Understanding the mechanisms of nuclear collisions: A complete study of the 10 B + 120 Sn reaction

PHYSICAL REVIEW C 103, 034616 (2021) Understanding the mechanisms of nuclear collisions: A complete study of the 10B+120Sn reaction L. R. Gasques ,1,*M. A. G. Alvarez ,2A. Arazi ,3B. V. Carlson,4L. C. Chamon ,1J. P. Fernández-García ,2 A. Lépine-Szily ,1J. Lubian ,5J. Rangel,5M. Rodríguez-Gallardo,2,6V. Scarduelli,1and V. A. B. Zagatto5 1Universidade de São Paulo, Instituto de Fisica, Rua do Matao, 1371, 05508-090 São Paulo, São Paulo, Brazil 2Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain 3Laboratorio TANDAR, Comisión Nacional de Energía Atómica, Avenida General Paz 1499, BKNA1650 San Martín, Argentina 4Departamento de Física, Instituto Tecnológico de Aeronáutica, Centro Técnico Aeroespacial, São José dos Campos, São Paulo, Brazil 5Instituto de Física da Universidade Federal Fluminense, 24210-346 Niterói, Rio de Janeiro, Brazil 6Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, Spain (Received 25 November 2020; accepted 8 March 2021; published 22 March 2021) Background: Reactions involving exotic and stable weakly bound nuclei have been extensively studied in recent years. Although several models have been successfully used to explain particular reaction outcomes, the answers to many questions remain elusive. In previous works, we presented elastic, inelastic, and transfer angular distributions for the 10B+120Sn system measured at ELab =31.5, 33.0, 35.0, and 37.5 MeV. The data set was analyzed through coupled reaction channels calculations in the context of the double-folding São Paulo potential. Purpose: We investigate nuclear reaction mechanisms for systems involving weakly bound projectiles. Method: Angular distributions for several nuclear reaction processes were measured for the 10B+120Sn system at ELab =39.70 MeV. Results: The new data set involves angular distributions for elastic scattering, projectile and target inelastic excitations, one-neutron pickup transfer, one-proton stripping transfer, deuteron pickup transfer, and 3,4He stripping transfer. We have also observed 10Be nuclei. The effect of the couplings to some nonelastic states on the angular distributions is discussed. Conclusion: The theoretical calculations within the coupled reaction channels formalism provide an overall good agreement with the corresponding inelastic, one-neutron stripping, one-proton pickup, one-deuteron pickup, and 3He stripping transfer data. However, to improve the description of the elastic scattering angular distribution, the inclusion of additional channels in the coupling scheme might be necessary. DOI: 10.1103/PhysRevC.103.034616 I. INTRODUCTION The production of isotopes far from the valley of stability has paved a new road in science for exploring fundamental aspects of the complex interaction of a quantum many body system involving nuclei with exotic neutron to proton ratios. However, even after many important technical developments, these species are still extremely difficult to produce in the laboratory. In contrast, most of the existing stable nuclei can be produced with standard techniques in copious amounts. Consequently, the investigation of heavy-ion reactions involving weakly bound stable nuclei represents one of the leading research subjects in low energy nuclear physics, and is an important tool to explore the properties of radioactive nuclei. Over many years, a significant number of different nuclear processes have been experimentally determined, revealing valuable information to guide the development of new theoretical models [1–8]. *Corresponding author: [email protected] In previous experimental campaigns carried out at the Institute of Physics of the University of São Paulo (USP), using the 8 MV Pelletron accelerator installed in the Open Laboratory of Nuclear Physics (LAFN, acronym in Portuguese), we have measured angular distributions of elastic scattering, inelastic excitations, and transfer processes at energies spanning the Coulomb barrier for several systems involving weakly bound projectiles [9–11]. The data have been analyzed within the coupled reaction channel (CRC) formalism using the well known double-folding São Paulo potential (SPP) [12] for the nuclear interaction. In particular, we also investigated the 10B+120Sn system at energies below and slightly above the barrier (VB≃35 MeV in the laboratory reference system): ELab =31.5, 33.5, 35, and 37.5 MeV. For this system, besides the CRC, we also performed continuumdiscretized coupled-channels (CDCC) calculations. 10Bis a weakly bound stable nucleus that may breakup into different partitions, the most energetically favorable being 10B→ 6Li +4He (Q=−4.461 MeV). As reported in Ref. [11], the effect of the couplings to the continuum on the elastic scattering cross sections was almost negligible for all those energies. It is worth mentioning that we did not consider the excitation 2469-9985/2021/103(3)/034616(12) 034616-1 ©2021 American Physical Society L. R. GASQUES et al. PHYSICAL REVIEW C 103, 034616 (2021) of the 120Sn target in these CDCC calculations. Recently, we also studied the reaction 10B+197Au. As part of a joint collaboration among research groups from Argentina, Brazil, Costa Rica, and Spain, the experiments were performed at two laboratories: LAFN and TANDAR (Tandem of Argentina), which is equipped with a 20 MV tandem accelerator. Elastic scattering, inelastic excitations, and transfer and fusion processes have been experimentally determined at several energies [13,14], below and well above the Coulomb barrier (VB≃50 MeV), up to ELab =61 MeV. In the present paper, we move forward with the investigation of the 10B+120Sn system, reporting on new measurements at ELab =39.70 MeV. At this energy, which is about 15% above the barrier height, we observed more reaction processes than were detected in the lower energy region [11]. In fact, apart from the elastic scattering channel, several processes were experimentally observed at ELab = 39.70 MeV, such as inelastic excitation of several 10Band 120Sn states, one-neutron (1n) pickup transfer, one-proton (1p) stripping transfer, deuteron pickup transfer, and 3,4He stripping transfer. We have also observed 10Be yields, which may have been produced by two different mechanisms: (i) the direct single-charge exchange (SCE), related to the isovector nucleon-nucleon interaction, and (ii) a two-step process, in which the incident 10Bcan undergo two possible sequential transfer reactions, in which a proton and a neutron are exchanged: 120Sn(10B,11B)119Sn followed by 119Sn(11B,10Be) 120Sb, and 120Sn(10B,9Be) 121Sb followed by 121Sb(9Be,10Be) 120Sb. The paper is organized as follows: details of the experimental setup and data analysis are discussed in Sec. II.The experimental results and theoretical CRC analyses are presented in Sec. III. A summary of the paper and the main conclusions are presented in Sec. IV. II. EXPERIMENTAL SETUP AND DATA ANALYSIS The experiment was carried out at the 30B scattering chamber of LAFN of USP, São Paulo, Brazil,which is equipped with an 8 MV tandem accelerator. The incident beam was produced by extracting atomic ions from an enriched 10Bisotope cathode mounted in a 32-position MC-SNICS ion source. After passing throughout the tank, the post-accelerated beam interacted with a 120Sn target with thickness of about 300 μg/cm2, evaporated on to 15 μg/cm2 carbon backing. For normalization, a thin layer of 197Au (≈50 μg/cm2) was evaporated over the 120Sn film. Taking into account the average energy loss of the 10Bincident particles in the middle of the target, the angular distributions were obtained at ELab ≈39.70 MeV. As depicted in Fig. 1, our detection system is composed of two different particle detector arrays: SATURN (Silicon Array & Telescopes of USP for Nuclear Reactions and Nuclear Applications) and STAR (Silicon Telescopes Array for low statistics nuclear Reactions). These arrays can be mounted in different configurations according to the necessity of each experiment. In the measurements presented in this paper, the SATURN array comprised a set of nine single semiconductor silicon surface barrier detectors mounted at the backward hemisphere, FIG. 1. Internal view of the scattering chamber at the 30B beam line of LAFN. giving information about the kinetic energy of the particles. For normalization of the cross sections, other two surface barrier detectors were mounted at 50◦and 60◦.Atsuchforward angles, the elastic scattering cross sections are the same as the Rutherford ones for both systems: 10B+120Sn and 10B+197Au. A typical spectrum obtained with a single detector mounted at θLab =170◦in the SATURN array is shown in Fig. 2. Several peaks are identified and labeled in the figure using different colors (see the figure caption). In the present experiment, the STAR array was mounted with only one (E,E) telescope, covering an angular range of about 40◦. The first detection stage (E) was formed by a20μm thick single sided silicon strip detector (SSSSD) with 16 strips. The second detector, with thickness of about 1000 μm(Er), was coupled to the Edetector. Both detectors were manufactured by Micron Semiconductor. Particle identification was performed based on the energy loss measurements of Eand residual energy Er. FIG. 2. Single-channel spectrum taken with a detector at θLab = 170◦mounted in the SATURN array. The arrows indicate the expected positions of peaks related to the elastic scattering of 10B on 120Sn target (black arrow), inelastic excitation of the 1+10B first excited state at 718.4 keV (purple), and excitation of the 2+(1173.3 keV) and 3−(2400.3 keV) 120Sn states (red). The peaks corresponding to different states of the 1npickup transfer 120Sn(10B,11B)119Sn are indicated by green arrows. 034616-2 UNDERSTANDING THE MECHANISMS OF NUCLEAR … PHYSICAL REVIEW C 103, 034616 (2021) FIG. 3. (E,ET) spectrum taken with the STAR array at θLab = 128.6◦. The dashed lines correspond to theoretical calculations of energy loss in the Edetector for several identified nuclei produced during the collision of 10Bon the target composed of 120Sn and 197Au. The rectangular area contains events of 11B(from neutron transfer) and 10B(from inelastic scattering to states with high excitation energies). Figure 3presents a typical two-dimensional (E,ET) spectrum obtained at θLab =128.6◦, where ET=E+Er. Taking into account the energy loss of the different particles traversing the Edetector, it was possible to identify each nucleus located in the respective bands. The dashed lines in the figure represent theoretical calculations for the energy loss in the Edetector as a function of the total energy ETof different nuclei. In the Z=5 band, the regions containing the highest counting rates correspond to the 10B elastically scattered on 120Sn and 197Au. Events corresponding to the inelastic scattering of 10B+120Sn and 10B+197Au can also be observed in the same band. They lie in the left side of the corresponding elastic scattering spots. The 11B yields, arising from the 1npickup transfer reactions with 120Sn and 197Au, can also be observed in the spectrum. The 120Sn(10B,11B)119Sn and 197Au(10B,11B)196Au reactions have, respectively, positive Qvalues of about 2.35 and 3.38 MeV for their ground states (g.s.). Therefore, some 11B events can be found on the right side (higher energies) of the elastic scattering, but the detected 11Bextend up to a region of high excitation energies (with boundaries represented through solid lines in the figure). Different regions, corresponding to Z=2, 3, 4, 5, and 6, are clearly observed in Fig. 3. Considering that 10Bcan be described as a cluster of 6Li +4He, the yields of both nuclei arising from the breakup channel should be quite similar. However, an inspection at the Z=2 and 3 regions of Fig. 3 shows that 4He are produced in excess, as compared with 6Li. A possible explanation lies on the fact that 4He nuclei are produced in copious amounts through the fusion of 10B projectiles impinging on 12Cpresent in the target. The incident energy (ELab =39.70 MeV) is much higher than the Coulomb barrier for the 10B+12Creaction. Another possible explanation for the excess of alpha particles would be the Mass 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 Count 0 5 10 15 20 25 30 Li 6 Li 7 FIG. 4. Number of events related to the lithium isotopes projected on the mass axis, obtained from the (E,ET) spectrum of Fig. 3using the method described in Ref. [15]. breakup of 6Li into an alpha and deuteron after the breakup of 10B. Nevertheless, this is a second step process and might be not very relevant at this bombarding energy. Also, other breakup or transfer reaction channels with positive Qvalues may produce alpha particles as well. As is well known, the mass separation between different isotopes is rather difficult in (E,ET) spectra, since the dependence of the energy loss of the particles on the mass m is weaker than the dependence on Z. Aiming to improve the resolution of the mass separation among particles with the same Z, a method of data processing described in Ref. [15] has been applied here. The main attribute of the method consists of the linearization of the data on the maxis using theoretical calculations of energy loss of the particles. In this paper, the masses of the nuclei are given in atomic mass units (amu). As can be observed in Fig. 4, a good separation of 6Li and 7Li has been achieved in our experiment. A fit of the 6Li (7Li) events considering a Gaussian shape results in peak positions at 6.12 ±0.06 (6.90 ±0.09), which are compatible with m=6(m=7). In fact, these small deviations of the peaks related to the mass are expected, since the method of Ref. [15] is based on the energy loss calculated for the average mass (in this case, m=6.5). Figure 5presents the projection of the 9Be and 10Be events on the maxis. Clearly, the mass resolution of the peaks becomes gradually worse as the Zof the particles increases. Even so, the separation of 9Be from 10Be is still quite good. In the case of the Z=5 band, the very intense peak of the 10Belastic scattering becomes impracticable to separate from the quite small yields of events relative to 11Bdetected with energies around those of the elastically scattered 10B.Even so, it is possible to distinguish 11Band 10Bin other energy regions far from the elastic scattering. Figure 6presents the projection on the mass axis of boron events restricted to the (E,ET) region with boundaries shown by the rectangular area in Fig. 3. 034616-3 L. R. GASQUES et al. PHYSICAL REVIEW C 103, 034616 (2021) Mass 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2 Count 0 10 20 30 40 50 60 70 80 90 Be 9 Be 10 FIG. 5. The same as Fig. 4, for the beryllium isotopes. III. EXPERIMENTAL AND THEORETICAL RESULTS Experimental elastic scattering angular distributions were obtained using both SATURN and STAR arrays. Concerning inelastic excitation, yields corresponding to the 1+ 1(E∗= 0.72 MeV) 10Bquadrupole state, and to the 2+ 1(1.17 MeV) quadrupole and the 3− 1(2.40 MeV) octupole 120Sn vibrational states have been experimentally determined. In addition, events still corresponding to 10Bwere detected with the STAR array in a relatively broad region of higher excitation energies (2.5⩽E∗⩽4.5 MeV). The experimental cross section for these events is related to the excitation of the projectile and/or target. Differential cross sections for the 1npickup, 1pstripping, and deuteron pickup transfer were determined through the corresponding yields observed in the spectra. Cross sections related to the production of 6Li, 7Li, and 10Be, that can be FIG. 6. Number of events related to the boron isotopes projected on the mass axis, obtained for events inside the (E,ET) region delimited by solid lines in Fig. 3. associated to breakup processes, were also determined in the experiment. CRC calculations were carried out assuming the SPP for the real part of the nuclear interaction [12]. We adopted a phenomenological Woods-Saxon (WS) parametrization for the imaginary part of the optical potential. Since several peripheral channels were explicitly considered in the coupling scheme, the parameters adopted for the imaginary potential, W0=80 MeV, ri0=0.8 fm, and ai=0.30 fm, were set to account only for the absorption of flux following barrier penetration, resulting in negligible strength in the surface region. In this condition, the theoretical cross sections are insensitive to reasonable variations of the imaginary potential parameter values. The CRC calculations were performed using the FRESCO code [16]. In the coupling scheme, we have included the first 1+ 1excited state of 10B, and the 120Sn vibrational states corresponding to the 2+ 1quadrupole and the 3− 1octupole. Since the 10Bprojectile is highly deformed, we have adopted the same procedure as described in Ref. [10], where the 10Bwas considered as a rotor and as a vibrator. As will be shown in the paper, although the global theoretical results are similar, the assumption of a rotational quadrupole state for 10Bprovides a slightly better description of the elastic and inelastic experimental data. As 10Bhas a 3+g.s., we have also investigated the effect of considering a real spin-orbit (s.o.) term in the central part of the optical potential. We have adopted the same parameter values applied in the case of the 10B+197Au system [14]: V0=6MeV,r0=1.06 fm, and a=0.6fm. As already commented, yields related to the inelastic excitation of nearby populated states of the projectile and target in the excitation energy region of 2.5⩽E∗⩽4.5 MeV have been experimentally observed. A realistic calculation treating explicitly all the many excited states present in this energy range is certainly impracticable. Therefore, in the CRC calculations, we adopted a schematic representation to simulate the effect of these states, which just assumes the coupling to a single 120Sn level at E∗=3.5 MeV. The values of spin and deformation of such a state have been varied in order to describe the experimental cross sections. In addition to the inelastic states, we have also considered the couplings to five states related to the 1npickup transfer, 120Sn(10B,11B)119Sn, corresponding to the g.s. and a few excited states of the 119Sn, and two states related to the 1p stripping transfer 120Sn(10B,9Be) 121Sb. With the purpose of simulating the effect of a large number of states, the procedure of assuming the coupling to only one state, with coupling parameter values adjusted to fit the data, was also adopted in the case of some transfer channels, as described herein. A. Elastic and inelastic angular distributions The experimental elastic scattering angular distribution measured at ELab =39.70 MeV is presented in Fig. 7.As adopted in several other figures, the black circles and green squares represent cross sections obtained with the SATURN array and STAR telescope, respectively. In panel (a) of Fig. 7, it is possible to observe the results of the full (including all inelastic and transfer couplings) CRC calculations, which 034616-4 UNDERSTANDING THE MECHANISMS OF NUCLEAR … PHYSICAL REVIEW C 103, 034616 (2021) 30 60 90 120 150 180 θc.m. (degree) 10-2 10-1 100 σel / σRuth no couplings Nr = 1.0 Nr = 0.88 10-2 10-1 100 σel / σRuth STAR SATURN vibrational without s.o. rotational without s.o. rotational with s.o. (a) (b) FIG. 7. Experimental cross sections for the elastic scattering of 10B+120Sn at 39.70 MeV bombarding energy. Theoretical results are represented by different lines (see text for details). have been obtained by (i) considering the 10Bnucleus to be a rotor with no s.o. potential (solid blue curve), or (ii) assuming the vibrational model for the 10Bnucleus and no s.o. potential (dashed-dotted red curve). Both assumptions result in similar elastic scattering cross sections, although the rotational model provides marginally better agreement with the data. Actually, the reduced chi-square value obtained with the rotational model is 98, whereas the vibrational model gives a value of 214. These somewhat large numbers are due to the quite small uncertainties of the elastic scattering data, which vary from 1% to 3%. In addition, a dashed black line is also shown in panel (a) of Fig. 7. This curve was obtained by considering the s.o. potential and the rotational model for 10Bin the CRC calculations. A comparison of the blue and black curves clearly shows that the effect of the s.o. interaction on the elastic scattering angular distribution is quite small. In any case, it is possible to assert that while the addition of the s.o. term slightly improves the agreement with the data in a region of intermediate scattering angles, it results in a slightly worse description of the data for θc.m.150◦. In order to verify the effect of the couplings on the elastic channel, the theoretical cross sections obtained with the single channel optical model (no couplings) are represented in panel (b) of Fig. 7by the dotted orange line. As can be observed, although the effect of the couplings on the elastic channel is strong, the cross sections obtained with the full CRC calculations (solid blue curve) slightly underpredict the data. This discrepancy, which becomes more relevant as the scattering angle increases, could be related to possible couplings not included in our CRC calculations. It is possible to improve the description of the data by considering a renormalization of the nuclear interaction. In order to obtain a good data fit it is necessary to multiply the real part of the SPP by a factor 0.88 [see the dashed cyan line in panel (b) of Fig. 7]. On the other hand, the discrepancy commented above could be related with couplings not included in our CRC calculations. This possibility is discussed in Sec. IV. In the case of the inelastic transitions, we have considered the reduced electromagnetic transition probability: B(Eλ, Ji→Jf)=1 2Ji+1|Jf||Eλ||Ji|,(1) where λis the multipolarity of the excitation, Jfand Jiare, respectively, the spins of the final and initial states associated with the transition matrix element for the Eλoperator. According to Refs. [17,18], we have determined the nuclear deformation δλvalue from the respective Coulomb transition probability, considering the effect of the finite diffuseness value of the nuclear density. The B(Eλ)↑values were adjusted to fit the inelastic scattering data. To ensure a satisfactory description of the experimental inelastic scattering angular distributions, we had to assume slightly different values for the B(E2) and B(E3) deformation parameters of 120Sn, while treating 10Bas a rotor or as a vibrator. Since the 10Bis strongly deformed, its inelastic coupling affects the cross sections of the other channels through the coupled-channels formalism. Particularly for the case in which 10Bisassumedtobearotor,wehavealso investigated the effect of considering a s.o. term in the central potential. To obtain a satisfactory description of the inelastic data, a further readjustment of the B(E2) and B(E3) 120Sn deformation parameters was required. The spin of the inelastic states considered in the coupling scheme, along with the corresponding transition mode, excitation energy, Coulomb transition probability and deformation length are given in Table I. The values obtained here for the B(E2,0+→2+)of120Sn and the B(E2,3+→1+)of10Bare consistent with the respective values that we presented earlier in Ref. [10]. For the excitation of the 120Sn 3−state, the E3 octupole transition values available in the literature show large discrepancies and large uncertainties. In the present work, in order to describe the experimental data, we found a B(E3) value which is lower than the average of values given in the literature [19–23]. The inelastic scattering angular distributions are presented in Fig. 8. Again the solid blue and dashed-dotted red lines represent, respectively, the CRC results obtained by assuming the rotational or vibrational model for 10B, without a s.o. potential. The dashed black line corresponds to CRC calculations when the s.o. term is considered in the central potential. In this case, the 10Bhas been treated as a rotor. Panel (c) of Fig. 8presents the inelastic scattering angular distribution associated with the relatively broad energy range of excitations of the projectile and target (2.5⩽E∗⩽4.5 MeV). As already mentioned, the corresponding theoretical cross sections were obtained within a simplified coupling scheme, in which a single 120Sn state with E∗=3.5 MeV was adopted to simulate the effect of all possible nearby populated excited states of the projectile and target. The corresponding coupling parameters are also presented in Table I, and resulted in a satisfactory description of the data [see panel (c) of Fig. 8]. Although it is clear that the total angle integrated inelastic cross sections 034616-5 L. R. GASQUES et al. PHYSICAL REVIEW C 103, 034616 (2021) TABLE I. Spin, excitation energies (MeV), transition amplitudes from the g.s. to the excited states (10−3e2bλ), and deformation lengths (fm), for the inelastic states included in the CRC calculations. The values given in the fifth and sixth columns are for the situation in which 10B is treated as a rotor, without the s.o. term in the central potential. The seventh and eighth columns were obtained in the rotational case, but this time including the s.o. The ninth and tenth correspond to the case in which 10Bis considered as a vibrator, without the s.o. potential. B(Eλ)↑δλB(Eλ)↑δλB(Eλ)↑δλ Nuclues Spin E∗λrotor, no s.o. rotor, with s.o. vibrator, no s.o. 10B1+0.72 2 0.35 0.95 0.31 0.85 0.35 0.95 120Sn 2+1.17 2 230 0.68 194 0.62 250 0.71 120Sn 3−2.40 3 58 0.62 48 0.56 68 0.67 120Sn 2+3.50 2 230 0.68 202 0.64 260 0.72 depend on the adopted model, the overall fit to the data is quite good in all the considered cases. Similar behavior also occurs in the cases of the transfer channels. Therefore, from now on we will present the CRC cross sections obtained assuming only the model in which 10Bis a rotor, without the inclusion of the s.o. potential. B. Transfer processes The transfer processes in heavy-ion experiments are generally highly selective as the description of their corresponding cross sections is governed by the kinematic conditions of the reactions. Part of this feature can be understood in terms of the Qvalue of the reaction, which is often compared to another quantity called the optimum Qvalue, Qopt, obtained from the matching conditions of the semiclassical trajectory [24]: Qopt =Ec.m.Zf PZf T Zi PZi T −1.(2) 100 120 140 160 θc.m. (degree) 0 0.2 0.4 0.6 0.8 1 0 1 2 3 dσ/dΩ (mb/sr) vibrational rotational rotational + s.o. 100 120 140 160 θc.m. (degree) 0 0.2 0.4 0.6 0.8 1 dσ/dΩ (mb/sr) 0.5 1 1.5 SATURN STAR 120Sn (2+)120Sn (3-) )b()a( )d()c( 10B (1+) FIG. 8. Inelastic scattering angular distributions for the (a) 2+ quadrupole and (b) 3−octupole 120Sn states. The cross sections corresponding to the inelastic states in the energy region of 2.5⩽ E∗⩽4.5 MeV are presented in panel (c). The inelastic scattering angular distribution for the 1+10Bstate is given in panel (d). The lines represent the theoretical results of the CRC calculations (see text for details). In Eq. (2), Ec.m.is the center-of-mass energy and Zf P,Zf T,Zi P,Zi Tare the atomic numbers of the nuclei in the final and initial partitions, respectively. Often, the value of Qopt is used to give an estimation of the energy region where the transfer cross section is expected to be largest. Table II shows the Qopt and Qgs values for some transfer processes, where Qgs is the Qvalue for the transfer to the g.s. of the final products. For the cases where Qgs is larger than Qopt, the transfer would preferentially populate states of the final nuclei with excitation energies around E∗ Theo =Qgs −Qopt. In contrast, if Qgs <Qopt, the transfer would populate states close to the g.s., i.e., E∗ Theo =0, and it could be rather inhibited. Table II also presents the values of E∗ Theo and E∗ Exp, where E∗ Exp is the average excitation energy related to the respective transfer process obtained from our experimental spectra. Due to the presence of the intense neighbor peak of elastic scattering, it was not possible to determine E∗ Exp for the neutron transfer. Indeed, events related to this channel were observed in a wide region of excitation energy, starting from the g.s. (see Fig. 3). In the CRC calculations, a WS shape with parameter values presented in Table III was assumed for the particle-core potentials of the transfer reactions. These parameters were adjusted to reproduce the SPP results at the surface region. 1. One-neutron transfer The experimental angular distributions for 1npickup were obtained from the yields of three groups related to different states of the residual nuclei. The first group includes the g.s. and the first three 119Sn excited states. The second group contains many states in the range of excitation energy varying from E∗=0.80 MeV to E∗=2.10 MeV. Detected 11Bnuclei TABLE II. Qgs ,Qopt,E∗ Theo,andE∗ Exp values for some transfer processes in the 10B+120Sn reaction. The quantities are provided in units of MeV. Exit channel Qgs Qopt E∗ Theo E∗ Exp 11B+119Sn 2.35 0 2.35 12C+118In 8.18 6.47 1.7 4.1 11C+119In −2.00 6.47 0 10Be +120Sb −3.24 5.5 9Be +121Sb −0.80 −6.77 6.0 7.1 7Li +123Te −4.78 −13.83 9.0 12.2 6Li +124Te −2.61 −13.83 11.2 12.4 034616-6 UNDERSTANDING THE MECHANISMS OF NUCLEAR … PHYSICAL REVIEW C 103, 034616 (2021) TABLE III. Parameter values of the WS potentials assumed for the cluster-core systems in the CRC transfer calculations. The V0 values presented in the table provide the right results for the binding energy when the compound system is in its ground state. Composite V0R0a system (MeV) (fm) (fm) n+10B46.4 3.00 0.61 n+119Sn 48.7 6.16 0.65 p+9Be 41.8 3.00 0.61 p+120Sn 131 6.16 0.65 d+10B41.8 3.00 0.75 d+118In 43.4 6.30 0.70 3He +7Li 136 2.90 0.62 3He +120Sn 31.2 6.30 0.66 related to these two groups have energies higher than that corresponding to the elastically scattered 10Band, therefore, the corresponding yields can be easily and accurately obtained from both single and (E,ET) spectra. The third group also contains many states, but this time in a higher region of excitation energies: 3.4⩽E∗⩽9.2 MeV. In this case, the data could be obtained only from the (E,ET) spectra. The depths of the WS potentials presented in Table III were adjusted to reproduce the experimental separation energies for one neutron in 10B(Sn=8.44 MeV) and 119Sn (Sn=6.17 MeV). The corresponding values of V0adjusted for the g.s. of (n+10B) and (n+119Sn) are given in Table III. Similar V0values were obtained for the excited states. The spectroscopic factors (C2Sj) associated with the g.s. transition and with the first three excited states of 119Sn are given in Table IV. We emphasize that these values were obtained in data fits performed in our earlier work at lower bombarding energies [10]. Panel (a) of Fig. 9presents experimental and theoretical CRC cross sections for 1ntransfer relative to the first group of states as described above. As can be observed, the description of the data is quite satisfactory. Concerning the CRC calculations associated with the yields observed in the second group of 1ntransfer, 0.80 ⩽ E∗⩽2.10 MeV, we have assumed a single state to represent all the nearby populated states in 119Sn. Within this simplified approach, we have varied the spin, excitation energy, and spectroscopy factor values associated with the coupled state in order to fit the experimental data. As shown in panel (b) of Fig. 9, with n=2, =2, J=5/2+,E∗=1.5MeV and C2Sj=10.2 we obtained an adequate fit to the data. TABLE IV. Level structure of 119Sn along with the spectroscopic factors for the overlap 120Sn |119Sn +n. E∗State (keV) (nj) Parity C2Sj 0.0 3s1/2(+) 0.58 23.8 2d3/2(+) 1.66 89.5 1h11/2(−) 3.35 787.0 1g7/2(+) 5.15 10-1 100 101 dσ/dΩ (mb/sr) 10-1 100 101 dσ/dΩ (mb/sr) STAR rotational 80 100 120 140 160 180 θc.m. (degree) 10-2 10-1 100 dσ/dΩ (mb/sr) 11B 0 < E* < 0.8 MeV 0.8 < E* < 2.1 MeV 3.4 < E* < 9.2 MeV (a) (b) (c) FIG. 9. Experimental cross sections for the 1ntransfer channel obtained from the yields associated with the three groups of states in different excitation energy regions of the residual nuclei. The curves represent the results of the CRC calculations (see text for details). A similar procedure was performed in the case of the third group, 3.4⩽E∗⩽9.2 MeV. The respective theoretical results shown in panel (c) of Fig. 9were obtained with n=2, =3, J=5/2−,E∗=6.0 MeV, and C2Sj=9.61. In the cases of groups two and three of 1ntransfer, there are other possible sets of spin, excitation energy and spectroscopy factor values that provide equally good agreement between data and theory. However, the shape of each theoretical distribution over the entire angular region depends on the choice of these parameters. Therefore, the total (angle integrated) transfer cross section may vary significantly from one choice to another. Our experiment was not particularly optimized for measuring angular distributions for one-nucleon transfer. The STAR telescope was fixed during the experiment and, therefore, the available data only cover a narrow region located at backward angles. Since the transfer angular distributions are peaked in the vicinity of the grazing angle, the theoretical cross sections are much higher around θ=80◦. This is the reason why our measurements did not determine the total transfer cross sections. We emphasize, however, that, as long as the experimental cross sections for the transfer process are well described by the CRC calculations, the effect of this coupling on the elastic scattering angular distribution (and other channels) is negligible, regardless of the choice of the aforementioned parameters. 2. One-proton transfer and 10B→1H+9Be breakup Figure 3shows that 9Be nuclei have been observed in the (E,ET) spectra. In Fig. 10, we present the projection of these events on the ETaxis, i.e., the figure represents the number of 9Be events as a function of the total energy of the detected particle. The E∗ Theo ≈6MeVfor1pstripping transfer 034616-7 L. R. GASQUES et al. PHYSICAL REVIEW C 103, 034616 (2021) ET (MeV) Count 20 22 24 26 28 30 0 4 8 12 16 20 24 transfer transfer + breakup FIG. 10. Energy projection of 9Be nuclei detected at θLab = 128.6◦with the STAR telescope. The vertical dashed red line separates the regions associated with the breakup and 1ptransfer processes. presented in Table II is in reasonable accordance with the region of highest 9Be yields of Fig. 10:ET(highest yields) ≈ 24 MeV ⇒ E∗ Exp ≈7 MeV (the conversion of ETto E∗was performed through the kinematics of the one-proton transfer process). The 1pstripping transfer populating several excited states of the residual nucleus 121Sb has also been reported in Ref. [3]forthe7Li +120Sn system. In the present case, we associate these yields with two different reaction processes. Part of the detected 9Be in fact must be associated with the 1pstripping transfer: 10B+120Sn →9Be +121Sb. Another fraction should be related to the breakup of 10Binto the fragments 1H+9Be: 10B+120Sn →9Be +1H+120Sn. To support this statement, it is necessary to introduce arguments related to the energy and kinematics of the detected particles. After calibrating the spectra, it was possible to infer that the detected energies of the 9Be nuclei (for instance, from ET≈19 MeV to ET≈29 MeV in Fig. 10) are associated (from kinematics) with an excitation energy region of 1.0⩽E∗⩽12.5 MeV. Therefore, the nuclei in the final partition of the one-proton transfer process, 9Be, 121Sb, or both nuclei, could be found in their excited states, which eventually decay by emitting γrays. On the other hand, the threshold of the binding energy of the 121Sb nucleus (121Sb →p+120Sn) is 5.8 MeV, preventing the occurrence of the breakup process at energies lower than this value. For energies higher than this threshold (indicated by the dashed red line in Fig. 10), the proton can also be transferred to the continuum. In order to account for the effect of these processes on the elastic channel, we again adopted the simplified approach that considers a proton transfer to a single 121Sb level, with excitation energy lower than the binding energy of 1H+120Sn. The corresponding 1ptransfer cross sections obtained within the CRC model are represented by the solid blue line in Fig. 11. We supposed a state with excitation energy of 5.5 MeV for the 121Sb nucleus, with spin J=1/2+,n=3, and =0. In these conditions, we verified that C2Sj=3.24 gives a satisfactory description of the data (which represent the total yield of 9Be detected). As for the 1ntransfer, we have considered a WS 80 100 120 140 160 θc.m. (degree) 10-1 100 101 dσ/dΩ (mb/sr) STAR rotational 9Be FIG. 11. Experimental angular distribution related to the observed 9Be nuclei. The curve was obtained assuming a schematic CRC calculation of 1ptransfer (see text for details). shape for the proton-core potentials. The parameter values of the WS potentials are given in Table III. As a result of our simulations, we point out that the inclusion of the 1ptransfer channel in the coupling scheme also has a negligible effect on the theoretical elastic scattering cross sections. 3. Other detected transfer and breakup processes As shown in Fig. 3, yields of 12Cwere produced with relatively low statistics from the deuteron pickup transfer reaction 120Sn(10B,12C)118In. The corresponding experimental cross sections are shown in Fig. 12. A meticulous inspection at Fig. 3suggests that some 11Cnuclei, coming from the proton pickup transfer reaction, could also be present in the Z=6 band. However, the contribution of 11Con the total cross section is likely to be very small since this process is hindered by Qopt considerations (see Table II). The difficulty in separating both nuclei in the mass range of carbon isotopes, associated with the low statistics observed in the spectra, imposes an important experimental challenge. Therefore, the 80 100 120 140 160 θc.m. (degree) 10-2 10-1 dσ/dΩ (mb/sr) STAR rotational 12C FIG. 12. Experimental angular distribution of 12Cnucleus coming from the deuteron pickup transfer reaction. The curve was obtained assuming a schematic CRC calculation of 1dtransfer (see text for details). 034616-8 UNDERSTANDING THE MECHANISMS OF NUCLEAR … PHYSICAL REVIEW C 103, 034616 (2021) 80 100 120 140 160 θc.m. (degree) 0.00 0.05 0.10 dσ/dΩ (mb/sr) STAR 0.00 0.05 0.10 0.15 0.20 dσ/dΩ (mb/sr) 6Li 7Li (a) (b) FIG. 13. Panels (a) and (b) present the experimental angular distributions of 6Li and 7Li, respectively. The curve presented in panel (b) was obtained assuming a schematic CRC calculation for the 3He transfer. A calculation for the 4He transfer process was not performed in this work (see text for details). corresponding experimental 12Ccross sections might have been slightly overestimated. We have again used a simplified coupling scheme for this channel, considering the transfer of the deuteron as a cluster through only one state of the 121Sb nucleus. The respective CRC cross sections are shown in Fig. 12 by the solid blue curve. As can be observed in the figure, assuming a single state for the 121Sb nucleus, with an excitation energy of 3.5 MeV, J=5+,n=4, =4, and C2Sj=4.41, we obtained a satisfactory description of the data. The somewhat large value of the spectroscopic factor is acceptable since we are simulating the contribution of a large number of states through a single 121Sb state. The WS parameters assumed for the deuteron-core potentials are given in Table III.This coupling also does not provide a significant contribution to the theoretical elastic scattering cross sections. Projectile-like fragments with Z=3 are clearly observed in the two-dimensional (E,ET) spectrum. 6Li has been formed by 4He transfer to unbound states lying in the continuum (breakup), since the threshold energy of the 4He +120Sn bound system is only 1.852 MeV. In fact, the detected energies of 6Li result, through kinematics, in a region of excitation energy of 8.2⩽E∗⩽22 MeV, with E∗ Exp =12.4 MeV (see Table II). The corresponding experimental cross sections for this process are shown in panel (a) of Fig. 13. The possibility of performing cross section calculations for the αtransfer to highly excited unbound states of the final nuclei will not be addressed in this paper. 120 130 140 150 160 170 θc.m. (degree) 10-2 10-1 100 dσ/dΩ (mb/sr) 10Be 11B FIG. 14. Experimental angular distribution of 10Be production (green squares). For comparison, the 11Bangular distribution is also shown in the figure. For the 3He stripping transfer process, 120Sn(10B,7Li) 123Te, the region of detected 7Li events indicates a respective excitation energy region of 8.0⩽E∗⩽18.0 MeV. As the binding energy for the 3He +120Sn system is 13.0 MeV, a fraction of the transfer cross sections is related to the population of unbound states in the continuum. The data shown in panel (b) of Fig. 13 correspond to the experimental 3He stripping transfer reaction cross sections. Once more, we have adopted a schematic model to simulate the effect of a large number of excited states of the 7Li and 123Te nuclei. The solid blue line in the figure was obtained considering a single state 3d5/2of 123Te, with E∗=9.2 MeV and C2Sj=19.4. Again, the high value of this spectroscopic factor is due to the large number of states being represented by this single one. As can be observed, the fit of the data is satisfactory. Table III presents the parameter values of the WS potentials assumed for the 3He-core partitions. Most importantly, the effect of this particular coupling on the elastic scattering angular distribution is insignificant. Figure 5shows the observed 10Be yields projected on the mass axis obtained using the method described in Ref. [15]. The formation of 10Be nuclei might be associated with the direct SCE, in which the interaction of protons and neutrons can be described in terms of meson exchange. For instance, a proton can become a neutron by emitting a π+meson. In addition, the observed 10Be can also be related to a two-step transfer process, where a sequential proton pickup followed by a neutron stripping (or vice versa) takes place. Such mechanisms show a strong correlation with the total kinetic energy available in the center-of-mass system [25,26]. At the bombarding energy of the experiment discussed in this paper, it is expected that the contribution of the direct SCE process is significantly smaller than the neutron-proton sequential transfer reaction. The experimental angular distribution obtained for the observed 10Be is presented in Fig. 14. Since it is a two-step process, and the information about the spectroscopic factors of 120Sb is very limited, we do not calculate 034616-9