α-particle production in 6He + 120Sn collisions

PHYSICAL REVIEW C 82, 034602 (2010) α-particle production in 6He +120Sn collisions P. N. de Faria,1R. Lichtenth¨ aler,1K. C. C. Pires,1A. M. Moro,2A. L´ epine-Szily,1V. Guimar ˜ aes,1 D. R. Mendes Jr.,1A. Arazi,3A. Barioni,1V. Morcelle,1and M. C. Morais1 1Instituto de Fisica, Universidade de S˜ ao Paulo, Caixa Postal 66318, 05314-970 S˜ ao Paulo, Brazil 2Departamento de FAMN, Universidad de Sevilla, Apartado 1065, E-41080, Sevilla, Spain 3Laboratorio Tandar, Departamento de Fisica, Comisi´ on Nacional de Energ´ ıa At´ omica, Avenida del Libertador 8250 (1429), Buenos Aires, Argentina (Received 17 May 2010; published 9 September 2010) The collision 6He +120Sn has been investigated at four energies near the Coulomb barrier. A large yield of αparticles has been detected, with energies around the energy of the scattered 6He beam. The energy and angular distributions of the αparticles have been analyzed and compared with breakup and neutron transfer calculations. DOI: 10.1103/PhysRevC.82.034602 PACS number(s): 21.45.−v, 24.10.Ht, 24.10.Eq, 25.60.−t I. INTRODUCTION The elastic scattering and reactions induced by low-energy neutron-rich and proton-rich projectiles on heavy and mediummass targets have been studied over recent years. A large total reaction cross section has been reported [1–4], compared to stable systems of the same mass. The reaction channels responsible for this large total cross section have not yet been completely identified although the projectile breakup, fusion, and one- and two-neutron stripping reactions are considered to be most important candidates. An intriguing question is how to separate the contributions from reactions proceeding via the equilibrated compound system (fusion) from other direct reaction channels. In fact, in the case of reactions induced by light exotic projectiles, one expects a mixing of the two scenarios. Because of the low binding energies and spatially extended distributions of nucleons in the projectile, there is a large probability that some nucleons of the projectile will fuse with the target, leaving a highly excited recoil nucleus, while the remaining projectile fragment follows with an energy and angular distribution typical of a direct reaction. This is the so-called incomplete fusion process. On the other hand, Q-optimum considerations indicate that the direct transfer of nucleons to excited states of the target below the particle emission thresholds (bound states) is very likely to occur. In principle, coincidence measurements between charged particles, neutrons, and γrays emitted during the reaction should provide us with means to reconstruct the kinematics of the reaction and distinguish between different mechanisms. However, with the present intensities and quality of the secondary beams, strong restrictions are imposed on the experiments. Despite these difficulties, experiments have been performed, using neutron–α-particle coincidence techniques [5–7], which allow the identification of the breakup and 1n- and 2n-transfer reaction channels in the 6He +209Bi scattering. More recently, the detection of the α-particle fragments in triple coincidence with neutrons and γrays of the decay of the residual nucleus in the collision of 6He +65Cu [8] allowed the identification of the 1nand 2nneutron transfers as important reaction channels. Despite the difficulties of the coincidence measurements, the analysis of the energy distribution of the charged particles emitted in the reactions can, in some cases, give some valuable information about the reaction mechanism. In this article we present an analysis of the energy and angular distributions of the αparticles emitted in the 6He +120Sn collision at four energies 17.4, 18.05, 19.8,and 20.5 MeV. We compare the experimental results with the theoretical predictions for several processes, namely, projectile breakup, 1nand 2ntransfer, and fusion-evaporation. II. EXPERIMENTAL MEASUREMENTS AND RESULTS The experiment was performed in the 8UD S˜ ao Paulo Pelletron Laboratory using the Radioactive Ion Beams in Brasil (RIBRAS) system [9,10]. The 7Li primary beam of energies in the range Elab =24–26 MeV and intensities of about 300 nA ewas focused on a 12 µm9Be foil in which the 6He beam was produced via the 9Be(7Li,6He)10B reaction. The 6He beam was collected and focused by the first solenoid on the secondary target position. A more detailed explanation of the RIBRAS system can be found in [1]. A 3.8 mg/cm2 120Sn (98.29%) foil was used as secondary target. An array consisting of four E(20 µm)-E(1000 µm) silicon telescopes allows the detection and identification of the charged particles emerging from the reaction. In Fig. 1we present some E-Etotal spectra, where Etotal =E+E. We clearly see the 6He particles elastically scattered in the target as well the 7Li2+beam contaminants. In the biparametric spectrum of Fig. 1one observes a group of counts along the α-particle line, at energies near to the energy of the 6He elastic peak. The α-particle energies are distributed over a broad region centered around 2/3 of the energy of the scattered 6He. In Fig. 2(left) we present the α-particle energy spectra projected on the total energy axis. The energy axis was obtained from the total energy signal (Etotal) by summing up the energy lossesoftheαparticles in one-half of the target thickness, assuming that the reaction took place in the middle of the target. Because of the low statistics we summed the spectra at a few angles around 50◦–75◦where the peak is more visible and calculated the double differential cross sections d2σ/ddE. The energies plotted in the xaxis and the cross sections can be directly compared to theoretical calculations. In Fig. 2(right) we present also the angular distributions of the αgroup. The angular distributions were obtained by integrating the counts of the entire αgroup in an energy region of about ±4MeV 0556-2813/2010/82(3)/034602(6) 034602-1 ©2010 The American Physical Society P. N. DE FARIA et al. PHYSICAL REVIEW C 82, 034602 (2010) FIG. 1. 6He +120Sn biparameteric spectra. The α-particle group is shown inside the poligon and the peak above corresponds to the 6He +120Sn elastic scattering around the centroid of the distribution. The normalization of the absolute cross sections was obtained using the gold target runs as described in [1]. III. ANALYSIS OF THE α-PARTICLE PRODUCTION CHANNEL The energies of the particles produced in a reaction depend on the kinematics of the reaction and the excitation energies of the nuclei populated in the exit channel. In order to disentangle the reaction mechanisms responsible for the production of these αparticles, the measured distributions have been compared with theoretical calculations assuming three possible reaction mechanisms, namely, elastic breakup to the 6He continuum, 1nand 2ntransfers from the projectile to the target, and particle evaporation following the formation of a compound nucleus. The results of the calculations are displayed in Fig. 2and will be discussed in the next subsections. A. The projectile direct breakup Within a direct breakup picture, the 2nremoval channel is interpreted as an inelastic excitation of the 6He projectile to its continuum states. The relevance of this mechanism has been investigated by means of continuum-discretized coupled-channels (CDCC) calculations. One has to bear in mind, however, that the breakup cross sections provided by this method are referred to the α+n+ncenter of mass. In principle, the αcross sections can be obtained from the CDCC breakup amplitudes by applying the appropriate kinematic transformation. This transformation has been already developed and applied to three-body CDCC (3b-CDCC) calculations [11], namely, a two-body projectile scattered by a target. An accurate treatment of the 6He +120Sn reaction would require a four-body reaction model. Although four-body CDCC calculations (4b-CDCC) are currently available for 6He reactions [12], convergence of the breakup observables has not yet been fully achieved and, in addition, the transformation to obtain the α-particle observables is still to be developed. For these reasons, we rely here on the 3b-CDCC calculations presented in Ref. [1]. Given the reasonable agreement found in that work for the elastic scattering between the 3b-CDCC and 4b-CDCC calculations, we believe that the breakup cross sections extracted from the former can provide us with a realistic estimate of this observable. In these 3b-CDCC calculations, we use the dineutron model proposed in Ref. [13]. In this model, the two halo neutrons are treated as a structureless cluster coupled to spin zero, bound to the αcore with an effective separation energy of 1.6 MeV. Continuum states are also treated within an α+2nmodel. Further details of the model and the CDCC calculations can be found in Refs. [13] and [1], respectively. For the calculation of the αcross sections 034602-2 α-PARTICLE PRODUCTION IN 6He +120Sn ... PHYSICAL REVIEW C 82, 034602 (2010) 0 10 20 30 40 50 0 100 200 300 0 10 20 30 40 0 200 400 0 10 20 30 40 d2σ/dΩdE mb/(sr MeV) 0 200 400 dσ/dΩ (mb/sr) 8 1012141618202224 Elab(MeV) 0 20 40 0306090 θc.m. (deg) 0 100 200 Elab=17.4 MeV Elab=18.05 MeV Elab=19.8 MeV Elab=20.5 MeV Θ=55-70 deg (1n)x4 (2n) Q-window FIG. 2. (Color online) Energy spectra (left) and the corresponding angular distributions (right) of the αparticles produced in the reaction 6He +120Sn. The histogram (left) and the filled circles (right) are the experimental data. The dotted Gaussian stands for the Qwindow for the 2ntransfer process, arbitrarily normalized. The solid line corresponds to the two-neutron distorted-wave Born approximation (DWBA) transfer calculation without any normalization. The dashed line corresponds to the breakup calculation without any normalization and the dot-dashed stands for the fusion-evaporation Projection Angular-momentum Coupled Evaporation (PACE) calculation arbitrarily normalized. The thin solid line plotted at E=19.8 MeV (left) is the 1nDWBA calculation, multiplied by a factor of 4 to make the curve more visible. from the breakup scattering amplitudes, we used the formalism and the codes developed in the work of Tostevin et al. [11]. The calculated energy distributions are shown in Fig. 2(left) by dashed lines. It is seen that the calculations underpredict the observed α-particle energies. In addition, the measured αyield can not be accounted for by the 3b-CDCC calculations. This is shown in Fig. 2(right), where we see that these calculations cannot reproduce either the shape or the magnitude of the measured angular cross section. The observed αyields are underestimated by about one order of magnitude, depending on the energy. The shape of the 3b-CDCC angular distributions indicates that the direct breakup mechanism should become more important at forward angles rather than at backward angles, where most of the αparticles are observed. We then conclude that the direct breakup mechanism can be responsible for some of the observed αparticles, but it is certainly not the main process involved. B. The neutron transfer reactions The measured αparticles can also be interpreted as coming from the one-neutron 120Sn(6He,5He)121Sn or two-neutron 120Sn(6He,α)122Sn stripping reactions. The 5He nucleus is unbound and decays into one neutron plus an αparticle. It is well known that particle transfer reactions have large cross section only for a window of Qreac values centered at the optimum Qvalue which can be estimated by the simple expression [14,15]: Qopt =Ec.m.Zpf Ztf ZpiZti −1,(1) where Zp,t,i,f stand for the atomic numbers of the projectile and target in the initial and final channels. Since the reaction Qvalue is obtained as the difference between the binding energies of the transferred particle in the final and the initial channels, Qreac =EBf −EBi with EB>0 for bound states and EBf =Egs Bf +Ex, the condition Qopt =Qreac basically defines a region of excitation energies Exin the final nucleus that will be populated. For the case of neutron transfer Qopt =0 and EBf ≈EBi. For weakly bound projectiles, the initial binding energy EBi is small and, as a consequence, EBf will also be small, thus resulting in the population of highly excited states in the final nucleus. Figure 3shows an excitation energy scheme which illustrates this idea for the 2ntransfer reaction 120Sn(6He,α)122Sn. It is seen that the 2ntransfer populates states between the 1nand 2nthresholds. 034602-3 P. N. DE FARIA et al. PHYSICAL REVIEW C 82, 034602 (2010) FIG. 3. Scheme showing the excitation energy region populated by the 2ntransfer leading to the 122Sn nucleus. The separation energies S1nand S2nfor the 122Sn nucleus are indicated in MeV. 1. Two-neutron transfer The dotted line in Fig. 2(left) is the result of a Q-window calculation (arbitrarily normalized) using a Gaussian shape (Ref. [15]) centered at the Qopt [see Eq. (1)] and considering the kinematics of the 2ntransfer reaction 120Sn(6He,α)122Sn. This simple Q-optimum calculation shows that the 2ntransfer would produce αparticles within the energy range of the measurements. To evaluate the importance of this mechanism we have performed DWBA calculations for the two-neutron transfer process, including states below and above the 2nthreshold. These calculations have been performed using the transfer to the continuum (TC) method [16,17], using the FRESCO code [18]. The distorted waves of the incoming channel were generated with the optical potentials derived in Ref. [1] from the fit of the elastic data. For the core-core interaction (4He +120Sn), as well as for the exit channel optical potential, we used the αinteraction of Ref. [19]. The internal wave function of the 6He nucleus is calculated assuming the same dineutron model used in the 3b-CDCC calculations. The dineutron cluster is assumed to be transferred as a single entity to 122Sn states. For the orbital angular momentum associated with the 2n-120Sn motion, lf, we considered values from lf=0tolf=8. For each value of lf, the continuum was discretized using bins of 1 MeV width, up to a maximum excitation energy of 9 MeV above the 2nbreakup threshold. For the states below this threshold, we considered a set of representative states, distributed at intervals of 1 MeV, following the same procedure proposed in Ref. [16]. For each lf, the number of nodes of the 2n-120Sn motion was determined from the Wildermuth condition (see, e.g., Ref. [20]), assuming that the transferred neutrons populate the lowest unoccupied single-particle states according to a simple shell-model picture to produce the state with the desired total angular momentum. For the transfer couplings, the post form of the transition operator was used. The calculated cross sections were transformed to the laboratory frame with the appropriate Jacobian. The resulting angular and energy distributions are compared with the data in Fig. 2without any normalization (solid lines). The shape of the angular distributions is in reasonable agreement with the data, indicating that the two-neutron transfer mechanism can play an important role. The angle-integrated 2ncross section is σα≈650 mb. This value remains approximately constant for the four energies and is of the order of σhalo [1] obtained from the elastic scattering analysis. It is clear from Fig. 2that the TC calculation underestimates a little the experimental cross sections. In this case, the angle-integrated cross section for the αparticles would be even larger than 650 mb. Given that the total reaction cross section is determined independently from the elastic scattering [1], a larger total αcross section would imply a smaller complete fusion cross section. Here we assume that the αcross section is coming entirely from a direct process and the complete fusion does not contribute to the αpeak. This will be discussed in more detail in Sec. III C. A possible suppression of the fusion cross section is an expected result for neutron-rich exotic systems above the barrier; however, given the uncertainties in the determination of the total cross sections, a definite conclusion about this issue is not possible. One has to bear in mind also that part of the discrepancies between the calculations and the data can arise from the approximations involved in these calculations. In particular, we use a very simple model for both the reaction mechanism and the structure of the initial and final nuclei. A proper treatment of this process would require a three-body description of the 6He nucleus as well as a more realistic description of the 122Sn two-neutron states. In addition, the calculations do not include any information on the 2nspectroscopic factor for the final nucleus, which, within the DWBA approximation, would affect the absolute normalization of the calculations. Notwithstanding these limitations, we believe that our schematic calculations are sufficiently realistic to support the conclusion that the 2ntransfer mechanism is a very important mechanism in this reaction at the measured angles. These conclusions are in agreement with those found in other 6He-induced reactions [16,21,22]. Despite the large differences found between the direct breakup (CDCC) and TC calculations, it is worth noticing that, strictly speaking, the states included in these TC calculations are not completely orthogonal to those included in the direct breakup calculations, and therefore their respective contributions cannot be simply added. In this sense, the direct breakup and transfer calculations should be considered as two different reaction models, each of them emphasizing a different set of final states; final states with low relative energy and angular momentum between the neutrons and the αcore are expected to be better described within the direct breakup model, whereas the transfer to the continuum method will be more suited to describe final states with small energy and angular momentum with respect to the target. In practice, because of the model space truncation required in both calculations and the different choice of the interactions, we do not expect the two calculations to provide the same results [17]. Furthermore, the fragment-target interactions that enter the CDCC calculations use optical potentials that describe the corresponding elastic scattering and, therefore, only the elastic breakup component is accounted for by this method. 2. One-neutron transfer We have considered also the reaction 120Sn(6He,5He)121Sn and the subsequent breakup of the 5He →α+n.We 034602-4 α-PARTICLE PRODUCTION IN 6He +120Sn ... PHYSICAL REVIEW C 82, 034602 (2010) performed DWBA calculations using the code FRESCO [18]. Because of the large number of excited levels in the 121Sn nucleus and the considerable spreading of the single-particle strength at the excitation energies around the optimum Q value, we did not attempt to include the physical states in this calculation. Instead, we assumed a simple model in which, for each single-particle configuration, the single-particle strength is distributed among a set of representative states of 121Sn that cover the region of excitation energies around the optimum Qvalue. In particular, the following single-particle levels were included: 2d3/2,1h11/2,3s1/2,1g7/2,2d5/2,2f7/2, and 3p3/2. For each configuration, we considered a set of five states at the excitation energies 0.919,1.919,2.919,3.919, and 4.919 MeV. These energies were chosen to cover the region from the low-lying states up to the one-neutron breakup threshold (6.171 MeV) of 121Sn in steps of 1 MeV. Three additional bins at 1.5,2.5,and 3.5 MeV excitation energies above the 1nthreshold were considered for each configuration. The spectroscopic factor for each representative state was taken as the sum of the experimental levels located around the excitation energies considered (see Table I in Ref. [23]). For the unbound states we used S=1. For the projectile overlap 5He|6He,weassumedap3/2configuration with spectroscopic factor S=2. The bound state wave functions for the final states were calculated using a Woods-Saxon well potential, with reduced radius r0=1.25 fm and diffuseness a=0.65 fm, and the depth adjusted to reproduce the appropriate one-neutron separation energy. The real part of the incoming optical potential was generated using the S˜ ao Paulo double-folding potential. The imaginary part was parametrized in terms of a Woods-Saxon shape with parameters V0= 28.8MeV,Ri=1.34 ×1201/3fm, and ai=1.185 fm. The core-core interaction (5He +120Sn), which appears in the remnant part of the transition operator, as well as the exit channel optical potential (5He +121Sn), were also represented by the same potential used for the incoming channel. The post form of the transition amplitude was used. The calculated cross sections were converted to the laboratory frame by applying the appropriate kinematic transformation, and the energy of the αparticles was calculated as Eα=0.8E5He. Here we make the simplifying assumption for the breakup process that the outgoing αparticle takes a fraction mα/m5He of the 5He kinetic energy. This can be justified by the fact that, in the 5He frame, the neutron takes most of the breakup energy (Ebup =890 keV, En=712 keV); however, the remaining α-particle energy (Eα=178 keV) might produce a non-negligible broadening of a few MeV on the energy of the αparticles. The result is shown by the thin solid line in Fig. 2(left) for the incident energy of 19.8 MeV. Although the calculated 1nyield has been multiplied by a factor of 4 (see Fig. 2), we see that the one-neutron transfer could contribute to the low-energy region. C. Fusion Part of the observed αyield might arise from evaporation following the formation of a compound nucleus. To evaluate the importance of this channel, we have performed complete fusion and decay calculations using the PACE program [24]. The complete fusion calculations for 6He +120Sn show that the compound nucleus 126Te would decay mainly by emitting neutrons and only a small fraction of the cross section (a few milibarns) would decay through α-particle emission. Cross sections of this order would not be detectable in our experiment. The calculated energy distribution of the evaporated αparticles is shown in Fig. 2(left) at 19.8MeV and is centered in the low-energy tail of the data in the same region populated by the breakup. However, because of the low cross section, we do not expect that the αparticles coming from the complete fusion would be seen in this experiment. We considered also the incomplete fusion of an αparticle with 2/3 of the laboratory energy of the 6He forming the 124Te compound nucleus and the decay by αparticles is still less probable than in the case of complete fusion. Thus we do not believe that complete fusion would give any significant contribution to the observed αyield. IV. CONCLUSIONS A large yield of αparticles has been observed in the 6He +120Sn reaction measured at energies around the Coulomb barrier. The angular and energy distributions of these αparticles have been compared with several reaction models, in order to disentangle the dominant reaction mechanisms. A kinematic analysis of the energy distributions leads to the conclusion that the neutron stripping transfer reactions are probably the dominant mechanisms contributing to the observed αyield. DWBA calculations and simple Q-optimum considerations indicate that the αparticles are probably produced in 2n- and 1n-stripping reactions to excited states of the final nucleus (122Sn and 121Sn, respectively). CDCC calculations show that the projectile breakup mechanism contributes only to the lower-energy region of the observed αspectrum. However, the magnitude of the calculated cross sections are found to be of the order of a few tens of millibarns, whereas the experimental cross section is on the order of a few hundreds of millibarns. This indicates that the direct breakup mechanism alone cannot explain the observed yields. Twoneutron transfer calculations, performed within the DWBA approximation, gave cross sections which agree better with the experimental results. The 2n-transfer angle-integrated cross sections are compatible with the total reaction cross sections measured from the elastic angular distributions. ACKNOWLEDGMENTS The authors thank the Fundac¸˜ ao de Amparo ` a Pesquisa do Estado de S˜ ao Paulo (FAPESP) and the Conselho Nacional de Desenvolvimento Cient´ ıfico e Tecnol´ ogico (CNPq) for financial support. This work has been partially supported by the Complementary Action PCI2006-A7-0654, funded by the Spanish Ministry of Education and Science. A.M.M. acknowledges the support by Spanish Ministerio de Ciencia e Innovaci´ on under Project No. FPA2006- 13807-c02-01, the local government of Junta de Andaluc´ ıa under the Excellence Project No. P07-FQM-02894, and the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042). 034602-5 P. N. DE FARIA et al. PHYSICAL REVIEW C 82, 034602 (2010) [1] P. N. de Faria et al.,Phys.Rev.C81, 044605 (2010). [2] N. Keeley, J. M. Cook, K. W. Kemper, B. T. Roeder, W. D. Weintraub, F. Marechal, and K. Rusek, Phys.Rev.C68, 054601 (2003). [3]E.F.Aguileraet al.,Phys.Rev.C79, 021601(R) (2009). [4]J.M.B.Shortoet al.,Phys. Lett. B 678, 77 (2009). [5] J. P. Bychowski et al.,Phys. Lett. B 596, 26 (2004). [6]J.J.Kolataet al.,Phys. Rev. C 75, 031302(R) (2007). [7] P. A. DeYoung et al.,Phys.Rev.C71, 051601(R) (2005). [8] A. Chatterjee et al.,Phys.Rev.Lett.101, 032701 (2008). [9] R. Lichtenth¨ aler et al.,Eur. Phys. J. A 25, s01, 733 (2005); Nucl. Phys. News 15, 25 (2005). [10] E. A. Benjamim et al.,Phys. Lett. B 647, 30 (2007). [11] J. A. Tostevin, F. M. Nunes, and I. J. Thompson, Phys.Rev.C 63, 024617 (2001). [12] M. Rodr´ ıguez-Gallardo, J. M. Arias, J. Gomez-Camacho, A. M. Moro, I. J. Thompson, and J. A. Tostevin, Phys. Rev. C80, 051601 (2009); M. Rodr´ ıguez-Gallardo, J. M. Arias, J. Gomez-Camacho, R. C. Johnson, A. M. Moro, I. J. Thompson, and J. A. Tostevin, ibid. 77, 064609 (2008); T. Matsumoto, T. Egami, K. Ogata, Y. Iseri, M. Kamimura, and M. Yahiro, ibid. 73, 051602 (2006); T. Matsumoto et al.,Nucl. Phys. A 738, 471 (2004). [13] A. M. Moro, K. Rusek, J. M. Arias, J. Gomez-Camacho, and M. Rodriguez-Gallardo, Phys.Rev.C75, 064607 (2007). [14] D. M. Brink, Phys. Lett. B 40, 37 (1972). [15] R. A. Broglia and A. Winther, Phys. Rep. 4, 153 (1972), (see pg. 191). [16] D. Escrig et al.,Nucl. Phys. A 792, 2 (2007). [17] A. M. Moro and F. M. Nunes, Nucl. Phys. A 767, 138 (2006); A. M. Moro et al.,ibid. 787, 463c (2007). [18] I. J. Thompson, Comput. Phys. Rep. 7, 167 (1988). [19] S. L. Tabor, B. A. Watson, and S. S. Hanna, Phys. Rev. C 11, 198 (1975). [20] G. R. Satchler, Direct Nuclear Reactions (Oxford University Press, New York, 1983), p. 721. [21] R. Raabe et al.,Nature (London) 431, 823 (2004). [22] E. F. Aguilera et al.,Phys.Rev.Lett.84, 5058 (2000); Phys. Rev. C 63, 061603(R) (2001). [23] M. J. Bechara and O. Dietzsch, Phys. Rev. C 12,90 (1975). [24] A. Gavron, Phys. Rev. C 21, 230 (1980). 034602-6