - - X  f / 2  (z - - X l / 2  Fig. 1. Spectra of (p, t) reactions on various isotopes of Sm. 2 1 6  Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 103~ I I° o ~ / / ~ +  io ° Lo A ÷ 2 S m  ( p , t ) A s r n  E p = 4 O M e V  O÷stcltes i i 146Sm g.s. 146Sm 2341 146 Sm 2958 146 Sm 3 0 5 9  146 Sm 3 7 5 t  Possible L=O 101 / , ~  ,o I'0 20 30 40 50 150 Sm 3045 x2 150 Sm 5219 150 Sm 5357 150 Sm 3721 ' I 8 cm (decj.) I J 148Sin ~s x2 148 Sm 1427 148 Sm 2373 150Srn gs 150Sm 735 150Sin 1251 x5 152Sm gs x2 152 Sm 687 152 Sm 1736 I I I I I I0 20 30 40 50 Fig. 2. Selected 0 ÷ angular distributions labeled by final nu- cleus and excitation energy (in keV). factor for the transferred dineutron. Shapes with mi- croscopic form factors are virtually identical. The opti- cal model parameters used and given in table 1 are not very much different from those listed in ref. [8],  It should be emphasized that the DWBA calculations have been done primarily to take into account the Q- value effects before comparing with any model predic- tions. One of  the main reasons for doing this experi- ment at Ep = 40 MeV is that the Q-value effects are rather small (+10%) over the range of  isotopes and ex- citation energies studies and are also independent of  the choice of  optical model parameters [9] .  The L = 0 shapes are rather unique and easily dis- tinguishable from the other L-transfers. Several new 0 + states have thus been identified at E x = 2341, 2958, 3059 and 3751 keV in 146Sm, Ex = 2373 keV in 148Sm andE x = 1736 keV in 152Sm. Tentative 0 + spin assignments are made to the states at E x = 3045, 3219, 3357 and 3721 keV in 148Sm and 1670 keV in 152Sm. We observe no L = 0 strengths to states at E x = 2611 keV in 146Sm andE x = 1923 keV in 148Sm, which have previously been assigned 0 ÷ from other (p, t) [ 2 - 4 ]  and (t, p) [5] experiments. The relative strengths of  transitions to the ground states and the first excited 0 + states obtained in previ- ous (p, t) experiments [ 2 - 4 ]  and in this experiment are shown, in fig. 3, as functions of  A. The strengths are normalized to 100 for the 148Sm(p, t)146Sm(g.s.). We immediately see that there are large discrepancies (over 50%) even in the g.s. strengths, especially for transitions to the 148,152Sm g.s. The Q-value effects have generally not been con- sidered for the earlier experiments, but they are not large enough to explain the discrepancies. Our results agree with those of  Oelert etal .  [4] within experimen- tal uncertainties for all except 152Sm g.s. where we dif. Table 1 Optical model parameters, (potentials in MeV, lengths in fro). V ro ao W v W' = 4 W D r d a d r e p 51.0 1.18 0.7 52.0 1.25 0.7 1.25 t 173.1 1.20 0.72 20.6 1.5 0.82 1.40 "2n" 1.25 0.65 cluster 217 Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 ~J E u) Z W Z 150 t.d > d 1 0 0  W 60 f40 [] 40 144 146 148 150 152 154 144 146 148 150 t52 154 A< A~ 5 0  I ~  19.0 MeV 0 206 MeV g . s . ~  g,S. (P J)  Z5.5 MeV IBA [[340.0 MeV (t,p) • 120MeV normalized here 144Sm 146Sm 148Sr n 150Sin 152Sm 154Sm A< Fig. 3. (a) Experimental (dots) and calculated (line) (p, t) and (t, p) relative g.s. to g.s. cross sections. The (p, t) data are nor- malized to 100 for 148Sm (p, t) 146Sm. The (t, p) data are normalized to the (p, t) results for A = 150. (b) Experimental (dots) and calculated (lines) (p, t) and (t, p) relative cross sec- tions for excited 0 + states. The same scale is used as in fig. 3a. Note that A denotes the final nucleus for (p, t), but the target nucleus for (t, p). fer by about 30%. Marked variations occur for the data of  Debenham and Hintz [2] and McLatchie et al. [3] for 150,152Sm even though they did their experiments at practically the same incident proton energy. Causes of  these discrepancies are not  apparent,  but  we believe our results reflect the true cross sections as practically all possible sources of uncertainties have been carefully monitored and accounted for. Only one investigation of  the (t, p) reaction on the Sm isotopes has been re- ported - at E t = 12 MeV by Bjerregaard et al. [5]. These relative strengths have also been plot ted in fig. 3. In the IBA model the (p, t) and (t,  p) strengths can be calculated by assuming that the two-neutron trans- fer is a collective process. Tile two-nucleon pickup op- erator, T(p, t) for 0 ÷ states can be written as T+(0) = A o S v ( Y 2  v - 2(rv)l/2 ' where 2~2 v is the size of the major shell (in this case 2~2 v = 44), and P/v is the boson number operator.  For the two-nucleon stripping (t,  p) reaction one has to take the hermitian conjugate of the above operator.  The IBA parameters describing the Sm nuclei were taken from ref. [1 ] ,  in which excitation energies and B(E2) values are reproduced very well. The calculated ground-state cross sections are shown in fig. 3a. The parameter A 0 was determined by normalizing to an overall best fit. As was stated before there is a big dis- crepancy between the different measurements. The clear minimum in cross section observed for A = 150 is predicted by the IBA calculation, but  the predicted increase in cross section when going from A = 146 to A = 148 is in contradiction with the present experi- ment. In the calculation for the (p, t) and (t, p) strengths to excited 0 + states there is no additional parameters For (t,  p) the 05 strengths are reasonably well repro- duced with the exception of  148Sm where the calcu- lated value is much too low. For (p, t)  the strengths are underpredicted for all nuclei but the behavior with A,  especially the maximum for 15°Sm, is reproduced very well. In summary, new results for the (p, t) reaction on Sm isotopes remove many of  the discrepancies present in earlier data. Calculations of the IBA type reproduce many of the observed features, but  detailed agreement with 2n transfer strengths is only fair. R e f e r e n c e s  [1] A. Arima and F. Iachello, Phys. Rev. C16 (1977) 2085; O. Scholten, F. Iachello and A. Arima, Ann. Phys. (NY) 115 (1978) 321, and references therein. [2] P. Debenham and N.M. Hintz, Nucl. Phys. A195 (1972) 385. [3] W. McLatchie, W. Darcey and J.E. Kitching, Nucl. Phys. A159 (1970) 615. [4] W. Oelert, G. Lindstrom and V. Reich, Nucl. Phys. A233 (1974) 237. [5] J.H. Bjerregaard, O. Hansen and O. Nathan, Nucl. Phys. 86 (1966) 145. [6] J. van der Plicht and J.C. Vermeulen, Nucl. Instrum. Methods 156 (1978) 103. [7] F.D. Becchetti and G.W. Greenless, Phys. Rev. 182 (1969) 1190. [8] H. Nann and B.H. Wildenthal, Phys. Rev. C13 (1976) 1009. [9] A. Saha and H T. Fortune, Phys. Rev. C, to be published. 218 

University of Groningen Research Database

  
 University of Groningen
Two neutron transfer in samarium isotopes and IBA model predictions
Saha, A; Scholten, O; Hageman, DCJM; Fortune, HT
Published in:
Physics Letters B
DOI:
10.1016/0370-2693(79)90582-3
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from
it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
1979
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Saha, A., Scholten, O., Hageman, DCJM., & Fortune, HT. (1979). Two neutron transfer in samarium
isotopes and IBA model predictions. Physics Letters B, 85(2-3), 215-218. https://doi.org/10.1016/0370-
2693(79)90582-3
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Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
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Download date: 22-05-2019
Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 
TWO NEUTRON TRANSFER IN SAMARIUM ISOTOPES AND IBA MODEL PREDICTIONS 
A. SAHA 1, O. SCHOLTEN, D.C.J.M. HAGEMAN and H.T. FORTUNE 2 
Kernfysisch Versneller Instituut, Groningen, The Netherlands 
Received 1 June 1979 
Marked inconsistencies in earlier data for two-neutron transfer strengths in the samarium isotopes make comparison with 
model predictions difficult. We compare here the results of a careful high-resolution (p, t) reaction study on 148,150,1s2,154 Sm 
at Ep = 40 MeV with IBA model predictions. 
The stable samarium isotopes ranging from N = 84 
to N = 90 encompass the region in which nuclei under- 
go a shape transition from vibrational to rotational. 
The interacting boson model (IBA) [1] predicts this 
change in the samarium isotopes in a natural and 
consistent way, and also explains rather well the en- 
ergy levels and electromagnetic transition rates. As 
two-neutron transfer eactions are rather sensitive to 
the overlap of the wave functions of the target and 
residual nuclei, it seemed natural to test the predic- 
tions of the IBA model for two-neutron transfer eac- 
tions with those obtained from experiments. 
Several investigations of (p, t) reactions and one 
study of (t, p) on the samarium isotopes have been re- 
ported [2 -5] ,  all at bombarding energies below 26 
MeV. However, inconsistencies among the data make 
comparison with theory difficult. Even for g.s. -+ g.s. 
transitions, discrepancies in the existing data are 
larger than the A-dependent effects predicted. Thus, 
we have performed a careful high-resolution study of 
the (p, t) reaction on the samarium isotopes in order 
to compare the results obtained with IBA model pre- 
dictions. 
Isotopically enriched targets of 148,150,152,154Sm 
were bombarded with 40 MeV protons from the KVI 
AVF cyclotron and the outgoing tritons were momen- 
1 Present address: University of Pittsburgh, Pittsburgh, PA 
15260, USA. 
2 Present address: University of Pennsylvania, Philadelphia, 
PA 19104, USA. 
turn analyzed and detected in the focal plane detec- 
tion system of the QMG/2 magnetic spectrograph [6]. 
The total target hickness for each target was obtained 
by normalizing the measured elastic count rate in the 
l o  angular ange 20 ° to 35 ° (in steps of 2 ~- ) to the cross 
sections obtained from the optical model parameters 
of Becchetti and Greenlees [7] for 40 MeV protons. 
This method of estimating the target hickness intro- 
duced an absolute uncertainty of about 10%, but since 
the elastic data for all the targets were taken at the 
same time under identical conditions, the relative un- 
certainty is better than +5%. Since the main source of 
error in the determination of the absolute differential 
cross section is the uncertainty in the measurement of
the target hickness, we estimate the uncertainty for 
the absolute differential cross section for all the iso- 
topes to be less than 10% and relative values to be 
within 5%. The g.s. cross sections we quote are for 
01a b = 14 °. 
The (p, t) spectra t 01a b = 6 ° are displayed in fig. 1. 
The experimental energy resolution varied between 15 
and 18 keV FWHM. Excitation energies listed on the 
(p, t) spectra were obtained from calibrations made by 
a least-squares polynomial fit to peaks having well- 
known energies. The results for each excitation energy 
were then averaged over at least six to eight angles. 
Standard eviations for the excitation energies are less 
than 5 keV for the strongly excited peaks. 
The angular distributions to the 0 + states are shown 
in fig. 2. The curves through the data points are re- 
suits of L = 0 DWBA calculations using a cluster form 
215 
Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 
I00  
50  
I00  
l 
u J50  
z 
Z 
I 
n," 
Ld  
0.. 
CO 
~-60 
0 
(.,) 
4O 
20 
60  
40  
20  
0 
0 
~ o 
] 
m~o 
o Xl /2  
# 
Xl /2  
t54Sm (p,t)IS2Sm 
Ep= 40  MeV 
~LAB. = 6 deg. 
o 
-o , . . -~  ~ ~ o ~ ~. { 
o~ 
o 
£ 
'SZSm (p,t) IS°sin 
t.- 
X l /2  - -  
15°Sm (p,t) ~48Sm 
o - o ~ o r-- 
200 400 
148Sin (p,t) 146Sm 
600 800 
CHANNEL NUMBER 
* - - -X  f /2  
(z 
- -X l /2  
Fig. 1. Spectra of (p, t) reactions on various isotopes of Sm. 
216 
Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 
103~ I 
I° o ~/ /~+ 
io ° 
Lo 
A÷2Sm (p , t )Asrn  Ep=4OMeV O÷stcltes 
i i 
146Sm 
g.s. 
146Sm 
2341 
146 Sm 
2958 
146 Sm 
3059 
146 Sm 
375t  
Possible L=O 
101 / ,~  
,o 
I'0 20 30 40 50 
150 Sm 
3045 
x2 
150 Sm 
5219 
150 Sm 
5357 
150 Sm 
3721 ' 
I 
8 cm (decj.) 
I 
J 
148Sin 
~s 
x2 
148 Sm 
1427 
148 Sm 
2373 
150Srn 
gs 
150Sm 
735 
150Sin 
1251 
x5 
152Sm 
gs 
x2 
152 Sm 
687 
152 Sm 
1736 
I I I I I 
I0 20 30 40 50 
Fig. 2. Selected 0 ÷ angular distributions labeled by final nu- 
cleus and excitation energy (in keV). 
factor for the transferred dineutron. Shapes with mi- 
croscopic form factors are virtually identical. The opti- 
cal model parameters used and given in table 1 are not 
very much different from those listed in ref. [8], It 
should be emphasized that the DWBA calculations 
have been done primarily to take into account the Q- 
value effects before comparing with any model predic- 
tions. One of the main reasons for doing this experi- 
ment at Ep = 40 MeV is that the Q-value effects are 
rather small (+10%) over the range of isotopes and ex- 
citation energies tudies and are also independent of 
the choice of optical model parameters [9]. 
The L = 0 shapes are rather unique and easily dis- 
tinguishable from the other L-transfers. Several new 
0 + states have thus been identified at E x = 2341, 
2958, 3059 and 3751 keV in 146Sm, Ex = 2373 keV 
in 148Sm andE x = 1736 keV in 152Sm. Tentative 0 + 
spin assignments are made to the states at E x = 3045, 
3219, 3357 and 3721 keV in 148Sm and 1670 keV in 
152Sm. We observe no L = 0 strengths to states at E x 
= 2611 keV in 146Sm andE x = 1923 keV in 148Sm, 
which have previously been assigned 0 ÷ from other 
(p, t) [2 -4]  and (t, p) [5] experiments. 
The relative strengths of transitions to the ground 
states and the first excited 0 + states obtained in previ- 
ous (p, t) experiments [2-4]  and in this experiment 
are shown, in fig. 3, as functions of A. The strengths 
are normalized to 100 for the 148Sm(p, t)146Sm(g.s.). 
We immediately see that there are large discrepancies 
(over 50%) even in the g.s. strengths, especially for 
transitions to the 148,152Sm g.s. 
The Q-value effects have generally not been con- 
sidered for the earlier experiments, but they are not 
large enough to explain the discrepancies. Our results 
agree with those of Oelert etal. [4] within experimen- 
tal uncertainties for all except 152Sm g.s. where we dif. 
Table 1 
Optical model parameters, (potentials in MeV, lengths in fro). 
V ro ao W v W' = 4 W D r d a d r e 
p 51.0 1.18 0.7 52.0 1.25 0.7 1.25 
t 173.1 1.20 0.72 20.6 1.5 0.82 1.40 
"2n" 1.25 0.65 
cluster 
217 
Volume 85B, number 2,3 PHYSICS LETTERS 13 August 1979 
~J 
E 
u) 
Z 
W 
Z 150 
t.d 
> 
d 100  
W 
60 f 40 [] 40 
144 146 148 150 152 154 144 146 148 150 t52 154 
A< A~ 
50 
I~  19.0 MeV 
0 206 MeV 
g .s .~ g,S. (P J )  Z5.5 MeV 
IBA [[340.0 MeV 
(t,p) • 120MeV 
normalized 
here 
144Sm 146Sm 148Sr n 150Sin 152Sm 154Sm 
A< 
Fig. 3. (a) Experimental (dots) and calculated (line) (p, t) and 
(t, p) relative g.s. to g.s. cross sections. The (p, t) data are nor- 
malized to 100 for 148Sm (p, t) 146Sm. The (t, p) data are 
normalized to the (p, t) results for A = 150. (b) Experimental 
(dots) and calculated (lines) (p, t) and (t, p) relative cross sec- 
tions for excited 0+ states. The same scale is used as in fig. 3a. 
Note that A denotes the final nucleus for (p, t), but the target 
nucleus for (t, p). 
fer by about 30%. Marked variations occur for the data 
of Debenham and Hintz [2] and McLatchie et al. [3] 
for 150,152Sm even though they did their experiments 
at practically the same incident proton energy. Causes 
of these discrepancies are not apparent, but we believe 
our results reflect the true cross sections as practically 
all possible sources of uncertainties have been carefully 
monitored and accounted for. Only one investigation 
of the (t, p) reaction on the Sm isotopes has been re- 
ported - at E t = 12 MeV by Bjerregaard et al. [5]. 
These relative strengths have also been plotted in fig. 3. 
In the IBA model the (p, t) and (t, p) strengths can 
be calculated by assuming that the two-neutron trans- 
fer is a collective process. Tile two-nucleon pickup op- 
erator, T(p, t) for 0 ÷ states can be written as 
T+(0) = AoSv(Y2  v - 2(rv)l/2 ' 
where 2~2 v is the size of the major shell (in this case 
2~2 v = 44), and P/v is the boson number operator. For 
the two-nucleon stripping (t, p) reaction one has to 
take the hermitian conjugate of the above operator. 
The IBA parameters describing the Sm nuclei were 
taken from ref. [1 ] ,  in which excitation energies and 
B(E2) values are reproduced very well. The calculated 
ground-state cross sections are shown in fig. 3a. The 
parameter A 0 was determined by normalizing to an 
overall best fit. As was stated before there is a big dis- 
crepancy between the different measurements. The 
clear minimum in cross section observed for A = 150 
is predicted by the IBA calculation, but the predicted 
increase in cross section when going from A = 146 to 
A = 148 is in contradiction with the present experi- 
ment. 
In the calculation for the (p, t) and (t, p) strengths 
to excited 0 + states there is no additional parameters 
For (t, p) the 05 strengths are reasonably well repro- 
duced with the exception of 148Sm where the calcu- 
lated value is much too low. For (p, t) the strengths 
are underpredicted for all nuclei but the behavior with 
A, especially the maximum for 15°Sm, is reproduced 
very well. 
In summary, new results for the (p, t) reaction on 
Sm isotopes remove many of the discrepancies present 
in earlier data. Calculations of the IBA type reproduce 
many of the observed features, but detailed agreement 
with 2n transfer strengths i  only fair. 
References  
[1] A. Arima and F. Iachello, Phys. Rev. C16 (1977) 2085; 
O. Scholten, F. Iachello and A. Arima, Ann. Phys. (NY) 
115 (1978) 321, and references therein. 
[2] P. Debenham and N.M. Hintz, Nucl. Phys. A195 (1972) 
385. 
[3] W. McLatchie, W. Darcey and J.E. Kitching, Nucl. Phys. 
A159 (1970) 615. 
[4] W. Oelert, G. Lindstrom and V. Reich, Nucl. Phys. A233 
(1974) 237. 
[5] J.H. Bjerregaard, O. Hansen and O. Nathan, Nucl. Phys. 
86 (1966) 145. 
[6] J. van der Plicht and J.C. Vermeulen, Nucl. Instrum. 
Methods 156 (1978) 103. 
[7] F.D. Becchetti and G.W. Greenless, Phys. Rev. 182 (1969) 
1190. 
[8] H. Nann and B.H. Wildenthal, Phys. Rev. C13 (1976) 1009. 
[9] A. Saha and H T. Fortune, Phys. Rev. C, to be published. 
218 


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Two neutron transfer in samarium isotopes and IBA model predictions

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