Tensor analyzing powers for 7 Li induced transfer breakup reactions

Tensor analyzing powers for 7Li induced transfer breakup reactions N. J. Davis and R. P. Ward School of Chemistry and Physics, Keele University, Keele, Staffordshire ST5 5BG, United Kingdom K. Rusek Department of Nuclear Reactions, The Andrzej Sołtan Institute for Nuclear Studies, Hoża 69, 00-681 Warsaw, Poland N. M. Clarke, G. Tungate, J. A. R. Griffith, S. J. Hall,*O. Karban,†I. Martel-Bravo,‡and J. M. Nelson School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom J. Gómez-Camacho Departmento de Física Atómica, Molecular y Nuclear, Facultad de Fisicas, Universidad de Sevilla, Aptdo. 1065, 41080 Sevilla, Spain T. Davinson, D. G. Ireland,§K. Livingston,§E. W. Macdonald, 储 R. D. Page,¶P. J. Sellin,** C. H. Shepherd-Themistocleous,†† A. C. Shotter,‡‡ and P. J. Woods School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland (Received 5 January 2004; published 7 June 2004) The T20 analyzing powers have been measured for the 120Sn共7Li,8Be→2 ␣ 兲119In and 120Sn共7Li,6Li*→ ␣ +d兲121Sn transfer breakup reactions, using a 70 MeV beam. The data exhibit excellent agreement with the results of coupled reaction channels calculations, providing an important test of these calculations when applied to the transfer breakup reaction mechanism. DOI: 10.1103/PhysRevC.69.064605 PACS number(s): 25.70.Hi, 25.70.Mn, 24.70.⫹s, 24.10.Eq I. INTRODUCTION Transfer breakup reactions are of particular interest because they combine two processes (the transfer of nucleons followed by breakup of the ejectile), whose individual mechanisms are well understood in isolation [1–6]. However, there has been little published on these reactions induced by the stable, lighter, heavy ions such as 7Li, which are relevant to studies of nuclei with binary cluster structures, and to complementary radioactive beam studies where the projectile nuclei have a large cross section for both nucleon transfer and, in particular, fragmentation. It is important to note that radioactive beams are polarized as a result of the fragmentation process used to create them. So use of the polarized 7Li beam provides a real test of a hypothetical radioactive beam experiment. If model predictions can achieve good agreement for transfer breakup reactions induced with stable nuclei, then model comparisons for radioactive beams become more meaningful. Coupled reaction channels (CRC)calculations have historically been found to provide a very good description of cross sections and analyzing powers for elastic and inelastic scattering and transfer reactions, including specifically those induced by 7Li [1,7,8]. More recently continuum discretized coupled channels (CDCC)calculations have been very successful in describing breakup reactions. In a previous publication [5]CDCC calculations were applied to 120Sn共7Li, ␣ t兲120Sn breakup analyzing powers. The ␣ plus triton cluster structure of 7Li resulted in a large breakup yield to these fragments. A detailed study was made of two mechanisms [9–11];(i)sequential breakup following excitation of the 7Li to the 4.63 MeV 共7/2−兲state, and (ii)the breakup into the ␣ particle plus triton continuum. The continuum breakup, which is strong at forward angles and falls off rapidly at larger angles, can be explained by the differential strong nuclear force between the target and fragments [12]in an ␣ particle plus triton cluster description of 7Li. The good agreement between the model calculations and the measured data provided an important test of the CDCC approach. The current challenge is to test thoroughly such coupled channels calculations with the more complex transfer breakup reactions. The aim of the current work is a measurement of the second rank 共T20兲analyzing powers for 7Li induced transfer breakup reactions, to investigate the applicability of CRC calculations to this reaction mechanism, which *Present address: Qinetiq Malvern, St. Andrews Road, Malvern, Worcestershire WR14 3PS, United Kingdom. †Present address: Velice 26, 37351 Driten, Czech Republic. ‡Present address: Departmento Fisica Aplicada, Facultad de Ciencias Experimentales, Campus de El Carmen, Universidad Huelva, 21071 Huelva, Spain. §Present address: Department of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ, Scotland. 储 Present address: General Accident Insurance, Perth, Scotland. ¶Present address: Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom. **Present address: Department of Physics, School of Electronics and Physical Sciences, University of Surrey, Guildford GU2 7XH, United Kingdom. ††Present address: CCLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom. ‡‡Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada, V6T 2A3. PHYSICAL REVIEW C 69, 064605 (2004) 0556-2813/2004/69(6)/064605(5)/$22.50 ©2004 The American Physical Society69 064605-1 is one step more complicated than breakup alone. These analyzing powers provide a particularly sensitive test of these theoretical models. An important feature of the measured data is that they have very low background because of the coincidence imposed by the data acquisition system, combined with software selection of particle identification and measurements of the angles and energies of the fragments. The result is that the specific transfer reaction and breakup reaction can be selected without ambiguity. A preliminary report containing some data and calculations from the current work have been recently published [13]. The purpose of the current paper is to provide a more comprehensive presentation and discussion of the transfer breakup analysis. II. EXPERIMENT Data for the transfer breakup reactions were obtained simultaneously with those for a previously reported study of polarized 7Li breakup on 120Sn [5], so the experimental procedure is the same. The experiment was performed using a 70 MeV polarized 7Li beam from the polarized heavy ion source [14]and accelerated by the tandem Van de Graaff accelerator, at the former Nuclear Structure Facility at Daresbury Laboratory. Optical pumping [15]was used in the ion source for polarization of the beam. Ions with each of the four spin substates were selected in turn, using a high frequency transition in a magnetic field to switch between substates. The polarization states were switched every few seconds, after a specified integrated beam current was measured, to minimize systematic errors due to beam drift or polarization fluctuations. A Wien filter was used to orient the polarization symmetry axis along the beam direction at the target. The beam polarization was determined from the 1H共7Li, ␣ 兲4He reaction [16]using a purpose-built, downstream polarimeter [17]. The measured magnitudes of second rank beam polarizations were typically t20=0.6. Measurements of first and third rank polarizations resulted in magnitudes no larger than 0.05 each. For the breakup and transfer breakup reactions a 2mgcm −2 120Sn target was used. The detection system consisted of two pairs of ⌬E.Edetector telescopes placed symmetrically, one pair on either side of the beam. The symmetric arrangement was used so that data from both sides of the beam could be summed, thus eliminating systematic errors arising from any shift in position of the beam on target and the effects of odd rank polarization components in the beam. The telescopes comprised 230 ␮ m thick p-njunction silicon ⌬Edetectors and 4 mm thick lithium drifted silicon Edetectors. Similar detectors placed behind the Edetectors acted as vetos to eliminate high energy protons, deuterons, and tritons which pass through the Edetectors. The detector collimators were 8 mm wide and 6 mm high with the centers for a given pair 12 mm apart. The detectors in each pair of telescopes were mounted symmetrically above and below the beam axis and 150 mm from the target. Reaction yields were obtained for each polarization state of the beam, from which analyzing powers were determined using the same method as used in the polarized 7Li breakup study [5], incorporating equations from the Madison Convention [18]. The detectors were energy calibrated using 5.486 MeV ␣ particles from 241Am sources mounted close to the detectors. Particle identification was performed using the ⌬Eand E signals. Fast timing was achieved by signals generated from the ⌬Epreamplifiers, used to start and stop a time to amplitude converter for each pair of telescopes. Data were transmitted to a computer via analog to digital converters and recorded event by event on tape. The T20 data for the 120Sn共7Li,8Be→2 ␣ 兲119In reaction and the effective T20 data for the 120Sn共7Li,6Li*→ ␣ +d兲121Sn reaction were obtained for a range of angles of the pairs of detector telescopes to the beam direction from 9° to 25° in the laboratory frame. III. CALCULATIONS CRC calculations were performed, using version FRXP.18 of the code FRESCO [19], for the 120Sn共7Li,8Be→2 ␣ 兲119In and 120Sn共7Li,6Li*→ ␣ +d兲121Sn reactions. For the 120Sn共7Li,8Be→2 ␣ 兲119In reaction the entrance channel optical potential was that of Cook [20]and the exit channel optical potential was determined from single folding using an empirical ␣ +120Sn optical potential [21]and 8Be= ␣ + ␣ cluster wave functions. A Gaussian shaped binding potential as proposed by Buck and Merchant [22]for 7Be=3He+4He was used: V共r兲=Voexp 冋 − 冉 r Ro 冊 2 册 .共1兲 The parameter Rowas chosen so as to reproduce the rms radius of the matter distribution of 8Be, 2.62 fm, predicted by Patra [23]. The 8Be ground state was assumed to be weakly bound, by just 0.01 MeV, and the potential depth, Vo, was adjusted to reproduce this. For the 120Sn共7Li,6Li*→ ␣ +d兲121Sn reaction the entrance channel optical potential was that of Cook [20]and the exit channel optical potential was determined from single folding using empirical ␣ +120Sn [21]and d+120Sn [24]optical potentials and 6Li= ␣ +dwave functions [25]calculated using the ␣ +dbinding potential proposed by Kubo and Hirata [26]. Spectroscopic amplitudes were obtained from Cohen and Kurath [27]and Turkiewicz et al. [28]. The coupling schemes used are shown in Figs. 1 and 2. The CDCC technique was used to generate the 8Be共2+兲and 6Li共3+兲resonance wave functions. In order that the calculations are manageable, 7Li breakup is not included. This approach is justified because second rank tensor analyzing powers for elastic scattering are mainly generated by 7Li ground state reorientation and coupling to the 7Li first excited state [29]. These are consequently the two entrance channel effects incorporated into the CRC calculations. To make a reasonable comparison of data with prediction, the detector configuration used for the breakup fragments needs to be considered. The 8Be case is the simplest because the 8Be is in its ground state so the fragment relative angular momentum is L=0 for the breakup. The L=0 breakup gives an isotropic distribution of ␣ fragment directions in the center of mass frame of the 8Be. A direct measurement of T20 for the transfer breakup reaction is consequently made because it N. J. DAVIS et al. PHYSICAL REVIEW C 69, 064605 (2004) 064605-2 does not matter where the detectors are placed relative to the reaction plane. The 6Li*case is somewhat more complicated because the 6Li*is in the 2.19 MeV 3+excited state. This is known to be a pure L=2 共 ␣ +d兲cluster state, so L=2 breakup of the state with no L=4 admixture can be assumed to a very good approximation. The L=2 breakup will result in an anisotropic fragment distribution and a consequent phase space effect due to detector positions. The analyzing powers measured for the 120Sn共7Li,6Li*→ ␣ +d兲121Sn reaction are consequently effective T20 which include a detector phase space effect. A technique was therefore developed to take this into account in calculating effective analyzing powers to compare with the data, by which the measured analyzing powers Tkq are modeled by a combination of the calculated polarization transfer coefficients Xkq,k⬘q⬘, which may be calculated from amplitudes generated by the FRESCO code, with tensors Ik⬘q⬘which are related to the detector geometry. This technique, which is described in detail in a previous publication [5], was applied to the transfer breakup via 6Li*. This involved the use of a probability function for the spatial distribution of the breakup fragments, calculated using a Monte Carlo simulation code [30]in which the collimator positions for the coincidence detection were defined. IV. RESULTS Details concerning the general techniques used for production of spectra and extraction of analyzing powers are provided in the previous 7Li breakup study [5], so only the key points relevant to the transfer breakup reactions of current interest are summarized here. An energy resolution of 0.4 MeV was obtained for the reaction particles. For the 120Sn共7Li,8Be→2 ␣ 兲119In reaction spectra were reconstructed corresponding to breakup via the 0+ground state of 8Be. The unresolved ground 9/2+and 0.31 MeV 1/2−first excited states of 119In were found to be populated strongly in these spectra. These are 1g9/2 and 2p1/2 single hole shell model states, respectively. For the 120Sn共7Li,6Li*→ ␣ +d兲121Sn reaction spectra were reconstructed corresponding to breakup via the 2.18 MeV 3+state of 6Li. These latter spectra were observed to contain three strong structures corresponding to the unresolved ground 3/2+, 0.006 MeV 11/2−first excited and 0.06 MeV 1/2+second excited states and many unresolved states around 1.2 and 2.7 MeV in 121Sn. The three states comprising the lowest excitation energy structure are the 2d3/2,1h11/2, and 3s1/2 single particle shell model states, respectively. Many of the states contributing to the two higher excitation energy structures have uncertain or unknown spin-parities, rendering calculations for these particular data impossible. The effect of the coupling schemes used for the calculations was investigated. Calculations showing the effect of 7Li reorientation and coupling to its first excited state are shown with the data for the 120Sn共7Li,8Be→2 ␣ 兲119In ground state reaction in Fig. 3. The sensitivity of T20 to the entrance channel is shown to be weak at the forward angles, although it can be concluded that the calculation using the full coupling scheme of Fig. 1 best reproduces the data. Calculations, using the full coupling scheme, for the 120Sn共7Li,8Be →2 ␣ 兲119In reaction are compared with the data in Fig. 4. The calcuations for the transfer breakup reactions leading to the ground and first excited states of 119In are very different. This shows how sensitive analyzing powers are to the reaction mechanism and spectroscopic factors. The data agree very well with the calculation assuming population of the 119In ground state. The calculation assuming population of the 119In first excited state does not reproduce the data. This indicates that only the ground state is significantly populated by the reaction and illustrates the usefulness of analyzing FIG. 1. Coupling scheme for 120Sn共7Li,8Be→2 ␣ 兲119In CRC calculations. The spins and parities refer to the projectile/ejectile. FIG. 2. Coupling scheme for 120Sn共7Li,6Li*→ ␣ +d兲121Sn CRC calculations. The spins and parities refer to the projectile/ejectile. FIG. 3. Results of CRC calculations for the 120Sn共7Li,8Be →2 ␣ 兲119In ground state reaction compared with data (ground and 0.31 MeV states in 119In are unresolved). The dotted line excludes 7Li reorientation and excitation while the solid line is for the full coupling scheme of Fig. 1. TENSOR ANALYZING POWERS FOR 7Li INDUCED…PHYSICAL REVIEW C 69, 064605 (2004) 064605-3 powers in distinguishing reactions to the unresolved states. The strong population of the 119In ground state can be understood in simple shell model terms. The 120Sn target nucleus has proton shells filled to the 1g9/2 shell inclusive. The 1g9/2 shell contains ten protons while the 2p1/2 shell contains two protons. The incoming 7Li picks up a proton. It would be expected from numbers of available protons to be five times more likely to pick up a 1g9/2 proton, leaving 119In ground state, than to pick up a 2p1/2 proton, leaving 119In first excited state. Also, the 1g9/2 shell model level is at a higher energy than the 2p1/2 level, albeit by not very much, which could serve to increase the likelihood of 119In ground state population further. Calculations without the detector phase space correction for the 120Sn共7Li,6Li*→ ␣ +d兲121Sn reaction assuming population of the ground 3/2+, 0.006 MeV 11/2−, and 0.06 MeV 1/2+states are shown with the unresolved data in Fig. 5. Good agreement is not achieved, although it could be argued on the basis of these calculations alone that the calculation for the 1/2+state, being predominantly negative, represents the data better than the calculations for the other two states, which are predominantly positive. Calculations with the detector phase space correction included are shown in Fig. 6, together with all the 120Sn共7Li,6Li*→ ␣ +d兲121Sn data. These illustrate the importance of the correction, included in the calculations of Fig. 6(c), which leads to far better agreement between the calculations and the data than obtained without the correction in Fig. 5. They also lead to a different conclusion than that arrived at from the uncorrected calculations alone, because once the correction is included all three calculations are very similar and agree with the data equally well. This means the relative contributions from the three states to the data are not important in assessing the success of the calculations. V. CONCLUSIONS Analyzing power angular distributions have been measured for the 120Sn共7Li,8Be→2 ␣ 兲119In and 120Sn共7Li,6Li* → ␣ +d兲121Sn transfer breakup reactions, using a 70 MeV beam. The results show that good coincidence transfer breakup measurements are possible and that CRC calculations do very well in reproducing T20 and effective T20 analyzing power data for the respective reactions in one of the first tests of these calculations for transfer breakup reactions. It is therefore expected that CRC calculations can provide a good foundation for the study of nuclear reactions of considerable complexity, especially those induced using radioactive beams. In particular, the theoretical and data analysis techniques developed and applied in the current work can be well utilized with data from radioactive beam induced reactions which involve fragmentation and provide a sound basis for such studies. Because of the sensitivity of analyzing powers FIG. 4. Results of CRC calculations for the 120Sn共7Li,8Be →2 ␣ 兲119In reaction compared with data (ground and 0.31 MeV states in 119In are unresolved). The solid and dotted lines assume population of the 119In 9/2+ground state and 0.31 MeV 1/2−first excited state, respectively. FIG. 5. Results of CRC calculations without detector phase space correction for the 120Sn共7Li,6Li*→ ␣ +d兲121Sn reaction. The data shown are effective T20. The dotted, solid, and dashed lines assume population of the 121Sn3/2+ground state, the 11/2−state at 0.006 MeV and the 1/2+state at 0.06 MeV, respectively. FIG. 6. Results of CRC calculations including detector phase space correction for the 120Sn共7Li,6Li*→ ␣ +d兲121Sn reaction to 121Sn (a)states around 2.7 MeV, (b)states around 1.2 MeV, and (c) unresolved ground, 0.006 and 0.06 MeV states. The data shown are effective T20. The dotted, solid, and dashed lines assume population of the 121Sn 3/2+ground state, the 11/2−state at 0.006 MeV, and the 1/2+state at 0.06 MeV in 121Sn, respectively. N. J. DAVIS et al. PHYSICAL REVIEW C 69, 064605 (2004) 064605-4 to details of what occurs during a reaction, they can be of use in determining reaction mechanisms and spectroscopic amplitudes of states populated in reactions. This would be particularly beneficial in radioactive beam studies where reactions of considerable complexity are likely. Measurements of analyzing powers for reactions induced by radioactive beams are therefore strongly encouraged in the future. ACKNOWLEDGMENTS This work was supported in part by the Engineering and Physical Sciences Research Council of the United Kingdom and by the State Committee for Scientific Research (KBN)of Poland. K.L. acknowledges additional financial support from Micron Semiconductor Ltd. [1]Y. Sakuragi, M. Yahiro, and M. Kamimura, Prog. Theor. Phys. Suppl. 89, 136 (1986). 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