Evidence of the effect of strong stripping channels on the dynamics of the 8 Li + 58Ni reaction

PHYSICAL REVIEW C 103, 064601 (2021) Evidence of the effect of strong stripping channels on the dynamics of the 8Li +58Ni reaction O. C. B. Santos ,*R. Lichtenthäler ,†K. C. C. Pires , U. Umbelino ,E.O.N.Zevallos ,A.L.deLara , A. S. Serra , V. Scarduelli , J. Alcántara-Núñez , V. Guimarães , A. Lépine-Szily , and J. C. Zamora Departamento de Física Nuclear, Instituto de Física, Universidade de São Paulo, 05508-090 São Paulo, Brazil A. M. Moro Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain and Instituto Interuniversitario Carlos I de Física Teórica y Computacional (iC1), Apartado 1065, E-41080 Sevilla, Spain S. Appannababu Department of Nuclear Physics, Andhra University, Visakhapatnam 530 003, India M. Assunção Departamento de Física, Universidade Federal de São Paulo, UNIFESP, 09913-030 Diadema, Brazil A. Barioni Departamento de Ciências do Mar, Universidade Federal de São Paulo, UNIFESP, 11070-100 São Paulo, Brazil R. Linares ,V.A.B.Zagatto , and P. N. de Faria Departamento de Física, Universidade Federal Fluminense do Rio de Janeiro, 24210-340 Rio de Janeiro, Brazil M. C. Morais INFES, Universidade Federal Fluminense, Santo Antônio de Pádua, 28470-000 Rio de Janeiro, Brazil V. Morcelle Universidade Federal Rural do Rio de Janeiro, Seropédica, 23890-000 Rio de Janeiro, Brazil J. M. B. Shorto Instituto de Pesquisas Energéticas e Nucleares, IPEN-CNEN/SP, 05508-000 São Paulo, Brazil Jin Lei Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy (Received 30 December 2020; revised 4 March 2021; accepted 6 May 2021; published 1 June 2021) The 8Li +58Ni collision is investigated at 23.9, 26.1, 28.7, and 30 MeV bombarding energies. Quasielastic angular distributions and the singles 7Li angular and energy distributions are presented. Coupled-reaction channels (CRC) calculations, which include the coupling of the elastic channel to 59Ni =58Ni +nstates above and below the neutron threshold, provide a simultaneous description of the quasielastic and transfer distributions and evidence the strong effect of the one-neutron transfer/breakup channels on the quasielastic scattering. The 7Li angular and energy distributions have been also successfully analyzed combining the continuum discretized coupled channels (CDCC) method, for the elastic breakup, and the IAV model of Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)], for the nonelastic breakup. These calculations indicate that most of the 7Li yields are due to nonelastic breakup contributions (transfer), whereas elastic breakup plays a minor role. DOI: 10.1103/PhysRevC.103.064601 I. INTRODUCTION Experiments with nuclei outside the valley of stability have been performed in several laboratories all over the world in *osv[email protected] †[email protected] recent decades. Interesting new phenomena have been observed related to the structure of the so-called exotic nuclei, in particular, in the light mass region where features such as cluster structure and neutron/proton halos are present. Clustering is a common property of light nuclei, such as helium, lithium, beryllium, and boron isotopes, and stems from their low binding energies and large spectroscopic factors for certain configurations [1]. In particular, the lithium 2469-9985/2021/103(6)/064601(10) 064601-1 ©2021 American Physical Society O. C. B. SANTOS et al. PHYSICAL REVIEW C 103, 064601 (2021) isotope chain has five known bound isotopes: 6–9,11Li. 6,7Li are stable with separation energies of 1.47 and 2.47 MeV to break up into α+dand α+trespectively, with ground state spectroscopic factors ranging from 0.85 to 1. Such small binding energies contrast with the separation energies for stable nuclei, which are in the range of 7–10 MeV. 11Li is a very exotic nucleus with a pronounced neutron halo [2–4]formed by the two valence neutrons weakly bound to the 9Li core; S2n=0.369 MeV. In addition to its low separation energy, the low angular momenta of the valence neutrons make their wave functions extend to large distances from the nuclear core, forming a nuclear halo. 6He (S2n=0.973 MeV) and 8B(Sp= 0.138 MeV) are other examples of exotic nuclei in this mass region which present neutron and proton halos, respectively. Although weakly bound, 8Li is not so exotic, with a separation energy of 2.03 MeV to dissociate into n+7Li [5–13]. Due to the projectile’s low binding energy and cluster structure, many reaction channels are open in the collisions between these near drip-line nuclei and stable target nuclei. At intermediate and high bombarding energies (from 20 MeV/nucleon up to 1 GeV/nucleon) projectile breakup appears as a dominant reaction mechanism and there is a vast amount of literature emphasizing the importance of breakup reactions in collisions induced by exotic nuclei [2–4,14]. In the low-energy domain (⩽10 MeV/nucleon), the projectile cluster and halo structure manifests as an enhancement in the total reaction cross section and a strong coupling between different reaction channels [15–24]. The identification of the reaction channels that effectively contribute to the total reaction cross section enhancement is still a challenge for both theory and experiment. For stable nuclei, fusion is the most important nonelastic process in terms of cross section, followed by inelastic scattering and particle transfer channels to bound states with lower cross sections. In the case of weakly bound exotic projectiles, breakup (noncapture breakup, incomplete fusion, etc.) and transfer channels are usually highly populated and may have cross sections comparable to fusion [16,25]. Experimental evidences indicate that these reactions populate mainly highly excited states below and above the particle emission thresholds of the recoil nucleus [16,25–29], and may strongly affect the elastic scattering and fusion cross sections via coupling channel effects. In this complex coupled channels picture, new experimental data seems to be of paramount importance to identify the dominant channels in each particular case. The importance of nuclei out of the valley of stability extends beyond the nuclear physics realm and may have consequences also in astrophysics. The synthesis of elements heavier than iron is one of the fundamental questions in nowadays cosmology. Nucleosynthesis proceeds through a series of capture reactions beginning in the light mass region and extending all the way up to the synthesis of heavier nuclei, and the importance of A=5,8 masses is notably relevant [30–32]. There are no stable nuclei of masses 5 and 8 and these gaps act as barriers to the synthesis of heavier elements. As a consequence, the presence of such nuclei in explosive scenarios could provide ways to overcome this barrier. In this paper we present new experimental data of reactions induced by the radioactive 8Li nucleus on a 58Ni target at four incident energies above the Coulomb barrier. A preliminary analysis of one of the angular distributions presented in this work has been published in Ref. [33]. Although similar systems have been investigated previously [11,12], here we present a more complete set of quasielastic scattering and neutron stripping angular distributions, covering an angular region from forward to backward angles around the grazing angle, where an enhancement of the quasielastic cross section with respect to the bare optical potential is clearly observed in the experimental data. The quasielastic scattering and the 7Li production channels have been analyzed and compared with several theoretical models. The paper is organized as follows. In Sec. II the experimental setup and the experimental data are presented. In Sec. III we discuss the theory and present the analysis results. In Sec. IV we draw our conclusions. II. EXPERIMENTAL SETUP The experiment was performed in the RIBRAS (Radioactive Ion Beams in Brasil) facility at the Nuclear Physics Open Laboratory (LAFN, acronym in portuguese) of the University of Sao Paulo [34–37]. The 7Li primary beam was delivered by the 8-UD Pelletron accelerator with 26–32 MeV energy and 200 enA impinging in the RIBRAS primary scattering chamber where a 12 μm9Be foil was used as production target. The 8Li beam was produced by the 9Be(7Li,8Li) reaction. The secondary 8Li particles are collected within the first solenoid angular acceptance (2◦⩽θ⩽6◦), selected, and focused on the scattering chamber where a 4.5mg/cm2gold foil was placed to scatter the 8Li particles and monitor the secondary beam intensity. The solenoid current was previously estimated, at each energy, using the TWSP code [38] for the 8Li trajectories along the solenoid all the way up to the secondary target and was varied around the calculated values in order to experimentally maximize the 8Lig.s.beam intensity in the secondary target position. The 8Li secondary beam intensity was of about 105pps during the experiment. A99.997% isotopically enriched, 2.1mg/cm258Ni foil was used as secondary target. Four E(25–50 μm)-E(1000 μm), 150 mm2area silicon telescopes were mounted in the rotating plate to detect and identify the scattered particles. The geometrical detection solid angles were of about 20.7 msr with an angular acceptance of approximately ±4.0◦. A “nose” with two sets of collimators was installed in front of the telescopes to ensure that all particles reaching the detectors were indeed coming from the secondary target. Two-dimensional E-Espectra obtained with 58Ni and gold targets are presented in Fig. 1.InFig.1(b) we basically see the secondary beam composition. The elastically scattered 8Li particles are well separated from the αparticles and other contaminants such as 6He, p,d,t.The8Li secondary beam is produced in the ground state (g.s.) and in its first excited state (0.98 MeV,1+) with 8.2 fs half-life. In Fig. 2we show a projection on the energy axis of the two 8Li peaks from 064601-2 EVIDENCE OF THE EFFECT OF STRONG STRIPPING … PHYSICAL REVIEW C 103, 064601 (2021) FIG. 1. Two-dimensional E-Espectra obtained with (a) 58Ni and (b) gold targets at θlab =35◦and incident energy of 26.1 MeV [37]. Figs. 1(a) and 1(b). With the gold target (b) it is possible to separate two 8Li elastic peaks but with the nickel target (a) at the backwards angles region it becomes very difficult to separate these two peaks. For this reason we decided to include both in the total 8Li peak area to calculate the cross sections in a consistent way. It is important to mention that the lower energy peak seen in Fig. 2includes both low energy events coming from the primary target and possible events from the 8Li(1+;0.98) excitation in the secondary target. However, the events from the 8Li excitation are of minor importance, as will be demonstrated in the next section. The 7Li events observed below the elastic 8Li peak in Fig. 1(a) are not present in the gold target spectrum, indicating that 7Li particles are not beam contaminants but are being produced in reactions with the 58Ni target. The 7Li line presents a wide energy distribution concentrated mainly below the elastic peak but extending also to higher energies. This energy distribution corresponds to the population of different excited states in the final (59Ni) nucleus, corresponding to different 58Ni(8Li,7Li) reaction Qvalues from its ground state (Qg.s. =7 MeV) up to higher excitation energies around and above 7 MeV (Q⩽0). At this point, we cannot decide whether these 7Li particles are coming from the neutron transfer or the 8Li breakup, as we will discuss in more detail further. The secondary beam intensity was monitored during the experiment by performing gold target runs before and after every 58Ni run. The cross sections were determined from the FIG. 2. Projection of the 8Li peaks from Fig. 1on the total energy axis. FWHMs for gold and nickel targets are shown in the figure. The solid lines are Gaussian fits. expression σNi cm(θ)=Nc Ni Nc Au Nb Au Nb Ni Nt Au Nt Ni JNi JAu σAu cm (θ),(1) where Ncis the number of counts in the peak of interest, Nbis the total number of incident 8Li beam particles during the run, Jis the Jacobian factor which transforms from the laboratory to the center-of-mass system, Ntis the areal density of the target in number of atoms/cm2, and σAu cm (θ)isthe8Li +197Au Rutherford cross section. We take the ratio Nb Au/Nb Ni as being equal to the ratio between the primary beam integrated currents in each run. Here we suppose that the 8Li production rate is constant in both the gold target and the adjacent Ni target runs. The advantage of this method is that it is independent of the detectors solid angles. The 8Li +58Ni elastic scattering and 7Li angular distributions, measured at 23.9, 26.1, 28.7, and 30 MeV, are shown in Figs. 3and 4. These energies are well above the Coulomb barrier V(lab) CB =13.55 MeV for this system [39]. The errors have been calculated considering two components: the statistical errors on the ratio Nc Ni/Nc Au in Eq. (1) and an additional term λwhich was obtained from the fluctuation in the σ/σRuth ratio measured with the gold target at forward angles. This fluctuation around σ/σRuth ≈1 was estimated to be of the order of 6% and was included in all data from 064601-3 O. C. B. SANTOS et al. PHYSICAL REVIEW C 103, 064601 (2021) 02040 60 80 Tc.m.(deg) 0 0.5 1 1 1 1 VVRuth OM-fit DF; Nr=1, Ni=0.6 Exp. // // // 23.9 MeV 26.1 MeV 28.7 MeV 30.0 MeV FIG. 3. The 8Li +58Ni elastic scattering angular distributions relative to Rutherford compared with optical model fits obtained with a double-folding potential (with scaling factors Nr=1andNi=0.6) supplemented with a derivative Woods-Saxon potential (solid lines). The dashed lines are optical model calculations obtained with the double-folding potential alone. forward to backward angles, being more relevant only at forward angles where the statistical errors are smaller. The 7Li production cross sections (Figs. 4and 5)were obtained by integrating the yields along the 7Li line shown in the E-Espectrum. In Fig. 5, we show the 7Li energy spectra as a function of the 58Ni(8Li,7Li) 59Ni reaction Qvalue. To obtain this distribution, the E7Li axis was transformed to Q=Qg.s. −Exwhere Qg.s. =7.0 MeV is the gs reaction Q value of the transfer reaction and Exis the excitation energy of the recoil nucleus. The latter is obtained from the measured E7Li using the analytical expression for the kinematics of the transfer reaction. The advantage of this procedure is that the Qvalue distribution does not depend on the scattering angle, whereas E7Li does, allowing the summation of the 7Li yields measured at different angles. The upper horizontal axis in Fig. 5stands for the excitation energy of the recoil nucleus 59Ni. The obtained 7Li energy distributions are consistent to what is expected from Q-optimum considerations for a neutron transfer reaction [40]. III. THEORETICAL ANALYSIS A. Optical model and coupled channels (CC) calculations The measured quasielastic differential cross sections were first compared with optical model calculations. The real part 50 100 150 200 50 100 150 200 0 20406080 Tlab (deg) 0 50 100 150 200 250 0 20406080 Tlab (deg) 0 50 100 150 200 250 300 EBU CRC Exp. NEB+EBU NEB 23.9 MeV 26.1 MeV 28.7 MeV 30.0 MeV dVd: (mb/sr) dVd: (mb/sr) FIG. 4. 7Li angular distributions compared with CRC (solid lines), CDCC (dotted), and IAV (dashed-dotted) calculations. Dashed lines are the sum of the CDCC and IAV. See text for more details. of the 8Li +58Ni potential was generated by a double-folding (DF) procedure, convoluting the M3Y nucleon-nucleon interaction with the 8Li ground-state density from the microscopic calculation of Descouvemont et al. [41] and the 58Ni groundstate density obtained from a Hartree-Fock calculation with the Skyrme SkX interaction [42]. For the Coulomb potential, we considered that of a uniformly charged sphere of radius Rc=1.25 ×(81/3+581/3) fm. For the imaginary part, we first attempted to use the same geometry as the real part, multiplied by some scaling factor (Ni). This procedure, however, did not provide reasonable fits of the data, unless unusually large values of Niwere adopted (Ni>1). For more standard 051015 Ex (MeV) 0 20 40 60 80 100 120 140 051015 Ex (MeV) 0 20 40 60 80 100 120 -10 -5 0510 Q (MeV) 0 50 100 150 200 250 -10 -5 0510 Q (MeV) 0 20 40 60 80 Exp. EBU+NEB NEB EBU 26.1 MeV 28.7 MeV 30.0 MeV d2V/d:dQ (mb/sr MeV) d2V/d:dQ (mb/sr MeV) 23.9 MeV FIG. 5. Experimental Q-value distribution derived from the measured 7Li energy distributions compared with CDCC (dotted) and IAV (dashed) calculations. Solid lines are the sum of the IAV and CDCC. The arrows separates the unbound (left) from bound (right) states in 59Ni. See text for details. 064601-4 EVIDENCE OF THE EFFECT OF STRONG STRIPPING … PHYSICAL REVIEW C 103, 064601 (2021) values (Ni≈0.6–0.8), the calculation does not reproduce well the measured distribution, as illustrated in Fig. 3(dashed line) for the choice Ni=0.6. The DF calculation (dashed line) clearly overestimates the cross sections at forward angles, around the Fresnel peak, and underestimates at intermediate angles. An effect that could contribute for the observed intermediate angle rise of the cross sections would be a contamination, in the elastic peak, of events coming from the 8Li(0.98; 1+) inelastic excitation, as discussed in Sec. II. To estimate this effect we performed CC calculations, including the coupling to the first (1+; 980 keV) and second (3+; 2.26 MeV) excited states of 8Li. Coulomb and nuclear excitation contributions were considered in the calculations, assuming the experimental value of the Coulomb excitation probability B(E2) = 55 e2fm4measured in Ref. [43] and a nuclear deformation length of 1.75 fm [13]. This deformation is considerably larger than that suggested by the microscopic calculation of Descouvemont et al. [41], so that we consider this calculation as an upper limit of the 8Li excitation effect on the elastic scattering. We calculated the ratio between the 8Li(0.98; 1+) inelastic excitation cross section and the elastic one, in the whole angular range of the measurements, and the conclusion was that the effect of the 1+would be, at most, a few percent of the elastic one (<8%) at angles between 40◦and 80◦.The magnitude of this effect is smaller than the error bars of the measurements in this angular region. Thus, neither the CC effect nor the possible 1+inelastic contamination provides a reasonable explanation for the observed intermediate-angles rise of the elastic angular distributions. Our results are in agreement with those of Ref. [43], where probabilities below 2.5% for the 1+inelastic excitation have been reported. Thus, from now on, we will refer to the data as pure elastic scattering angular distributions. In order to describe the intermediate rise within the optical model (OM), we supplemented the imaginary part of the DF potential with a surface (derivative) Woods-Saxon potential with adjustable parameters [17]. The fit was weakly sensitive to the normalization factor Ni, so the latter was conveniently kept fixed to Ni=0.6 (see the discussion in Sec. III D) whereas the depth (Wd), the radius (rd), and the diffuseness (ad) were adjusted to reproduce the measured elastic data. This yielded the values Wd=92 MeV, rd=1.25 fm, and ad=0.263 fm. The results of these calculations are compared with the data in Fig. 3. The solid line is the OM fit with the surface derivative term included and the dashed line corresponds to the double-folding calculation with Nr=1 and Ni=0.6 without the surface derivative term. The need for the inclusion of a surface imaginary potential is interpreted as an indication of strongly coupled direct reaction channels, which cannot be simply described by a mere scaling of the double-folding potential. Natural candidates are the channels responsible for the 7Li production since this is the main product observed in the spectra (cf. Fig. 1). Since the removed neutron is not measured, several processes might in principle contribute to the 7Li production. These processes can be divided into two categories. On one hand, there are the so-called elastic breakup (EBU) channels, in which the projectile dissociates into 7Li +nwhereas the target remains in its ground state. On the other hand, there are those processes which involve some nonelastic interaction of the removed neutron with the target nucleus, which we denote globally as nonelastic breakup (NEB). The latter include the neutron stripping channels leading to bound states of the 59Ni nucleus, but also processes in which the neutron is transferred to states above the 58Ni +nthreshold, such as the formation of a highly excited 59Ni compound nucleus. Since the present measurements are inclusive with respect to the removed neutron, these processes cannot be unambiguously disentangled with the data alone. To elucidate the nature of these processes and their effect on the elastic scattering cross section, in the next sections the measured elastic and inclusive breakup cross sections are compared with several model calculations. EBU and NEB channels are evaluated, respectively, with the CDCC and IAV methods. Finally, coupled-reaction-channels (CRC) calculations have been performed to investigate the influence of these channels on the elastic cross sections. B. CDCC calculations For the CDCC calculations, the 8Li projectile was described as 7Li(g.s.) +n. For simplicity, the 7Li spin was ignored. The 8Li ground state was modeled as a valence neutron occupying a 1p3/2orbital and bound by Sn=2.033 MeV. The projectile breakup is described as inelastic excitations of this valence neutron to higher excited states lying in the continuum. These continuum states are discretized in energy bins for each angular momentum configuration, with max =3 and up to an excitation energy of εmax =9.3 MeV. The CDCC calculations require also optical potentials for the n-58Ni and 7Li +58Ni systems. For the former, the parametrization of Koning and Delaroche [44] was adopted. For the 7Li+58Ni potential, the global parametrization of Cook [45] was initially considered, but the depths of the real and imaginary parts were further adjusted in order to best fit existing elastic scattering data for this system from Refs. [46–49] and constrained using dispersion relations, according to the analytic prescription of Ref. [50]. Following this work, the depth of the imaginary part was parametrized as W(E)=W01 πarctan E−E0 +1 2,(2) which, using the subtracted dispersion relation, gives an energy-dependent correction term to the real part [50], V(E)=− W0 πln ⎛ ⎝1+E−E0 2⎞ ⎠+V0.(3) The extracted values, evaluated at the present incident energies, are V0=89.03 MeV, r0=1.286 fm, a0=0.853 fm, W0=27.221 MeV, E0=17.954 MeV, =23.279 MeV, rI= 1.739 fm, aI=0.809 fm, and rc=1.3 fm, and the radii were defined by Rx=rxA1/3 T. The CDCC calculations were performed with the code FRESCO [51] and the 7Li angular and energy distributions were extracted from the calculated breakup scattering amplitudes using the formalism and codes developed in Ref. [52]. 064601-5 O. C. B. SANTOS et al. PHYSICAL REVIEW C 103, 064601 (2021) 02040 60 80 Tc.m.(deg) 0 0.5 1 1 1 1 VVRuth Exp. CDCC: no continuum CDCC CRC // // // 23.9 MeV 26.1 MeV 28.7 MeV 30.0 MeV FIG. 6. The 8Li +58Ni elastic scattering angular distributions relative to Rutherford compared with CDCC (dashed lines) and CRC (solid lines) calculations at the four measured incident energies. The dotted lines are single-channel calculations obtained omitting the coupling to breakup channels in the CDCC calculations. The results of these calculations are compared with the elastic data in Fig. 6and with the 7Li angular and Qdistributions in Figs. 4and 5, respectively. To highlight the effect of the breakup channels on the elastic cross sections, single-channel calculations, in which the breakup channels are omitted, are also shown in Fig. 6(dotted lines). The comparison of these single-channel calculations with the full CDCC results shows that the coupling to the breakup channels produces a reduction of the cross section at the rainbow peak, and a slight increase at intermediate angles. The effect is, however, too mild to explain satisfactorily the data at these scattering angles. The arrows shown in Fig. 5, placed at Q=−2.03 MeV, indicate the neutron separation threshold of 59Ni (Sn=9MeV). Thus, the events with Q>−2.03 MeV (Q<−2.03 MeV) correspond to the population of bound (unbound) states of the 59Ni nucleus. It can be seen that about one-half of the 7Li yield is associated with the population of 59Ni bound states. By construction, this contribution is absent in the CDCC calculations. Moreover, even for Qvalues corresponding to breakup (i.e., Q<−2.03 MeV), the calculations largely underpredict the magnitude of the measured cross sections. These results clearly indicate that the elastic breakup mechanism is not the main contributor for the 7Li production and that the 7Li yields are mostly produced by one-neutron transfer channels and other NEB mechanisms. These NEB contributions will be addressed in the next subsection with the aid of the IAV model. C. Nonelastic breakup contributions According to the already discussed Q-value distributions, the range of excitation energies in the recoil system 59Ni is very broad, spanning from bound states up to well above the neutron separation threshold. Explicit inclusion of all these states would render the calculation very involved. Furthermore, the spin-parity assignment as well as their individual spectroscopic amplitudes are in many cases poorly known, particularly for states in the continuum. The inclusive breakup model of Ichimura, Austern, and Vincent (IAV) [53] provides a simpler and efficient alternative in which the distribution of populated states is encoded in a suitably chosen optical potential. The model is based on a participant-spectator picture of the reaction, which can be schematically represented as a+A→b+B∗, where the projectile adissociates into b+x, but only the fragment b(the spectator particle) is detected. The participant particle xcorresponds to the unobserved particle (the neutron in our case). The residual nucleus B∗denotes any possible final state of the x+Asystem. Below the x+Athreshold (n+58Ni in our case), these states correspond to bound states of the Bsystem (59Ni) and hence the underlying process is just a conventional oneneutron stripping [54,55]. Above the x+Athreshold, the IAV method enables one to separate the inclusive cross section into EBU and NEB contributions, with the latter being associated with the absorption of the x+Aoptical potential. The mathematical details of the method can be found in the original work of IAV [53] as well in more recent applications [55–58]. In the present work, we adopt the distorted-wave Born approximation (DWBA) version of the IAV method, in which the entrance channel wave function is described as the product of the projectile ground-state wave function times a distorted wave describing the elastic scattering. For the former, we use the same neutron-7Li model employed in the CDCC calculations. The 8Li +58Ni distorted wave was generated with the optical model fit discussed in Sec. III A and shown in Fig. 3. The comparison of these calculations with the 7Li angular and Q-value distributions is shown in Figs. 4and 5, respectively. In addition to the NEB contribution, we display the total inclusive breakup contribution (EBU+NEB). The agreement with the data is very satisfactory at the four measured bombarding energies. As anticipated, NEB represents the dominant contribution of the 7Li yields. From the Q-value distribution, we see that the IAV calculations reproduce also the region corresponding to bound states. This result is less obvious, since the n+58Ni potential adopted in these calculations is not meant to describe the neutron negative energies. Part of this agreement might be due to the fact that the experimental energy resolution did not allow us to resolve specific bound states of the residual nucleus, and therefore only the gross features of the spectrum are observed. From these results, it is also plausible that these strong NEB channels (including transfer to bound states) are also responsible for the deviation of the elastic scattering data 064601-6 EVIDENCE OF THE EFFECT OF STRONG STRIPPING … PHYSICAL REVIEW C 103, 064601 (2021) with respect to the double-folding calculations presented in Sec. III A. Being based in the DWBA approximation, the IAV model does not permit us to study the effect of NEB channels on the elastic data. To study such an effect, we have performed further calculations in which these couplings are included, approximately, within the CRC framework. D. CRC calculations The CRC method is a variational approach of the scattering process, in which the total wave function of the system is expanded in a set of internal states of two or more mass rearrangements [59,60]. The radial coefficients appearing in this expansion are obtained by solving a set of coupled integrodifferential equations. The method was originally devised to incorporate the effect of strong transfer channels in situations in which the first-order approximation (DWBA) is not valid. Included states are typically the ground state and a few low-lying excited states for the considered rearrangements. In the present case, we aim to use this method to describe the coupling of the elastic channels with the states of the 59Ni system. As the number of states in this energy range is expected to be enormous, we adopt an approximate procedure in which the physical states of the 59Ni system are replaced by a set of representative doorway states. For each angular momentum configuration (nj) above the Fermi level in 58Ni, we assume that the full single-particle strength can be described by a representative state, located at an excitation energy given by the centroid of the single-particle states belonging to this configuration, according to the analysis of the 58Ni(d,p)59Ni reaction by Iwamoto et al. [61]. According to the results listed in Table 3 of Ref. [61], the relevant configurations are 2p3/2, 1f5/2,2p1/2,1g9/2,2d5/2, and 3s1/2. It should be noted that the summed spectroscopic factors shown in that table, which were obtained from a DWBA analysis of the data, are in some cases significantly smaller than unity. The missing strength might correspond to unidentified levels but also to higher excited states lying in the continuum. In our calculations, we assign unit spectroscopic factor to all the above configurations, with the aim of accounting for this missing strength. We note also that, in addition to the aforementioned configurations, other higher single-particle configurations are also possible but, since they were not observed in the data of [61], we associate them with continuum states without significant bound states counterparts and, as such, they are described by a set of continuum bins. In this way, the calculation is meant to account, approximately, for the transfer of the neutron to both bound and unbound orbits of the 59Ni residual nucleus. Although one cannot make a one-by-one identification of the doorway states with the physical states of the system, completeness of the single-particle basis ensures that coupling with all relevant transfer channels is included. We take into account the removal of the neutron from 1p1/2and 1p3/2configurations, leaving the 7Li in its first excited state. The required spectroscopic amplitudes for the 8Li →7Li +ndecomposition, considering 8Li in its g.s. or 1+ excited state, have been taken from Ref. [62]. For 8Li(3+)→ 7Li +n, the required spectroscopic amplitude, corresponding TABLE I. Total reaction and 7Li production cross sections for the 8Li +58Ni reaction at the incident energies measured in this work. NEB and EBU cross sections were obtained through IAV and CDCC calculations, respectively. Energy σCRC reac σOM-fit reac σCRC bu σNEB+EBU bu σNEB bu (MeV) (mb) (mb) (mb) (mb) (mb) 23.9 1354 1194 244 291 262 26.1 1484 1322 242 290 261 28.7 1606 1446 236 284 255 30.0 1657 1500 233 281 252 to the p3/2configuration, was calculated following the same procedure adopted in Ref. [62], giving the value of 0.632. As for the 8Li projectile, the CRC model space included, in addition to the 8Li ground state, the bound excited state (1+; 980.8 keV) and the narrow 3+resonance at Ex=2.25 MeV. Nuclear couplings between these three states were included by means of transition potentials generated by folding the M3Y nucleon-nucleon interaction with 8Li transition densities of Descouvemont et al. [41] and the target Hartree-Fock ground state density. Coulomb couplings were also included assuming a rotor model with matrix elements derived from the electric transition probability B(E2,1+→2+)=1.6W.u. also computed in [41]. Transfer couplings from the 8Li ground state as well as from the considered excited states were included. The CRC method requires also optical potentials for the entrance (8Li +58Ni) and exit (7Li +59Ni∗) channels. These are to be understood as bare potentials, which are meant to describe the interaction between the colliding partners in absence of the considered couplings. In practice, these bare potentials are adjusted so that the full CRC calculation reproduces the elastic scattering data. For the exit-channel optical potential, we adopted the parameters of the 7Li +58Ni potential discussed in Sec. III B. For the entrance channel, we found that a very good reproduction of the elastic data could be obtained by just removing the surface imaginary potential introduced in the OM analysis of Sec. III A and keeping the double-folding potential with scaling factors Nr=1 and Ni= 0.6. A reduction in the strength of the bare imaginary potential with respect to the optical model potential is expected since the couplings to the transfer channels are explicitly taken into account [63,64]. The same scaling factors were assumed for the transition potentials between the 8Li states. The results of these calculations are compared with the elastic data in Fig. 6and with the 7Li angular distributions in Fig. 4. Both observables are nicely explained by the calculations. Comparing the data with the full CRC calculation confirms the large influence of these channels on the elastic scattering, as was anticipated. In Table Iwe present the total reaction cross sections1obtained from the OM-fit (Fig. 3) and CRC calculations (Fig. 6), as well as the angle integrated 1The reaction cross section quoted here follows the definition of the FRESCO code [51]. 064601-7 O. C. B. SANTOS et al. PHYSICAL REVIEW C 103, 064601 (2021) transfer/breakup cross sections from CRC, IAV+CDCC, and IAV calculations (Fig. 4). We end this section by noting that the conclusions of this work regarding the importance of the coupling to the oneneutron stripping channels are consistent with those found in Ref. [62]forthe8Li +208Pb reaction. IV. SUMMARY AND CONCLUSIONS New experimental data of the 8Li +58Ni elastic scattering and the 58Ni(8Li,7Li) reaction are presented at four incident energies above the Coulomb barrier. The 8Li beam was produced at the Radioactive Ion Beams in Brasil (RIBRAS) facility. A system of four silicon E-Etelescopes was used to detect the reaction products and identify the 8Li and 7Li isotopes with resolution sufficient to clearly separate the two isotopes. Angular and energy distributions were obtained for the elastic scattering and for the 7Li fragments. The 7Li angular distributions present a “bell shape” with a peak around the grazing angle, characteristic of a transfer process. The 7Li energy distributions indicate that the 59Ni recoil system is being populated in a broad excitation energy distribution below and above the neutron emission threshold, centered in the energy around the expected Qoptimum for a neutron transfer reaction. The elastic scattering angular distributions were first compared to the optical model using double-folding (DF) potentials. The optical model calculations with pure double-folding potential do not reproduce the angular distributions, overestimating the Fresnel peak and underestimating the cross sections for larger angles. An absorptive surface derivative term added to the DF potential was adjusted to reproduce the angular distributions indicating that the elastic scattering is largely influenced by strongly coupled direct reaction channels. Continuum discretized coupled Channels calculations, considering the effect of the 8Li breakup into n+7Li, reduce the elastic cross sections in the region of the rainbow peak, slightly increasing the cross section at larger angles, but not enough to explain the data. Moreover, these CDCC calculations largely underestimate the measured 7Li cross sections. By contrast, inclusion of nonelastic breakup contributions, computed with the model of Ichimura, Austern, and Vincent, provides a very good agreement with the 7Li data for both angular and energy distributions. Since the IAV model does not allow one to describe the effect of the NEB on the elastic channel, a CRC analysis was performed considering the coupling between elastic scattering and the neutron transfer channels populating bound and unbound states of 59Ni. The agreement with both the elastic scattering and transfer angular distributions is remarkable, nicely reproducing the intermediate angles rise observed in the elastic distributions, revealing the strong influence of the neutron stripping channels on the 8Li +58Ni scattering. ACKNOWLEDGMENTS This work has been partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq/MCTI (Brazil); by Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP (Brazil), Contracts No. 2019/02759-0, No. 2019/07767-1, No. 2016/17612-7, and No. 2013/22100-7; by Coordenação de Aperfeiçoamento de Pessoal de Nével Superior, Brasil (CAPES), Finance Code 88887.355019/2019; and by Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, FAPERJ (Brazil). A.M.M. is supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (including FEDER funds) under Project No. FIS2017-88410-P and by the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 654002. [1] C. Beck, Proceedings of the International Symposium on Exotic Nuclei, Exon-2018 (World Scientific, Singapore, 2018), pp. 9– 16. [2] I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N. Yoshikawa, K. Sugimoto, O. Yamakawa, T. Kobayashi, and N. Takahashi, Phys.Rev.Lett.55, 2676 (1985). [3] T. Kobayashi, O. Yamakawa, K. Omata, K. Sugimoto, T. Shimoda, N. Takahashi, and I. Tanihata, Phys.Rev.Lett.60, 2599 (1988). [4] N. A. Orr, N. Anantaraman, S. M. Austin, C. A. Bertulani, K. Hanold, J. H. Kelley, D. J. Morrissey, B. M. Sherrill, G. A. Souliotis, M. Thoennessen, J. S. Winfield, and J. A. Winger, Phys.Rev.Lett.69, 2050 (1992). [5] A. Lépine-Szily and R. Lichtenthäler, Nucl. Phys. A 787,94 (2007), in Proceedings of the Ninth International Conference on Nucleus-Nucleus Collisions. [6] F. D. Becchetti, W. Z. Liu, K. Ashktorab, J. F. Bajema, J. A. Brown, J. W. Jänecke, D. A. Roberts, J. J. Kolata, K. L. Lamkin, A. Morsad, R. J. Smith, X. J. Kong, and R. E. Warner, Phys. Rev. C 48, 308 (1993). [7] S. Mukherjee, N. N. Deshmukh, V. Guimarães, J. Lubian, P. R. S. Gomes, A. Barioni, S. Appannababu, C. C. Lopes, E. N. Cardozo, K. C. C. Pires, R. Lichtenthäler, A. Lépine-Szily, D. S. Monteiro,J.M.B.Shorto,P.N.deFaria,E.Crema,V.Morcelle, M. C. Morais, and R. Pampa Condori, Eur. Phys. J. A 45,23 (2015). [8] A. Barioni, V. Guimarães, A. Lépine-Szily, R. Lichtenthäler, D.R.MendesJr.,E.Crema,K.C.C.Pires,M.C.Morais,V. Morcelle, P. N. de Faria, R. P. Condori, A. M. Moro, D. S. Monteiro, J. M. B. Shorto, J. Lubian, and M. Assunção, Phys. Rev. C 80, 034617 (2009). [9] V. Guimarães, R. Lichtenthäler, O. Camargo, A. Barioni, M. Assunção, J. J. Kolata, H. Amro, F. D. Becchetti, H. Jiang, E. F. Aguilera, D. Lizcano, E. Martines-Quiroz, and H. Garcia, Phys. Rev. C 75, 054602 (2007). [10] O. Camargo, V. Guimarães, R. Lichtenthäler, V. Scarduelli, J. J. Kolata, C. A. Bertulani, H. Amro, F. D. Becchetti, H. Jiang, E. F. Aguilera, D. Lizcano, E. Martinez-Quiroz, and H. Garcia, Phys. Rev. C 78, 034605 (2008). [11] A. Pakou, D. Pierroutsakou, and M. Mazzocco, Eur.Phys.J.A 51, 55 (2015). 064601-8 EVIDENCE OF THE EFFECT OF STRONG STRIPPING … PHYSICAL REVIEW C 103, 064601 (2021) [12] A. Pakou, N. Keeley, D. Pierroutsakou, M. Mazzocco, L. Acosta, X. Aslanoglou, A. Boiano, C. Boiano, D. Carbone, M. Cavallaro, J. Grebosz, M. La Commara, C. Manea, G. Marquinez-Duran, I. Martel, C. Parascandolo, K. Rusek, A. M. Sánchez-Benétez, O. Sgouros, C. Signorini, F. Soramel et al., Eur.Phys.J.A51, 90 (2015). [13] J. J. Kolata, V. Z. Goldberg, L. O. Lamm, M. G. Marino, C. J. O’Keeffe, G. Rogachev, E. F. Aguilera, H. García-Martínez, E. Martinez-Quiroz, P. Rosales, F. D. Becchetti, T. W. O’Donnell, D. A. Roberts, J. A. Brown, P. A. DeYoung, J. D. Hinnefeld, and S. A. Shaheen, Phys.Rev.C65, 054616 (2002). [14] T. Nakamura and Y. Kondo, Clusters in Nuclei, Lecture Notes in Physics Vol. 848 (Springer, Berlin, 2012), p. 67. [15] P. N. de Faria, R. Lichtenthäler, K. C. C. Pires, A. M. Moro, A. Lépine-Szily, V. Guimarães, D. R. Mendes Jr., A. Arazi, M. Rodríguez-Gallardo, A. Barioni, V. Morcelle, M. C. Morais, O. Camargo Jr., J. Alcantara Nuñez, and M. Assunção, Phys. Rev. C81, 044605 (2010). [16] P. N. de Faria, R. Lichtenthäler, K. C. C. Pires, A. M. Moro, A. Lépine-Szily, V. Guimarães, D. R. Mendes Jr., A. Arazi, A. Barioni, V. Morcelle, and M. C. Morais, Phys. Rev. C 82, 034602 (2010). [17]P.Mohr,P.N.deFaria,R.Lichtenthäler,K.C.C.Pires, V. Guimarães, A. Lépine-Szily, D. R. Mendes, A. Arazi, A. Barioni, V. Morcelle, and M. C. Morais, Phys. Rev. C 82, 044606 (2010). [18] K. C. C. Pires, R. Lichtenthäler, A. Lépine-Szily, V. Guimarães, P. N. de Faria, A. Barioni, D. R. Mendes Junior, V. Morcelle, R. Pampa Condori, M. C. Morais, J. C. Zamora, E. Crema, A. M. Moro, M. Rodríguez-Gallardo, M. Assunção, J. M. B. Shorto, and S. Mukherjee, Phys.Rev.C83, 064603 (2011). [19] K. C. C. Pires, R. Lichtenthäler, A. Lépine-Szily, and V. Morcelle, Phys.Rev.C90, 027605 (2014). [20] K. C. C. Pires, S. Appannababu, R. Lichtenthäler, and O. C. B. Santos, Phys. Rev. C 98, 014614 (2018). [21] V. Morcelle, R. Lichtenthäler, R. Linares, M. C. Morais, V. Guimarães, A. Lépine-Szily, P. R. S. Gomes, J. Lubian, D. R. Mendes Junior, P. N. De Faria, A. Barioni, L. R. Gasques, J. M. B. Shorto, K. C. C. Pires, J. C. Zamora, R. P. Condori, V. Scarduelli, J. J. Kolata, H. Amro, F. D. Becchetti et al.,Phys. Rev. C 89, 044611 (2014). [22] V. Morcelle, K. C. C. Pires, M. Rodríguez-Gallardo, R. Lichtenthäler, A. Lépine-Szily, V. Guimarães, P. N. Faria, D. R. Mendes Junior, A. M. Moro, L. R. Gasques, E. Leistenschneider, R. Pampa Condori, V. Scarduelli, M. C. Morais,A.Barioni,J.C.Zamora,andJ.M.B.Shorto,Phys. Lett. B 732, 228 (2014). [23] V. Morcelle, R. Lichtenthäler, A. Lépine-Szily, V. Guimarães, K. C. C. Pires, J. Lubian, D. R. Mendes Junior, P. N. de Faria, J. J. Kolata, F. D. Becchetti, H. Jiang, E. F. Aguilera, D. Lizcano, E. Martinez-Quiroz, and H. Garcia, Phys. Rev. C 95, 014615 (2017). [24] E. Benjamim, A. Lépine-Szily, D. R. Mendes Jr., R. Lichtenthäler, V. Guimarães, P. R. S. Gomes, L. C. Chamon, M. S. Hussein, A. M. Moro, A. Arazi, I. Padron, J. Alcantara Nuñez, M. Assunção, A. Barioni, O. Camargo Jr., R. Z. Denke, P. N. de Faria, and K. C. C. Pires, Phys. Lett. B 647, 30 (2007). [25] S. Appannababu, R. Lichtenthäler, M. A. G. Alvarez, M. Rodríguez-Gallardo, A. Lépine-Szily, K. C. C. Pires, O. C. B. Santos, U. U. Silva, P. N. de Faria, V. Guimarães, E. O. N. Zevallos, V. Scarduelli, M. Assunção, J. M. B. Shorto, A. Barioni, J. Alcántara-Núñez, and V. Morcelle, Phys.Rev.C99, 014601 (2019). [26] S. Santra, S. Kailas, V. V. Parkar, K. Ramachandran, V. Jha, A. Chatterjee, P. K. Rath, and A. Parihari, Phys.Rev.C85, 014612 (2012). [27] M. K. Pradhan, A. Mukherjee, S. Roy, P. Basu, A. Goswami, R. Kshetri, R. Palit, V. V. Parkar, M. Ray, M. Saha Sarkar, and S. Santra, Phys. Rev. C 88, 064603 (2013). [28] K. J. Cook, I. P. Carter, E. C. Simpson, M. Dasgupta, D. J. Hinde, L. T. Bezzina, S. Kalkal, C. Sengupta, C. Simenel, B. M. A. Swinton-Bland, K. Vo-Phuoc, and E. Williams, Phys. Rev. C 97, 021601(R) (2018). [29] K. J. Cook, E. C. Simpson, L. T. Bezzina, M. Dasgupta, D. J. Hinde, K. Banerjee, A. C. Berriman, and C. Sengupta, Phys. Rev. Lett. 122, 102501 (2019). [30] E. Leistenschneider, A. Lépine-Szily, M. A. G. Alvarez, D. R. Mendes, R. Lichtenthäler, V. A. P. Aguiar, M. Assunção, R. P. Condori, U. U. da Silva, P. N. de Faria, N. Deshmukh, J. G. Duarte, L. R. Gasques, V. Guimarães, E. L. A. Macchione, M. C. Morais, V. Morcelle, K. C. C. Pires, V. B. Scarduelli, G. Scotton et al.,Phys.Rev.C98, 064601 (2018). [31] D. R. Mendes, A. Lépine-Szily, P. Descouvemont, R. Lichtenthäler, V. Guimarães, P. N. de Faria, A. Barioni, K. C. C. Pires, V. Morcelle, R. Pampa Condori, M. C. Morais, E. Leistenschneider, C. E. F. Lima, J. C. Zamora, J. A. Alcantara, V. Zagatto, M. Assunção, and J. M. B. Shorto, Phys. Rev. C 86, 064321 (2012). [32] S. K. Das, T. Fukuda, Y. Mizoi, H. Ishiyama, H. Miyatake, Y. X. Watanabe, Y. Hirayama, S. C. Jeong, H. Ikezoe, M. Matsuda, K. Nishio, and T. Hashimoto, Phys.Rev.C95, 055805 (2017). [33] O. C. B. Santos, R. Lichtenthäler, K. C. C. Pires, A. M. Moro, U. Umbelino, E. O. N. Zevallos, M. Assunção, S. Appannababu, J. Alcántara-Núñez, A. L. de Lara, V. Scarduelli, V. Guimarães, A. Lépine-Szily, A. S. Serra, R. Linares, V. A. B. Zagatto, P. N. de Faria, V. Morcelle, M. C. Morais, A. Barioni et al.,J. Phys.: Conf. Ser. 1291, 012030 (2019). [34] R. Lichtenthäler, A. Lépine-Szily, V. Guimarães, C. Perego, V. Placco, O. Camargo jr., R. Denke, P. N. de Faria, E. A. Benjamim, N. Added, G. F. Lima, M. S. Hussein, J. Kolata, and A. Arazi, Eur.Phys.J.A25, 733 (2005). [35] A. Lépine-Szily, R. Lichtenthäler, and V. Guimarães, Eur. Phys. J. A 50, 128 (2014). [36] R. Lichtenthäler, M. A. G. Alvarez, A. Lépine-Szily, S. Appannababu, K. C. C. Pires, U. U. da Silva, V. Scarduelli, R. P. Condori, and N. Deshmukh, Few Body Syst. 57, 157 (2016). [37] R. Lichtenthäler, O. C. B. Santos, A. Serra, U. Umbelino, K. C. C. Pires, J. R. B. Oliveira, A. Lépine-Szily, P. N. de Faria, and V. Morcelle, Eur.Phys.J.A57, 92 (2021). [38] R. Lichtenthäler (unpublished). [39] A. S. Freitas, L. Marques, X. X. Zhang, M. A. Luzio, P. Guillaumon, R. P. Condori, and R. Lichtenthäler, Braz. J. Phys. 46, 120 (2016). [40] D. M. Brink, Phys. Lett. 40B, 37 (1972). [41] P. Descouvemont and E. C. Pinilla, Few-Body Syst. 60,11 (2019). [42] B. A. Brown, Phys.Rev.C58, 220 (1998). [43] J. A. Brown, F. D. Becchetti, J. W. Jänecke, K. Ashktorab, D. A. Roberts, J. J. Kolata, R. J. Smith, K. Lamkin, and R. E. Warner, Phys.Rev.Lett.66, 2452 (1991). [44] A. J. Koning and J. P. Delaroche, Nucl. Phys. A 713, 231 (2003). [45] J. Cook, Nucl. Phy. A 388, 153 (1982). 064601-9