The 28Si( 7Li, t) 32S reaction has been studied at 48 MeV. Using a Î±t potential overlap based on a microscopic cluster model, the full finite-range distorted wave Born approximation analysis was carried out for nine low-lying states; 0.0 MeV (0+), 2.23 MeV (2+), 3.78 MeV (0+), 4.46 MeV (4+), 5.01 MeV (3-), 5.80 MeV (1-), 6.76 MeV (3-), 7.43 MeV (1-) and 8.49 MeV (1-) of the residual nucleus. A re-analysis was also done for the same states of 32S having an Î±d overlap for the reaction 28Si (6Li, d) 32S at 75.6 MeV. Theoretical spectroscopic factors have been calculated for the measured even-parity states of 32S using the shell model code OXBASH. The spectroscopic factors were compared for both the reactions

Avasthi, D.K.

Datta, S.K.

Lagare, M.T.

Madhusoodhanan, T.

Mandal, A.

Mandal, S.

Puttaswamy, N.G.

Raja Rao, M.

Shyam, R.

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This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 14.139.155.11This content was downloaded on 05/02/2016 at 09:23Please note that terms and conditions apply.Study of -transfer reaction 28Si( 7Li,t) 32SView the table of contents for this issue, or go to the journal homepage for more1999 J. Phys. G: Nucl. Part. Phys. 25 1897(http://iopscience.iop.org/0954-3899/25/9/309)Home Search Collections Journals About Contact us My IOPscienceJ. Phys. G: Nucl. Part. Phys. 25 (1999) 1897–1907. Printed in the UK PII: S0954-3899(99)99796-7Study of -transfer reaction 28Si( 7Li; t) 32ST Madhusoodhanan†, Samit Mandal‡, R Shyam§, M Raja Rao†,M T Lagarek, N G Puttaswamy†, A Mandal‡, D K Avasthi‡ and S K Datta‡† Department of Physics, Bangalore University, Bangalore—560 056, India‡ Nuclear Science Centre, PB No 10502, New Delhi—110 067, India§ Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Calcutta—700 064, Indiak Department of Physics, Gulbarga University, Karnataka—585 106, IndiaE-mail: bangphy@nsc.ernet.in (T Madhusoodhanan)Received 30 November 1998, in final form 23 March 1999Abstract. The 28Si. 7Li; t/ 32S reaction has been studied at 48 MeV. Using a t potential overlapbased on a microscopic cluster model, the full finite-range distorted wave Born approximationanalysis was carried out for nine low-lying states; 0.0 MeV (0+), 2.23 MeV (2+), 3.78 MeV (0+),4.46 MeV (4+), 5.01 MeV (3−), 5.80 MeV (1−), 6.76 MeV (3−), 7.43 MeV (1−) and 8.49 MeV(1−) of the residual nucleus. A re-analysis was also done for the same states of 32S having and overlap for the reaction 28Si (6Li, d) 32S at 75.6 MeV. Theoretical spectroscopic factors havebeen calculated for the measured even-parity states of 32S using the shell model code OXBASH. Thespectroscopic factors were compared for both the reactions.1. IntroductionDirect transfer of one or more nucleons between the colliding nuclei is one of the most widelyused means for obtaining information on the nuclear shell structure. Single-nucleon transferis a selective and direct probe of single-particle shell structure, while two-nucleon transferprovides knowledge of pairing correlations in nuclei. Transfer reactions are very sensitive tothe tail of the nuclear wavefunctions and thus to the radius and the diffusivity of the ion–ionpotential. Multi-nucleon transfer reactions are extremely useful in obtaining information onnuclear structure, selectively exciting many-particle many-hole states in light nuclei. It plays avital role in the study of the cluster states of the residual nucleus. One such interesting problemis the determination of -cluster states through the four-nucleon (-) transfer reaction.The -transfer reaction is only possible with ions havingA D 6 or more. This reaction hasattracted a lot of interest because of the simplicity of the reaction mechanism involved whichcomes from the good spatial symmetry of the -particle as well as its zero spin and isospin.Since the -particle has a very large binding energy it behaves almost like an elementaryparticle and it is possible to have -cluster state in a nucleus.At forward angles the -transfer reactions at an incident energy above the Coulomb barrierhave a dependence on the transferred angular momentum [1]. These reactions also relatedirectly to the -cluster states and reveal the -cluster nature of the states involved. The simpleway of understanding the -transfer reaction is through (6Li, d) or (7Li, t) reactions becausethe ground states of these projectiles can be considered to have the structure of a -clusterand the deuteron or triton, respectively [2]. Over a wide range of mass numbers systematic0954-3899/99/091897+11$30.00 © 1999 IOP Publishing Ltd 18971898 T Madhusoodhanan et alstudies have been performed for the (6Li, d) and (d, 6Li) reactions [3–7]. Comparative studiesbetween (6Li, d) and (7Li, t) reactions [8, 9] are scarce.In this paper we report such a comparative study of (7Li, t) and (6Li, d) reactions on a Sitarget. The (7Li, t) reaction shows more features of a direct reaction mechanism comparedwith the (6Li, d) reaction [10]. The other measurement of (6Li, d) which we took from theliterature was performed using the cyclotron facility and a spectrograph. There the advantageis due to high beam current. The high resolution of energy spectrum obtained in a magneticspectrograph also helps. In our measurement with a Pelletron machine and solid-state detectortelescopes we did not get enough beam current. Also, very good energy resolution to obtainsharp peaks for the weak low-lying states was not possible. Small solid angles had to be used.Because of these limitations the quality of our data is somewhat poorer than in [11]. We havemeasured the (7Li, t) cross section data and obtained the (6Li, d) data from the literature [11].The (7Li, t) reaction was studied at 48 MeV. The absolute spectroscopic factors have beenderived by using microscopically calculated wavefunctions for 7Li and 6Li in the full finite-range distorted wave Born approximation (DWBA) calculations [12]. Shell model calculationswere also performed to obtain the -spectroscopic factors of the 32S nucleus for the even-paritystates using the OXBASH [13] computer code.2. Experimental detailsThe experiment was performed with momentum analysed 48 MeV 7Li3+ beam obtained fromthe 15UD Pelletron at NSC, New Delhi, and using the 1.5 m diameter general-purposescattering chamber (GPSC). The beam intensity on the target was about 10 pnA. A self-supporting natural Si target (92.23% 28Si, 4.67% 29Si and 3.10% 30Si) was used in theexperiment. The target was prepared from a thin silicon wafer by first ion-implanting up to thedesired depth and then preferentially etching out this depth. Target thickness was determinedby the energy loss of an -particle from a 241Am source. The stopping power values for thispurpose were calculated from TRIM [14].The experimental arrangement for the measurement of outgoing triton consisted of three1E–E telescopes, each with 1 mm 1E and 5 mm Si(Li) E detectors. The forward telescopesubtended a solid angle of 0.5 msr while the one kept at a backward angle subtended a solidangle of 1 msr. Two monitor detectors were used for cross section normalization and thesewere placed at 9.Conventional particle-identification electronics was used in the experiment. The energyresolution was about 100 keV. Figure 1 shows a typical energy spectrum of tritons obtainedduring the experiment at 18. It shows well-seperated peaks for all the analysed states. AFaraday cup connected to a current integrator was used to obtain the total charge. The absolutecross section was calculated using the Faraday cup counts and checked against monitor crosssection which is predominantly due to Rutherford scattering.The signals were processed through an AD811 module ADC in a CAMAC crate and thedata was stored on magnetic tapes with the Micro-Vax computer system using the ONLINEcomputer program [15]. The data were collected using an event-by-event mode and stored inmagnetic tapes for offline analysis. The angular distributions were measured from lab D 6–40 in steps of 4.Study of -transfer reaction 28Si. 7Li; t/ 32S 1899Figure 1. Energy spectrum obtained for tritons at 18 for the reaction 28Si. 7Li; t/ 32S at 48 MeVbeam energy.Figure 2. Elastic angular distribution of 7Li on natural Si at 48 MeV. The curve shows the opticalmodel fit with the potential parameters of table 1.1900 T Madhusoodhanan et alFigure 3. Angular distribution of the reaction 28Si. 6Li; d/ 32S. The solid curve represents theexact finite-range DWBA calculation.3. Theoretical analysisThe angular distribution data was analysed in the framework of the DWBA using the exactfinite-range computer code DWUCK5 [12]. For the determination of absolute -spectroscopicfactors the projectile cluster overlap is very important. Therefore, in the analysis, t potentialoverlap has been calculated on the basis of a fully microscopic cluster model [16] whichapplies the Volkov 2 force and reproduces the exact t separation energy. The entrancechannel wavefunction for the 7Li+ 28Si reaction was calculated from optical model parameters,extracted by fitting the elastic cross section measured at 48 MeV. The computer code SNOOPY[17] was used for searching the optical model parameters. While searching the parametersGRID and SEARCH options were combined to reduce the chi-squared value to a minimum.Figure 1 shows the fit to 7Li elastic data. The exit channel parameters are taken from [18]. Theparameters used for the description of the entrance- and exit-channel distorted waves are listedin table 1. For the case of the 6Li + 28Si reaction parameters given by Tanabe et al [11] havebeen employed. For the bound states of 32S a target plus -cluster wavefunction generated ina Woods–Saxon well of radius 1.3 A1=3t and diffuseness of 0.73 fm was used. The well depthStudy of -transfer reaction 28Si. 7Li; t/ 32S 1901Figure 4. Angular distribution of the reaction 28Si. 6Li; d/ 32S. The solid curve shows the exactfinite-range DWBA calculation.was adjusted to reproduce the binding energy of the -bound levels in the final nuclear state.The single-particle configuration for the system . 28Si +/was taken to be (sd)4 and (sd)3(fp)1for the positive and negative parity states, respectively. For the 6Li wavefunction we used anoverlap wavefunction calculated microscopically [19]. The number of radial nodes N wasfixed by the oscillator energy conservation relation 2N +L DP4iD1 2ni + li where .ni; li/ arethe shell model quantum numbers of the individual nucleons and (N;L) describes the radialquantum number and orbital quantum number of the cluster with respect to the core. Thisequation gives 2N + L D 8 and 9 for even- and odd-parity states. In the DWUCK5 code thesum over all possible l-values are included. So, in the (7Li, t) case the  being in a l D 1 stateis taken into account in the calculations. For the states unbound against -particle emission,DWBA calculations with form factors corresponding to weak binding (EB D −0:1 MeV)were performed. The variation in the very small binding energy did not produce significantdifferences.Shell model calculations were also performed to obtain theoretical estimates of the alphaspectroscopic factors for even-parity states using the computer code OXBASH [13]. For thesecalculations we have generated the single-particle states for 32S, 28Si and the -particle asdescribed below. The single-particle states for 28Si and 32S have been generated using SD1902 T Madhusoodhanan et alFigure 5. Angular distribution of the reaction 28Si. 6Li; d/ 32S. The solid curve shows the exactfinite-range DWBA calculation result.Table 1. The optical model parameters used for the DWBA calculations.V rr ar W Wd ri ai rCChannel (MeV) (fm) (fm) (MeV) (MeV) (fm) (fm) (fm)7Li + 28Si 180.72 1.21 0.832 12.4 — 2.1 0.756 1.2t + 32S 145.0 1.14 0.73 19.8 — 1.59 0.8 1.116Li + 28Si 176.5 1.3 0.7 32.9 — 1.7 0.9 1.4d + 32S 62.833 1.25 0.7338 13.0 12.0 1.25 0.751 1.3model space and the universal s–d interaction W of Wildenthal [20]. For the cluster, the SDmodel space and SU3 interaction [21] have been used. For the ground state spectroscopicfactor, the cluster and the residual nucleus are assumed to be in their respective groundstates. The spectroscopic factors of the excited states have been calculated by taking theoverlap between the ground state of the cluster and the excited state of the residual nucleus.Core excitation has been neglected. The excitation energies obtained as a byproduct of thespectroscopic factor calculations are found to agree with experimental values to within 200–300 keV. The spectroscopic factor values are shown in table 2. The negative-parity statesStudy of -transfer reaction 28Si. 7Li; t/ 32S 1903Figure 6. Angular distribution of the reaction 28Si. 7Li; t/ 32S. The solid curve shows the exactfinite-range DWBA calculation.cannot be accommodated in this scheme, because the (sd)3(fp)1 configuration requires the-particle to be distributed over two major shells. We did not attempt any such calculations.4. Discussion and conclusionFigures 3–8 show the experimental and theoretical (6Li, d) and (7Li, t) angular distributionsfor different states in 32S. In both the cases, except for the 4.46 MeV 4+ state, the calculatedcurves agree fairly well with the experimental cross sections. The DWBA curves calculatedfor the (6Li, d) angular distributions show a systematic deviation from earlier work [11] whichmay be attributed to the form factors used for the 6Li which are calculated microscopically.It is observed that the population of states, especially 3.78 MeV 0+ and 4.46 MeV 4+through the (7Li, t) reaction, are found to be very weak. This may be because those statesare not good -cluster states. The full finite-range DWBA curves are normalized to theexperimental data through chi-squared minimization to extract the -spectroscopic factorsfor the reaction 28Si. 7Li; t/ 32S at 48 MeV and the values obtained through the re-analysisof the 28Si. 6Li; d/ 32S reaction at 75.6 MeV. The absolute spectroscopic factors of different1904 T Madhusoodhanan et alFigure 7. Angular distribution of the reaction 28Si. 7Li; t/ 32S. The solid curve shows the exactfinite-range DWBA calculation.Table 2. Absolute spectroscopic factors for the -particle transfer reaction 28Si. 7Li; t/ 32S at48 MeV and 28Si ( 6Li; d/ 32S at 75.6 MeV, from Tanabe et al [11].Shell model resultsSpectroscopic factorsEx Energy(MeV) J . 7Li; t/ . 6Li; d/ . 6Li; d/ [11] S (calc.)0.00 0+ 0.33 0.91 1.00 0.74 0.002.23 2+ 0.11 0.46 0.45 0.22 2.153.78 0+ 0.05 0.37 0.53 0.17 3.754.46 4+ 0.47 0.17 0.20 0.01 4.705.01 3− 0.28 0.51 0.495.80 1− 0.08 0.51 0.536.76 3− 0.29 0.88 —7.43 1− 0.57 1.24 1.28.49 1− 1.05 2.47 2.1Study of -transfer reaction 28Si. 7Li; t/ 32S 1905Figure 8. Angular distribution of the reaction 28Si. 7Li; t/ 32S. The solid curve shows the exactfinite-range DWBA calculation.states along with the Tanabe et al values are shown in table 2 (the absolute value of S for theground state from [11] is quoted in parenthesis). In order to take into account the differentoverall normalization we have calculated the relative spectroscopic factors which are shown intable 3. The S values obtained through the (7Li, t) reactions are found to be smaller than thevalues extracted through the (6Li, d) reactions, especially in the case of the excited 3.78 MeV(0+) and 5.80 MeV (1−) states. For the 3.78 MeV 0+ state only a few angles are shown inthe figure. This is due to the difficulties in the extraction of the cross section at certain angleswhere the population of the state is very weak. The cluster configuration for the excited 0+state in 32S is not clear. The particles may have to cross the fp shell for this arrangement andtherefore may have low probability at this excitation energy. This may be one of the reasonswhy the 3.78 MeV 0+ and 4.46 MeV 4+ states are weakly populated. We do not claim that thespectroscopic factors extracted for these states are very meaningful.The theoretical fit to the ground state of 32S with our microscopic wavefunction for 6Liis found to be better than the one shown in [11]. For the 2.23 MeV 2+ state the theoretical fitin the case of the (6Li, d) reaction is found to be better than in the case of the (7Li, t) reaction.The relative spectroscopic factor of this particular state with the (7Li, t) reaction gives a veryclose value to the shell model prediction. Through the (6Li, d) reaction the value is found to1906 T Madhusoodhanan et alTable 3. The relative spectroscopic factors for the -transfer reactions (6Li, d) and (7Li, t) reactionon 28Si.Ex J (7Li, t) (6Li, d) Shell model0.00 0+ 1.00 1.00 1.002.23 2+ 0.33 0.51 0.303.78 0+ 0.15 0.41 0.234.46 4+ 1.42 0.19 0.015.01 3− 0.85 0.565.80 1− 0.24 0.566.76 3− 0.88 0.977.43 1− 1.73 1.368.49 1− 3.18 2.71be around 35% higher than the (7Li, t) reaction. The 6.76 MeV level is found to be in goodagreement for the J D 3− state. The relative spectroscopic factors of this state are foundto be within 10% between the two reactions. The relative values of S for 7.43 MeV (1−)and 8.49 MeV (1−) states are found to be 1.73 and 3.18, respectively, in the case of (7Li, t)reactions.The S values of the low-lying states of 32S, except the 4.46 MeV 4+ state, obtainedfrom the (6Li; d) and (7Li; t) reactions agree with shell model predictions. The differences inspectroscopic factors may be attributed partly to the influence of multistep processes.In conclusion, we have measured the -spectroscopic factors of 32S through the (7Li, t)reaction at 48 MeV and compared with the (6Li, d) reaction. The shell model values have beencalculated for the low-lying even-parity states. The relative spectroscopic factors for the strongstates of 32S through the (7Li, t) reaction is found to agree fairly well, within experimental errors,with the (6Li, d) reaction. For the very weak, and possibly non-cluster states (e.g. 3.78 MeV0+ and 4.46 MeV 4+), we do not claim any degree of success.AcknowledgmentsWe gratefully acknowledge the help of the NSC Pelletron crew during the experiment. Wealso acknowledge the partial financial support obtained from UGC for performing this study.References[1] Bromley A (ed) 1984 Treatis on Heavy Ion Science vol 1 (New York: Plenum) p 714[2] Kunz P D 1960 Ann. Phys., Lpz. 11 275[3] Becchetti F D, Janecke J and Thorn C E 1978 Nucl. Phys. A 305 313[4] Apagyi B and Vertse T 1980 Phys. Rev. C 21 779[5] Yamaya T, Saito M, Fujiwara M, Itahashi T, Katori K, Suechiro T, Kato S, Hatori S and Ohkubo S 1993 Phys.Lett. B 306 1[6] Gutbrod H H, Yoshida H and Bock R 1971 Nucl. Phys. A 165 240[7] Oelert W, Berg G P A, Djaloeis A, Mayer-Borieke C and Turek P 1983 Phys. Rev. C 28 73[8] Puhlhofer F, Ritter H G, Bock R, Brommundt G, Schmidt H and Bethge K 1970 Nucl. Phys. A 147 258[9] Becchetti F D, Flynn E R, Hanson D L and Sunier J W 1978 Nucl. Phys. A 305 293[10] Baranger M and Vogt E (eds) 1972 Advances in Nuclear Physics vol 5 (New York: Plenum) p 461[11] Tanabe T, Yasue M, Sato K, Ogino K, Kadota Y, Taniguchi Y, Obori K, Makino K and Tochi M 1981 Phys. Rev.C 24 2556[12] Kunz P D 1978 Computer code DWUCK5 (University of Colorado Version)[13] Brown B A, Etchegoyen A, Rae W D M and Godwin N S 1984 OXBASH Computer CodeStudy of -transfer reaction 28Si. 7Li; t/ 32S 1907[14] Ziegler J F, Biersack J P and Littmark V 1985 The Stopping and Ranges of Ions in Solids vol 1 (New York:Pergamon)[15] Bhowmik R K, Goyal D K and Naithani S 1991 DAE Nucl. Phys. Symp. B 34 393[16] Shyam R, Lovas R G, Pal K F, Sharma V K and Nagarajan M A 1985 J. Phys. G: Nucl. Phys. 11 1199[17] Schwandt P 1984 Optical model potential code for elastic scattering analysis IUCF Report No. 84-X (IndianaUniversity Cyclotron Facility)[18] Becchetti F D Jr and Greenlees G W 1971 Polarization Phenomena in Nuclear Reactions ed H H Barschall andW Haeberli (Wisconsin: University of Wisconsin Press) p 682[19] Lovas R G 1983 Private communication[20] Wildenthal B H 1982 Bull. Am. Phys. Soc. 27 725[21] Elliot J P 1985 Rep. Prog. Phys. 48 171

Study of Î±-transfer reaction 28Si( 7Li, t) 32S

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Study of Î±-transfer reaction 28Si( 7Li, t) 32S

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