Breakup of 6Li + p at near-barrier energies and the effect on elastic scattering

PHYSICAL REVIEW C 95, 054614 (2017) Breakup of 6Li +pat near-barrier energies and the effect on elastic scattering V. Soukeras,1A. Pakou,1,*F. Cappuzzello,2,3L. Acosta,4,5C. Agodi,2N. Alamanos,6S. Calabrese,2,3D. Carbone,2 M. Cavallaro,2A. Cunsolo,2A. Di Pietro,2J. P. Fernández-García,2P. Figuera,2M. Fisichella,2A. Foti,3,5N. Keeley,7 G. Marquìnez-Duràn,8I. Martel,8M. Mazzocco,9,10 D. Pierroutsakou,11 K. Rusek,12 G. Santagati,2,3 O. Sgouros,1E. Stiliaris,13 E. Strano,9,10 D. Torresi,9,10 and K. Zerva1 1Department of Physics and HINP, University of Ioannina, 45110 Ioannina, Greece 2INFN Laboratori Nazionali del Sud, via S. Sofia 62, 95125, Catania, Italy 3Dipartimento di Fisica e Astronomia, Universita di Catania, via S. Sofia 64, 95125, Catania, Italy 4Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico D. F. 01000, Mexico 5INFN–Sezione di Catania, via S. Sofia 64, 95125, Catania, Italy 6CEA-Saclay, DAPNIA-SPhN, 91191, Gif-sur-Yvette, France 7National Centre for Nuclear Research, Andrzeja Sołtana 7, 05-400, Otwock, Poland 8Departamento di Fisica Aplicada, Universidad de Huelva, E-21071, Huelva, Spain 9Departimento di Fisica e Astronomia, Universita di Padova, via Marzolo 8, I-35131, Padova, Italy 10INFN–Sezione di Padova, via Marzolo 8, I-35131, Padova, Italy 11INFN–Sezione di Napoli, via Cinthia, I-80126, Napoli, Italy 12Heavy Ion Laboratory, University of Warsaw, Pasteura 5a, 02-093, Warsaw, Poland 13Institute of Accelerating Systems and Applications and Department of Physics, University of Athens, Greece (Received 2 March 2017; published 18 May 2017) Exclusive breakup measurements have been performed for the 6Li +psystem in inverse kinematics at 6Li incident energies of 25 and 29 MeV. The results are considered in the Continuum Discretized Coupled-Channels framework, together with elastic scattering data at 16, 20, 25, and 29 MeV, obtained simultaneously in the same experiment and reported previously. Good agreement between data and theory is observed, interpreted as evidence for strong coupling to the continuum. The direct and sequential (via the 6Li 31+resonance) breakup cross sections are found to be equally large at the higher incident energies but the dominant effect on the elastic scattering is due to coupling to the sequential breakup. This effect remains dominant even at the lowest energy of 16 MeV, despite the negligible cross section for excitation of the resonance at this low incident energy. DOI: 10.1103/PhysRevC.95.054614 I. INTRODUCTION Many weakly bound nuclei possess a single bound state, the ground state, and a broad featureless continuum plus a small number of low-lying unbound resonant states. Due to their low binding energies, they may be easily excited above their particle emission thresholds; hence the breakup of such nuclei induced by the Coulomb and nuclear fields of suitable targets could be a useful tool to investigate their structure and benchmark coupling effects on their elastic scattering. The simplest breakup process occurs for interaction with a proton target, with excitation mainly by the nuclear field. In addition, nucleon scattering is one of the simplest and most valuable tools for probing the structure of a nucleus. For measurements of this type involving radioactive nuclei, the inverse kinematics technique is adopted whereby a beam of the radioactive species of interest is incident on a proton-rich target, and the halo or skin-like nature of the projectile may be probed as long as the potential is known. It was shown previously [1,2] that at energies 3 to 6 times the Coulomb barrier the microscopic potential of Jeukenne, Lejeune, and Mahaux (JLM) [3] without any couplings to continuum is not adequate to describe the elastic scattering data for 6,7Li on protons, with these light *Corresponding author: [email protected] nuclei being strictly speaking outside its range of validity. On the other hand, the Continuum Discretized Coupled-Channels (CDCC) approach, where couplings to the continuum are explicitly taken into account, describes these data very well. However, for a more effective interpretation of experimental data in a coupled channel scheme, a global description of all the reaction channels involved is required. In this spirit, we present here systematic breakup measurements in their own right and also as complementary measurements to existing elastic scattering and 6Li +p→4He +3He data. These latter two measurements were made under the same experimental conditions as the present data and have been previously analyzed [1,4] but will be reconsidered in this study as part of a global picture. The 6Li nucleus exhibits a pronounced cluster structure with a very low binding energy in the α-dchannel of 1.47 MeV. Therefore, breakup is expected to be significant in reactions involving this nucleus. It has mainly been investigated in exclusive measurements at near-barrier energies on light [5,6], medium [7–11], and heavy targets [12–20]. Interest has also been shown in the effect of breakup on the elastic scattering [21–23]. The only existing breakup measurement, p+6Li, reported in Ref. [24], was performed at energies well above the Coulomb barrier (∼12 ×VC). Moreover, neither the total breakup cross section nor angular distributions in the center-of-mass system are given in 2469-9985/2017/95(5)/054614(7) 054614-1 ©2017 American Physical Society V. SOUKERAS et al. PHYSICAL REVIEW C 95, 054614 (2017) Ref. [24] so comparisons with the present work cannot be made. In the following sections, we will first present the details of the experimental setup and the data reduction procedure (Sec. II), then we will proceed with details of our theoretical calculations (Sec. III), discussing the effect of breakup coupling on the elastic scattering, and finally we will present our concluding remarks (Sec. IV). II. EXPERIMENTAL DETAILS AND DATA REDUCTION The experiment was performed at the MAGNEX facility of the Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud (INFN-LNS) in Catania, Italy. Beams of 6Li3+ions were accelerated by the TANDEM accelerator for elastic scattering measurements at energies of 16, 20, 25, and 29 MeV and impinged on a 240 μg/cm2CH2target. Experimental details and an analysis of the elastic scattering data were reported previously in Ref. [1]. A breakup measurement was performed at the two higher energies, 25 and 29 MeV (4.17 MeV/u and 4.83 MeV/u), employing a thicker target of 308 μg/cm2to improve statistics. The αfragments were momentum analyzed by the MAGNEX spectrometer [25–27], whose optical axis was set at θopt =4◦, subtending an angular range between −1to10 ◦, and were detected by its focal plane detectors [28,29]. MAGNEX worked with full horizontal angular acceptance and a rather well-open vertical acceptance as the counting rate due to breakup was rather low. The elastically scattered 6Li ions were swept out by the chosen magnetic fields, which allowed the detection of αparticles in energy slices of 8.4 to 13.3 MeV and 11 to 15.5 MeV for the 25- and 29-MeV runs, respectively. A small remnant of elastic scattering was rejected off-line by the appropriate cuts in two-dimensional E−(E +E) spectra, obtained via the gas (E denotes the energy loss in the gas) and silicon (E denotes the residual energy in the silicon detectors) detectors of the focal plane [28,29]. Our data reduction technique, based on the ray reconstruction of the data, is described in Refs. [30–33]. The second breakup fragments (the deuterons) were detected in a silicon detector fixed at θlab =5◦, subtending an angular range between 4.2◦⩽θlab ⩽5.8◦. To prevent deterioration from Rutherford scattering, this detector was masked by 30.8- and 43.6-μm tantalum foils for the measurements at 25 and 29 MeV, respectively. These foils absorbed all heavy particles but allowed protons and deuterons associated with the energy of the first solution to the double-valued equation of the reaction kinematics to pass through. Light particles associated with energies of the second kinematic solution were blocked by these foils, and therefore our data are limited to the forward angular range (10◦to 90◦) in the center-of-mass frame. This was, however, a minor problem for the extraction of the total breakup yield since the angular distribution of the breakup fragments is predicted to be flat by our calculations. Exclusive yields were determined for pairs of angles every 0.5◦for αparticles observed in MAGNEX over the angular range 0◦to 10◦, combined with deuterons observed in the fixed angle detector at 5◦. Two-dimensional spectra for the 25- and 29-MeV runs displaying the energy of αparticles recorded in MAGNEX versus the energy of deuterons or Energy - α (MeV) α - p → α - d → Carbon → → Energy - d(p) (MeV) 8 10 12 14 8 10 12 14 4 6 8 10 12 14 FIG. 1. Upper figure: Two-dimensional plot at 25 MeV (4.17 MeV/u) representing coincident events of the two 6Li breakup fragments. Energy of αparticles (energy α) vs energy of deuterons or recoiling protons (energy d(p)). The αparticles were detected in the MAGNEX spectrometer over the angular range θlab =0to10 ◦, while the deuterons and the recoiling protons were detected in a silicon detector fixed at θlab =5◦. The observed loci for α-pcoincidences and α-dcoincidences due to breakup of 6Li on protons and α-d coincidences due to breakup on carbon are indicated on the figure. Lower figure: Superimposed on the experimental spectrum, denoted by the black dots, are simulated events for the first kinematic solution of the resonant and direct breakup, denoted by the red and green dots, respectively. recoiling protons detected in the 5◦detector are shown in Figs. 1and 2. One-dimensional coincidence spectra from the 5◦detector are shown in Figs. 3and 4for the 25- and 29-MeV runs, respectively. It is evident that the recoiling protons are well discriminated from the deuterons. In the two-dimensional spectra, the loci at the extreme right are due to carbon, present in the CH2target. It should be noted that the background due to carbon was of the order of ∼11% to 15% and hardly affected the main breakup data. This can be more clearly seen in the one-dimensional coincidence spectra displayed in Figs. 3and 4. Superimposed on these spectra are spectra obtained with a carbon target (shown in green), appropriately normalized, reflecting this background. The exclusive yields were transferred to laboratory double differential cross sections (d2σ/dαdd) using a detection efficiency estimated through a Monte Carlo three-body simulation code [34,35]. Our code takes into account the 6Li +preaction, leading to an excited state of 6Li∗with an angular distribution determined in the CDCC calculation to be described below. The 6Li acquires randomly an energy inside one of the energy bins as specified in the CDCC framework. This includes either the resonant bin at 2.186 MeV (0.716 MeV above the breakup threshold), or any one of the continuum bins. 054614-2 BREAKUP OF 6Li +pAT NEAR-BARRIER . . . PHYSICAL REVIEW C 95, 054614 (2017) Energy - α (MeV) α - p → α - d → Carbon → Energy - d(p) (MeV) 10 12 14 16 10 12 14 16 02468101214 FIG. 2. Same as in Fig. 1but for 29 MeV (4.83 MeV/u). The excited lithium breaks into two fragments, αand deuteron, with one emitted with a randomly assigned specific energy and momentum and the second with energy and momentum fulfilling the conservation laws in the rest frame of 6Li∗. The energy distributions of the fragments thus obtained in Counts Energy - d(p) (MeV) α - p → 0 100 200 300 400 4 6 8 10 12 14 16 FIG. 3. Exclusive breakup spectrum, acquired in the 5◦silicon detector with a CH2target at 25 MeV (α-dor pcoincidences). The results of simulations of the first kinematic solution for α-d coincidences are denoted by the dot-dashed red line. The peak at the left corresponds to αcoincidences with the recoiling protons. The spectrum in green represents an exclusive spectrum acquired with a carbon target, appropriately normalized. The dashed blue line represents a simulation of the 6Li +p→5Li +d→α+p+d reaction, arbitrarily normalized (see text). Counts Energy - d(p) (MeV) α - p → 0 50 100 150 200 250 02468101214 FIG. 4. Same as in Fig. 3but for 29 MeV (4.83 MeV/u). the rest frame of 6Li∗are transformed to the laboratory system by imposing a Galilean transformation followed by the appropriate rotation. The results of our simulation for the energy distributions are presented in the two-dimensional αversus deuteron energy spectra in Figs. 1and 2and the one-dimensional spectra for deuterons in Figs. 3and 4for the 25- and 29-MeV runs, respectively. In the two-dimensional spectra, the red dots denote the simulation of sequential breakup via the 31+resonance while the green dots denote the simulation of direct, nonresonant breakup. The very good agreement between the experimental data and the simulation based on the CDCC binning of the continuum confirms the realistic philosophy behind this theoretical approach. It should be noted that another process which could contribute to α-dcoincidences is the neutron-stripping reaction: 6Li + p→5Li +d→α+p+d, with a Qvalue of −3.44 MeV, which, however, according to preliminary calculations, is expected to have very low probability. The results of a simulation of this process shown on Figs. 3and 4by dashed blue lines show clearly that it does not affect the breakup data. III. THEORETICAL DETAILS: CDCC CALCULATIONS For the CDCC calculations, we follow the same technique as in Ref. [36], where we present calculations for the same system but at a much higher energy, 155 MeV (25.8 MeV/A). An α+dcluster model of 6Li was adopted, with all the parameters of the model including discretization and truncation described in detail in Refs. [1,37]. In addition to the nonresonant continuum, the 31+resonance was taken into account and was treated as a momentum bin with a width corresponding to 0.1 MeV. The central parts of the 6Li +poptical potentials were derived as previously [36] from empirical p+αand p+dpotentials using the Watanabe single-folding method. The optical potentials were obtained from existing p+dand p+αelastic scattering 054614-3 V. SOUKERAS et al. PHYSICAL REVIEW C 95, 054614 (2017) TABLE I. Optical model potentials for the 4He +psystem deduced by fitting existing data [43,44] adopting a Woods-Saxon potential (real and imaginary volume terms). The nuclear radius was RV(W)=rV(W)×41/3fm and the Coulomb radius was RC= 1.25 ×41/3fm. E(MeV) V(MeV) rV(fm) aV(fm) W(MeV) rW(fm) aW(fm) 29 49.811 1.10 0.477 0.040 1.10 0.477 25 52.278 0.039 20 55.567 0.038 16 58.230 0.037 studies at E=2.52 to 5 MeV/u[38–44]. These p+dand p+αelastic scattering data were fitted by simple Woods- Saxon form factors with real volume and imaginary volume parts for the p+αsystem and real volume and surface imaginary terms for the p+dsystem. The optical model potential parameters are given in Tables Iand II for the p+αand p+dsystems, respectively. A proton spin-orbit potential of Thomas form with parameters Vso =4.26 MeV, rso =1.10 fm, and aso =0.35 fm was added to the diagonal 6Li +pWatanabe folding potentials. These potentials were fed into FRESCO calculations [45]. The output of this code gives angular distributions for both elastic scattering and breakup. The breakup results are compared with the data in Figs. 5 and 6for the 25- and 29-MeV runs, respectively. They are in satisfactory agreement, although the general trend is for the calculations to underestimate the data. The experimental breakup cross sections, obtained by integration of the experimental angular distributions extended to all angles assuming the CDCC calculation shape, are given in Table III.The calculated elastic scattering angular distributions are compared with the data obtained in the same experiment and reported previously [1]inFigs.7,8,9, and 10. For the sake of completeness, we present here the elastic scattering data at all four energies, i.e., 16, 20, 25, and 29 MeV. Since we wished to investigate the effect of coupling to breakup on the elastic scattering, we also performed one-channel (no coupling) calculations and calculations with coupling to direct excitation of the continuum only, omitting coupling to the 31+ resonance. All theoretical results, full CDCC, one-channel, and CDCC with coupling to direct breakup only are compared with the data in Figs. 7,8,9, and 10 for 16, 20, 25, and TABLE II. Optical model potentials for the 2H+psystem deduced by fitting existing data [38–42] adopting a Woods-Saxon potential (real volume and imaginary surface terms). The nuclear radius was RV(W)=rV(W)×11/3fm and the Coulomb radius was RC=1.30 ×11/3fm. E(MeV) V(MeV) rV(fm) aV(fm) W(MeV) rW(fm) aW(fm) 29 66.958 1.25 0.501 0.715 1.20 0.517 25 70.274 0.700 20 74.696 0.679 16 78.276 0.663 dσ/dΩc.m. (mb/sr) θc.m. (deg) E=25 MeVCDCC CDCC - resonant present data 0 10 20 30 40 50 0 20406080100 FIG. 5. Experimental and theoretical angular distributions in the center of mass for the breakup of 6Li on a proton target at 25 MeV (4.17 MeV/u). The experimental data, referring to the first kinematic solution, are shown by the filled red stars. The solid black line represents the full CDCC calculation. The dot-dashed red line denotes the result of a CDCC calculation taking into account coupling to the 31+resonant state only. 29 MeV, respectively. As can be seen, in general coupling to the continuum is strong and the full CDCC calculations describe the elastic scattering reasonably well at all energies. Moreover, we find that coupling to direct breakup makes a very slight change from the one-channel calculation and therefore the important coupling is that to the resonant breakup. dσ/dΩc.m. (mb/sr) θc.m. (deg) E=29 MeVCDCC CDCC - resonant present data 0 20 40 60 0 20 40 60 80 100 FIG. 6. Same as in Fig. 5but for 29 MeV (4.83 MeV/u). 054614-4 BREAKUP OF 6Li +pAT NEAR-BARRIER . . . PHYSICAL REVIEW C 95, 054614 (2017) dσ/dΩc.m.(mb/sr) θc.m.(deg) p(6Li,6Li)p, E=16 MeV CDCC 1 - channel CDCC - only direct coupling present data 1 10 102 103 104 0 20 40 60 80 100 120 140 160 180 FIG. 7. Elastic scattering of 6Li +p at 16 MeV (2.67 MeV/u). The data are compared with full CDCC calculations (solid black line), one-channel calculations (dot-dashed blue line), and calculations with coupling to direct breakup only (dashed green line). The uncertainty of the experimental data is included in the size of the stars. IV. DISCUSSION AND SUMMARY We have measured the exclusive breakup of 6Li on a proton target at two near-barrier energies, 25 and 29 MeV (4.17 and 4.83 MeV/u) in inverse kinematics. The αfragments were measured in the MAGNEX spectrometer spanning an angular range from 0 to 10◦, in coincidence with the deuteron dσ/dΩc.m.(mb/sr) θc.m.(deg) p(6Li,6Li)p, E=20 MeV CDCC 1 - channel CDCC - only direct coupling present data 1 10 102 103 104 0 20 40 60 80 100 120 140 160 180 FIG. 8. Same as in Fig. 7but for 20 MeV (3.33 MeV/u). dσ/dΩc.m.(mb/sr) θc.m.(deg) p(6Li,6Li)p, E=25 MeV CDCC 1 - channel CDCC - only direct coupling present data 1 10 102 103 104 0 20 40 60 80 100 120 140 160 180 FIG. 9. Same as in Fig. 7but for 25 MeV (4.17 MeV/u). fragments detected in a silicon detector fixed at 5◦.Dueto the specific experimental conditions, that is, the mask in front of the 5◦detector, events with energies corresponding to the second kinematic solution were not observed and the angular range of the measurement was limited to forward angles. In a global interpretation of the data within the CDCC approach, our study included comparisons between theory and simultaneous measurements of elastic scattering and breakup angular distributions as well as total breakup and absorption cross sections, the last two included in Table III. dσ/dΩc.m.(mb/sr) θc.m.(deg) p(6Li,6Li)p, E=29 MeV CDCC 1 - channel CDCC - only direct coupling present data 1 10 102 103 104 0 20 40 60 80 100 120 140 160 180 FIG. 10. Same as in Fig. 7but for 29 MeV (4.83 MeV/u). 054614-5 V. SOUKERAS et al. PHYSICAL REVIEW C 95, 054614 (2017) TABLE III. Reaction cross sections for the 6Li +psystem: Experimental breakup cross sections, σbr, CDCC breakup cross sections (in parentheses the sequential breakup cross section via the 31+resonance), σC br, absorption cross sections according to CDCC, σC abs, experimental absorption cross sections measured previously via the 6Li +p→4He +3He reaction, σabs [4]. E(MeV) σbr (mb) σC br (mb) σC abs (mb) σabs (mb) 29 370 ±64 269.4(143.3) 109.5 95 ±2 25 235 ±46 200.0(117.0) 133.0 131 ±6 20 102.9(37.5) 162.0 140 ±8 16 69.7(0.03) 130.7 111 ±2 Overall, the interpretation of the data in this framework was found to be satisfactory. In more detail, the agreement of the theoretical with the experimental elastic scattering angular distributions was good, while the description of the breakup angular distributions was reasonable but with some tendency of theory to underpredict the data. The effect of breakup coupling on the elastic channel was strong, with the most significant contribution coming from sequential breakup via the first resonance at 2.186 MeV. This is in accordance with similar findings for medium and heavy mass targets [22,23]. From an inspection of Table III, where in the third column we present total breakup cross sections and in parentheses sequential breakup cross sections via the 31+resonance, we can conclude that the sequential breakup accounts for ∼50% of the total breakup for the highest two energies, ∼38% at 20 MeV and almost zero for the lowest energy, 16 MeV. However, the importance of the influence of breakup coupling on the elastic scattering is not correlated with the magnitude of the breakup cross section; for example, at the lowest energy of 16 MeV coupling to the sequential breakup via the 31+ resonance had the strongest influence, while the cross section for this breakup mode was almost zero (see Table III), thus presenting an example of a “virtual” coupling effect. A similar situation was met with for the elastic scattering of 7Li from a proton target recently reported in Ref. [35]. In that case, the cross section for excitation of the first (7/2−)α+tresonance was determined to be ∼0.5 mb compared a total breakup of 66 mb, while the coupling to resonant breakup was found to be dominant. It is also important to make comparisons with other observables deduced from the CDCC calculations, for example, the absorption. In Table III, the calculated absorption cross sections are compared with experimental values for the 6Li +p→4He +3He reaction, the only other available reaction channel at these energies, measured simultaneously with the breakup but reported in Ref. [4]. The agreement with the data is very good, giving further support to a global interpretation of the 6Li +preaction in the CDCC framework and the validity of the experimental data. In summary, the present exclusive breakup measurements for the 6Li +p→α+d+pprocess, performed for the first time at near-barrier energies (∼5×VC), considered together with elastic scattering data and cross sections for the 6Li +p→4He +3He reaction channel, present in total good agreement with CDCC calculations. The cross sections for sequential breakup via the 31+resonance at 2.186 MeV are strong for 6Li incident energies of 29, 25, and 20 MeV and coupling to this breakup mode has the most important effect on the elastic scattering. 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