Four-body effects in the He6+Ni58 scattering

Physics Letters B 732 (2014) 228–232 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Four-body effects in the 6He +58Ni scattering V. Morcelle a,b, K.C.C. Pires c,d, M. Rodríguez-Gallardo e, R. Lichtenthäler d,∗, A. Lépine-Szily d, V. Guimarães d,P.N.deFaria b, D.R. Mendes Junior b,A.M.Moro e, L.R. Gasques d, E. Leistenschneider d,R.PampaCondori d, V. Scarduellid,M.C.Morais f, A. Barionig,J.C.Zamora i, J.M.B. Shorto h aUniversidade Federal de Itajubá, Campus Itabira, MG 35900-030, Brazil bInstituto de Física, Universidade Federal Fluminense, Niterói, RJ 24210-340, Brazil cUniversidade Tecnológica Federal do Paraná, Campus Cornélio Procópio, PR 86300-000, Brazil dInstituto de Física, Universidade de São Paulo, C.P. 66318, 05389-970 São Paulo, Brazil eDepartamento de FAMN, Facultad de Física, Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla, Spain fCentro Brasileiro de Pesquisas Físicas, CBPF, Rio de Janeiro, RJ 22290-180, Brazil gDepartamento de Física da Terra e do Meio Ambiente, Instituto de Física, Universidade Federal da Bahia, Campus Ondina, BA 40210-340, Brazil hInstituto de Pesquisas Energeticas e Nucleares – IPEN, 05508-000 São Paulo, Brazil iTechnische Universität Darmstadt, Germany article info abstract Article history: Received 19 December 2013 Received in revised form 12 March 2014 Accepted 19 March 2014 Available online 26 March 2014 Editor: V. Metag We present angular distributions of the 6He +58Ni scattering measured at three bombarding energies above the Coulomb barrier: Elab =12.2MeV,16.5MeV,and 21.7 MeV. The angular distributions have been analysed in terms of three- and four-body Continuum-Discretized Coupled-Channels calculations considering the effect of the 6He breakup. A behaviour in the cross section at large angles has been observed which was reproduced only by the four-body Continuum-Discretized Coupled-Channels calculation. ©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. 1. Introduction Low-energy reactions induced by light exotic nuclei have been investigated over the last years using secondary beams of 6He, 11Be, and 11Li [1–7]. These nuclei show a common characteristic which is their cluster structure, composed by a ‘stable’ core plus one or two weakly bound neutrons. Due to the low binding energies and low angular momenta of the valence neutrons, their wave function extends over large distances from the core, forming a kind of halo whose density is much lower than the normal nuclear matter. In addition, 6He and 11Li are examples of three-body systems in nature. They are called Borromean nuclei (in allusion to the Borromean rings) and are bound only if their three constituents are present. The 6He nucleus is composed by an alpha particle plus two neutrons, but any binary sub-system of its components is unbound, 5He is unbound and so is the di-neutron system. The characteristics of such light neutron rich nuclei make them very interesting in several aspects. Some of them may play a role in astrophysical explosive scenarios [8–11],actingasbridgesto overcome the instability gaps at A=5 and A=8 and participating *Corresponding author. in the synthesis of heavier elements. They may also have importance in more general issues such as in the many-body problem in physics and the possible existence of three-body states such as Efimov resonances [12,13]. The fact that some exotic nuclei present a neutron halo has consequences from the reaction mechanism and the nuclear structure points of view. Due to their low binding energies, 0.973 MeV for 6He, 0.5 MeV for 11Be, and 0.37 MeV for 11Li, these projectiles are likely to breakup in the collision with a target. Moreover, the long range of the neutron halo increases its reactivity favouring one and two neutron transfer reactions [14]. Due to the looselybound neutrons, reactions can occur even at energies around and below the Coulomb barrier and can take place at rather large distances from the target. From the experimental point of view, some characteristics have been observed in the elastic scattering of exotic beams which differ from collisions with stable projectiles. The elastic angular distributions of 6He and 11Li on heavy targets such as 120Sn [2] and 208Pb [15,6,7], and 11Be on intermediate mass targets such as 64Zn [4], present a damping of the Fresnel oscillations which is usually observed at forward scattering angles and at energies above the Coulomb barrier. On the other hand, a considerable enhancement in the total reaction cross section with respect to the stable nuclei http://dx.doi.org/10.1016/j.physletb.2014.03.043 0370-2693/©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. V. Morcelle et al. / Physics Letters B 732 (2014) 228–232 229 Fig. 1. (Color online.) Two-dimensional spectrum obtained with the 6He beam and 58Ni target at θlab =30◦and Elab =21.7MeV. with similar masses has been observed [2,5]. Both phenomena are related to each other and have been interpreted as a consequence of the coupling with the projectile breakup and possibly the neutron transfer reactions. In first order, the breakup removes flux from the elastic scattering and takes place either in the long-range Coulomb field (Coulomb breakup) or in the short-range nuclear field (nuclear breakup) [16]. Coulomb breakup dominates at large distances, where the nuclear short-range interaction is negligible and the high angular-momentum partial waves participate, thus removing flux at corresponding forward angles. A similar phenomenon has been seen in the past (see for instance [17])for heavy stable systems in which the Coulomb excitation is an important reaction channel. As we go to lighter targets the Coulomb interaction becomes less important and for very light systems the nuclear breakup dominates. Nuclear breakup is a diffractive process which takes place in a localized space region around the surface of the colliding nuclei where the short-range nuclear interaction is dominant. As a consequence, it tends to affect more the large angles region as it was seen in the 6He +9Be scattering [3], where the breakup effects appear mainly at large angles. Here we present new data for 6He on an intermediate mass target, 58Ni. 2. Experimental setup The experiment was performed in the São Paulo Pelletron AcceleratorusingtheRIBRASsystem[18,19].A7Li3+primary beam of energies Elab =18.0,22.0,and 27.0 MeV and intensity of I≈ 200 nAe was used to produce the 6He2+secondary beam by the 9Be(7Li,6He)10B reaction in the primary target of RIBRAS. The primary beam intensity was measured by a Faraday cup (which covers 0 ⩽θ⩽2 degrees) connected to a current integrator to provide the total incident charge at each run. A 12 μm 9Be foil was used as primary target. The secondary target consisted of a 58Ni isotopically enriched foil of 2.2mg/cm2. The selection of the secondary beam was performed by the first solenoid of the RIBRAS system. Four E(1000 μm)–E(20 μm) telescopes formed by silicon detectors were mounted in the intermediate scattering chamber to detect and identify the reaction products. A two-dimensional (E–E) spectrum can be seen in Fig. 1. The secondary beam contaminations at this position can be seen in Fig. 1 as the low-energy peak of 7Li2+, the higher energy peak of α-particles (E(α)=1.5E(6He)) and lighter particles such as deuterons and tritons. These contaminations do not affect our results since they are well separated from the elastic peak. Runs using a 197Au target have been performed during the experiment in order to normalize the data and to monitor the secondary beam Fig. 2. (Color online.) Elastic angular distributions for 6He +58Ni system at Elab = 21.7 MeV (upper panel), 16.5 MeV (middle panel), and 12.2 MeV (lower panel). Three- and four-body CDCC calculations are also shown. intensity. The cross sections have been obtained by normalization with respect to the Gold target runs, for which the cross sections are described solely by Rutherford scattering formula. Thus we obtained expressions for the cross sections which are independent of the solid angles of the detectors [2,3]: σ6He+58Ni(θ) =NNi c NAu c NAu b NNi b NAu t NNi t JNi JAu σ6He+197Au Ruth (θ), (1) where Ncis the area of the peak of interest, Nbis the total number of incident 6He beam particles during the run, Ntis the areal density of the target in atoms/cm2and Jis the transformation factor from the laboratory to the center of mass system. The total number of 6He beam particles Nbis proportional to the number of particles of the primary beam Nb=ε×N7Li, where ε≈10−7is the production rate and N7Li is proportional to I, the primary beam integrator. Then, the equality NAu b NNi b =IAu INi holds if the production rate εis constant between different runs. The 6He +58Ni angular distributions have been obtained in the θlab =15◦–75◦angular range with steps of 3◦in the laboratory system. They are presented in Fig. 2 for three energies, Elab =12.2,16.5,and 21.7 MeV. The error bars of the experimental points are pure statistical and no systematic errors have been included. Statistical errors appear in both terms NNi,Au cand have been propagated through the expression above. Possible sources of systematic errors would be in the target thickness ratio and in the ratio of the integrators. The target thicknesses should not give an important contribution to the errors since they have been measured, by energy loss measurements using an alpha-source of 241Am, with a precision of about 7%, which is much smaller than the statistical errors. In addition, systematic deviations in the target thickness measurement would affect the three distributions in the same way. The ratio of the integrators IAu/INi on the other hand could be an additional source of errors due to possible variations in the production rate between Gold and Ni target runs. Variations of about 20% or even more in the production rate have been observed during the experiments. To better control this possible source of errors we performed measurements of the production rate, with Gold target, just before and just after each Ni target run, and used the 230 V. Morcelle et al. / Physics Letters B 732 (2014) 228–232 Table 1 Optical potentials used in the CDCC calculations at the three energies, respectively, for α+58Ni (top row) and n+58Ni (bottom row). Elab (MeV) V0 (MeV) r0 (fm) a0 (fm) W0 (MeV) ri (fm) ai (fm) Wd (MeV) rd (fm) ad (fm) Ref. 12.2 60.00 1.62 0.54 0.50 1.62 0.54 15.84 1.52 0.44 [31] 61.36 1.45 0.57 – – – 1.28 1.45 0.50 [30] 16.5 165.90 1.62 0.40 11.40 1.62 0.4 23.98 1.52 0.44 [29] 42.00 1.46 0.35 6.09 1.46 0.35 – – – [29] 21.7 135.10 1.35 0.64 7.64 1.34 0.50 18.97 1.52 0.44 [29] 42.00 1.46 0.35 6.09 1.46 0.35 – – – [29] average value of NAu band IAu for normalization. We believe that this procedure should account for most of the variations in the production rate. Additional systematic deviations in the integrator measurements (IAu) could still be present but should be minimized by the procedure of taking the ratios of these quantities, in formula (1). Finally, it is not easy to give a precise determination of the magnitude of remnant systematic errors. Comparisons between data and calculations in previous experiments [2,3] indicate that, differences between 15–20% in the normalization of individual angular distributions could exist. However, in the present experiment, we believe that the errors in the overall normalization of the angular distributions are considerably smaller than that. 3. Analysis of the elastic angular distributions Theoretical approaches have been developed over the last decades to describe the scattering of neutron (and also proton) halo exotic nuclei [6,20–26]. Due to the low binding energy of the projectiles, there is a strong coupling between the elastic scattering and breakup channels that must be taken into account. The Continuum-Discretized Coupled-Channels (CDCC) [27] framework allows to assess these effects. The CDCC model space includes both, the bound and unbound states of the projectile, allowing the evaluation of the projectile breakup and its consequences on the elastic scattering. Since the unbound states form a continuum of energy and their wave-functions are non-normalizable, in the CDCC formalism the continuum is discretized in terms of energy sub-intervals (bins) up to a maximum energy. A bin is a square-integrable state constructed as a linear superposition of the scattering states in that energy sub-interval. The CDCC framework was first developed for three-body reactions, i.e., for two-body projectiles such as 11Be. Nevertheless, the three-body CDCC method can be applied to Borromean nuclei such as 6He within a di-neutron model, that is, by assuming a two-body model for 6He consisting of an alpha core plus a dineutron particle. An improvement in this three-body model was proposed by Moro et al. [28] to take into account four-body effects by using an effective two-neutron separation energy in 6He (S2n=1.6 MeV instead of 0.973 MeV). This modification better reproduces the 6He nucleus ground-state wave function and the B(E1)strength obtained within a three-body model description of 6He. More recently, the CDCC framework has been extended to four-body reactions [24]. Within the four-body CDCC method, the 6He nucleus is described as a three-body system, an alpha core plus two neutrons. In a previous work [2],the scattering of 6He nucleus on a heavier target, 120Sn, was studied using both, the four- and improved three-body CDCC models. The calculations were very close to each other and reproduced fairly well the experimental elastic data. On the other hand, the same study on a light target, 9Be [3],reveals that the agreement between both models is not that good, mainly at large angles. In this work, we address the scattering of 6Heonamedium- mass target, 58Ni. We perform, and compare with elastic data, standard three-body, improved three-body, and four-body CDCC calculations. The α+58Ni and n+58Ni optical potentials used here have been obtained from actual data and are shown in Table 1.The 2n+58Ni potential, used on the standard and improved three-body CDCC calculations, was obtained by a single folding model using the n+58Ni optical potential, shown in Table 1, and the neutron– neutron density distribution obtained from Ref. [28]. Continuum states with =0−4 were included in the three-body calculation in order to obtain a full convergence. In the present three-body calculations, for each partial wave, the continuum is truncated at a maximum excitation energy of ε=6,9,and 15 MeV respectively for 12.2, 16.5, and 21.7 MeV incident energies, and discretized into about 5 bins, evenly spaced in the linear momentum space. The four-body calculations include bins up to 7, 8, and 9 MeV for the incident energies 12.2, 16.5, and 21.7 MeV, respectively, in order to get convergence. The inclusion of states with angular momenta Jp=0+,1−,2+,3−was sufficient. For both, three- and four-body calculations, full convergence is checked by two criteria: the total cross section as a function of the total angular momentum Jmust converge (be very small) for high Jand the elastic angular distributions are not sensitive to variations in the number of bins, the maximum energy, and number of angular momenta used in the calculation [24,28]. The results of the calculations are shown in Fig. 2.Thedotted black line is the four-body CDCC without coupling to the continuum. The solid red line corresponds to the full four-body CDCC calculation. The dashed blue and dash-dotted green lines are the three-body calculations with 0.973 MeV and 1.6MeVtwo-neutron separation energies, respectively. We can see from Fig. 2 that the effect of the coupling to the breakup channel is clearly the flux removal from the forward angles region, reducing the elastic cross section in the region of the Fresnel peak. This behaviour is well reproduced by the three- and fourbody models used here. At large angles, however, we observe that the fall of the angular distribution is less steep than expected by the three-body calculations and it is reproduced only by the four-body calculation. Both threebody calculations fail to reproduce the data in this angular region. The improved three-body model comes closer to the data than the standard three-body, but it is not sufficient to reproduce them. The results of the CDCC calculations presented here are quite stable with respect to variations in the parameters of the optical potentials of n+58Ni and α+58Ni, which, together with the 6He wave function, are the main ingredients to obtain the 6He +58Ni interaction. We performed variations (±10%) in the strengths V and W, the radius and diffuseness of the 16.5MeVn+58Ni optical potential around the values of Table 1 and, the effect in the final three- and four-body calculations was of only a few percent, much smaller than the actual difference between three- and four-body results of Fig. 2. The sensitivity to variations in the α+58Ni potential was found to be even smaller, as expected since the energies are close to the Coulomb barrier. The sensitivity to variations in the V. Morcelle et al. / Physics Letters B 732 (2014) 228–232 231 Fig. 3. (Color online.) TELP and Bare potentials from standard three- and fourbody CDCC calculations for the 6He +58Ni system at an incident energy of Elab = 16.5MeV. number of bins and of angular momenta used in the calculations was also very small, provided that convergence has been reached. In order to better understand the dynamics of the coupling to the breakup channel, it is interesting to look at the characteristics of the polarization potential which comes out from the CDCC calculations. Polarization potentials are in general very complicated non-local quantities but, a trivially local equivalent potential (TELP) can be obtained [32] which displays the main features of the coupling. In Fig. 3 we present, for the incident energy Elab = 16.5 MeV, the TELP potential extracted from the CDCC calculations as a function of the distance Rbetween 6He and 58Ni. The polarization potential from the standard three-body CDCC is shown by the dashed blue line and the four-body by a solid red line. We also plot the 4b-Bare (red dotted) and the sum 4b-Bare+TELP (red dash-dot-dash). One of the main characteristics of the polarization potential from breakup is the long-range absorptive imaginary part in the surface region and outwards. This long-range absorption describes the loss of flux to the combined effect of the nuclear and Coulomb breakup. The real part of the polarization potential, on the other side, is repulsive in the region of the surface of the system (R≈6–7 fm) and it is due to the nuclear breakup. As we see from the total Bare+TELP curves, the effect of the polarization potential is to enhance the Coulomb barrier, reducing the fusion cross section at this energy. Similar qualitative characteristics, such as the long range imaginary and the repulsive real potentials, have been observed in the CDCC polarization potentials in lighter systems [3] and seem to be general features of the polarization potentials derived from CDCC calculations, in the case of neutron halo projectiles. Even in the context of the Optical Model, applied to the analysis of exotic heavy systems such as 6He +120Sn [33] and others [34], the inclusion of a surface absorptive term in the optical potential appears to be a necessary condition to correctly reproduce the energy dependence of the angular distributions. Such an absorptive surface term simulates the dynamics of peripheral reactions, such as breakup and neutron transfers, that are taking place in the region near to the Coulomb barrier. Another important information that one can obtain from the elastic scattering is the total reaction cross section. The total reaction cross sections obtained from the present four-body CDCC calculations are of 1185, 1833, and 2185 mb, respectively for Elab =12.2,16.5,and 21.7 MeV. We transformed these cross sections and energies using the recipe of Gomes et al. [35], to be able to compare them with data for stable weakly bound systems such as 6,7Li and 9Be [36,37] on similar mass targets. We found a consistent enhancement of about 40–50% in the total reaction cross section for 6He+58Ni with respect to the stable weakly bound 6,7Li and 9Be. This result is in agreement with previous results from similar analysis of intermediate mass and heavy systems [14,39, 40]. However, for lighter systems such as 6He +9Be and 6He +12C the enhancements are lower, around 25% [38] or less [20]. 4. Summary and conclusions We measured the 6He +58Ni scattering at three energies slightly above the Coulomb barrier. We performed standard and improved three-body CDCC calculations and the more appropriate four-body CDCC calculations. Both three-body models fail to reproduce the experimental elastic data for the whole angle range. On the other hand, four-body CDCC calculations reproduce very well the experimental data without any parameter adjustment. 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