Interaction of 8 He with 208Pb at near-barrier energies: 4 He and 6 He production

PHYSICAL REVIEW C 98, 034615 (2018) Interaction of 8He with 208Pb at near-barrier energies: 4He and 6He production G. Marquínez-Durán,1I. Martel,1A. M. Sánchez-Benítez,2L. Acosta,3J. L. Aguado,1R. Berjillos,1A. R. Pinto,1T. García,1 J. A. Dueñas,4K. Rusek,5N. Keeley,6,*K. W. Kemper,7,5M. A. G. Álvarez,8M. J. G. Borge,9A. Chbihi,10 C. Cruz,9 M. Cubero,11,12,9J. P. Fernández-García,8B. Fernández-Martínez,13 J. L. Flores,14 J. Gómez-Camacho,13,8J. A. Labrador,13 F. M. Marqués,15 A. M. Moro,8M. Mazzocco,16 A. Pakou,17 V. V. Parkar,1,†N. Patronis,17 V. Pesudo,9D. Pierroutsakou,18 R. Raabe,19 R. Silvestri,18 N. Soi´ c,20 Ł. Standyło,5I. Strojek,6O. Tengblad,9R. Wolski,21,22 and Z. Abou-Haidar13 1Science and Technology Research Centre (STRC), University of Huelva, 21071 Huelva, Spain 2Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Facultad de Ciencias Experimentales, Universidad de Huelva, 21071 Huelva, Spain 3Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364, Distrito Federal 01000, Mexico 4Departamento Ingeniería Eléctrica y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, 21071 Huelva, Spain 5Heavy Ion Laboratory, University of Warsaw, ul. Pasteura 5a, 02-093 Warsaw, Poland 6National Centre for Nuclear Research, ul. Andrzeja Sołtana 7, 05-400 Otwock, Poland 7Department of Physics, Florida State University, Tallahassee, Florida 32306, USA 8Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, 41080 Seville, Spain 9Instituto de Estructura de la Materia, CSIC, 28006 Madrid, Spain 10GANIL, CEA and IN2P3-CNRS, B.P. 5027, 14076 Caen Cedex, France 11Escuela de Física, Universidad de Costa Rica, 11501 apdo. 2060 San José, Costa Rica 12CICANUM, Universidad de Costa Rica, 11502 apdo. 2060 San José, Costa Rica 13Centro Nacional de Aceleradores (Universidad de Sevilla, Junta de Andalucía, CSIC), 41092 Seville, Spain 14Departamento de Ingeniería Eléctrica, Universidad de Huelva, 21071 Huelva, Spain 15Laboratoire de Physique Corpusculaire, 14050 Caen Cedex, France 16Dipartimento di Fisica and INFN, Università di Padova, 35131 Padova, Italy 17Department of Physics and HINP, University of Ioannina, 45110 Ioannina, Greece 18INFN - Sezione di Napoli, Via Cintia, 80126 Napoli, Italy 19KU Leuven, Intituut voor Kern-en Stralingsfysica, Celestijnenlaan 200D, 3001 Leuven, Belgium 20Rudjer Boškovi´c Institute, Bijenicka 54, 10000 Zagreb, Croatia 21Institute of Nuclear Physics PAN, Kraków, Poland 22Flerov Laboratory of Nuclear Reactions, JINR, Dubna 141980, Russia (Received 7 June 2018; revised manuscript received 16 August 2018; published 28 September 2018) Angular distributions for the inclusive 4He and 6He production cross sections in the 8He +208Pb system at incident energies of 16 and 22 MeV measured at the SPIRAL facility of the GANIL laboratory are presented. Using a combination of kinematical arguments and distorted wave Born approximation (DWBA) calculations, neutron transfer reactions were inferred to be the dominant contributors to both inclusive cross sections. Modeldependent values for the ratios of two- to one-neutron stripping, σ2n/σ1n, were derived and compared with previous results for 8He and 6He projectiles incident on other heavy targets. Three- and four-neutron stripping were inferred to be the main processes leading to 4He production, although the exact mechanism remains to be elucidated. DOI: 10.1103/PhysRevC.98.034615 I. INTRODUCTION Recently, precise data for the elastic scattering of 8He from a 208Pb target at an incident energy of 22 MeV, slightly above the Coulomb barrier, were presented and compared with existing data for 6He +208Pb at the same incident energy *Corresponding author: nicholas.keele[email protected].pl †Present address: Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India. [1]. A larger total reaction cross section was obtained for 8He than for 6He, suggesting an increased neutron stripping cross section for 8He that more than compensates for an expected lower breakup cross section than 6He, due to its higher breakup threshold and probable weaker dipole coupling to the continuum. Some experimental studies of the reactions of 8He incident on heavy targets at near-barrier energies have already been performed. Direct and fusion-evaporation reactions for the 8He +208Pb system were studied at 26 MeV via γspectroscopy [2]. Although the statistics were low, the 2469-9985/2018/98(3)/034615(7) 034615-1 ©2018 American Physical Society G. MARQUÍNEZ-DURÁN et al. PHYSICAL REVIEW C 98, 034615 (2018) observed population of low-spin states in 209Pb suggests a strong 1nstripping process, with a cross section comparable to that for the most probable fusion-evaporation channel, 208Pb(8He,4n)212Po, to within a factor of about 2 in favor of fusion evaporation. In Refs. [3,4], measurements of heavy residue production in the 8He +197Au system at several near-barrier energies are presented. Excitation functions are reported which show that neutron stripping dominates over fusion for energies up to about 10 MeV above the barrier. Coupled reaction channels (CRC) calculations that describe the total neutron transfer strength provide a good simultaneous description of the fusion excitation function, suggesting that breakup is not as important for 8He as for 6He. A comparison between the fusion cross sections (σFus)forthe 4,6,8He +197Au systems showed that σFus for 6He and 8He are similar at energies below the barrier and larger than for 4He. In this work, we present inclusive 4He and 6He production angular distributions for the 8He +208Pb system at incident energies of 16 and 22 MeV. A combination of kinematics and calculations enables a number of conclusions to be drawn concerning the relative importance of neutron stripping reactions, as well as an upper limit on the fusion cross section at 22 MeV. II. EXPERIMENT AND DATA ANALYSIS The experiment was carried out at the SPIRAL facility of the GANIL laboratory in Caen, France, and a detailed description of the experimental setup was given in Refs. [1,5]. As shown in these works, the double-sided silicon strip detector E-Etelescopes of the GLORIA array [5] provided clear separation between the He isotopes produced in the interaction between the beam and target so that the 8He, 6He, and 4He yields were unambiguously extracted. The strip detectors are subdivided into pixels, defined as the intersection of a p strip (vertical) and an n strip (horizontal), see Ref. [5], with each pixel covering 3–4◦in the laboratory frame at the target. The Eand Estages of the telescopes were 40 μm and 1 mm thick, respectively. The rapid variation of the elastic scattering as a function of scattering angle required great care in determining the angle of each pixel since, as usual with radioactive beams, the beam spot on target was large, ∼3.5 mm in diameter. The procedure for establishing the detection angle of a given strip is given in Ref. [1] and relied on comparing a detailed simulation of the detection system with the elastic scattering in the region where it is dominated by Coulomb scattering. In addition to the previously reported elastic scattering data at a 8He incident energy of 22 MeV [1], elastic scattering data were also obtained at 16 MeV and 6He and 4He yields at both energies. Figure 1(a) shows the events from all the strip detectors gated on 4He at 22 MeV. The vertical axis is the total energy deposited in a given telescope as a function of the scattering angle. The intense horizontal line at the bottom of the figure corresponds to αparticles arising from fusion-evaporation events, matching very well the α-decay energies of 212Po. There are two other main groups, the first at scattering angles between 60 and 160◦from neutron transfer reactions and a second, weaker group at forward angles, between 20 and 40◦, from 8He →4He +4nbreakup. FIG. 1. (a) Total energy vs scattering angle for events gated on 4He produced in the 8He +208Pb interaction at an incident energy of 22 MeV. Regions corresponding to the different production mechanisms are labeled. (b) Number of counts vs energy for events gated on 4He summed over pixels at a scattering angle of θlab =94.5◦.The numbered arrows denote the energy of 4He ejectiles corresponding to the optimum Qvalues of Table II for the following reactions: (1) 208Pb(8He,4He)212Pb, (2) 208Pb(8He,5He →4He +n)211Pb, and (3) 208Pb(8He,6He∗1.8→4He +2n)210Pb. For reactions 2 and 3, the arrows mark the centers of the energy distributions of 4He arising from the decay of the 5He 3/2−ground-state resonance and the 6He 1.8-MeV 2+resonance, respectively; see text for further details. The narrow peak at approximately 8.8 MeV corresponds to αparticles from the decay of the ground state of 212Po produced by fusion evaporation. These regions are drawn following many published heavyion reaction data, where it is always found that for energies below the Coulomb barrier the transfer cross section peaks at 180◦and falls off more or less rapidly as the scattering angle decreases until it becomes negligible at forward angles. For incident energies just above the Coulomb barrier, the transfer angular distributions exhibit the classical bell-shaped peak structure, with the peak angle gradually moving to more forward angles as the incident energy increases. Both incident energies studied in this experiment were sufficiently low that there was a clear kinematic separation between transfer and breakup and any 4He and 6He events at forward angles necessarily arise from breakup processes since the transfer cross sections will be negligible in this region. There may be some slight overlap of breakup and transfer contributions 034615-2 INTERACTION OF 8He WITH 208Pb AT NEAR- … PHYSICAL REVIEW C 98, 034615 (2018) FIG. 2. (a) Total energy vs scattering angle for events gated on 6He produced in the 8He +208Pb interaction at an incident energy of 22 MeV. Regions corresponding to the different production mechanisms are labeled. (b) Number of counts vs energy for events gated on 6He summed over pixels at a scattering angle of θlab =70◦.The numbered arrows denote the energy of 6He ejectiles corresponding to the optimum Qvalues of Table II for the following reactions: (1) 208Pb(8He,6He)210Pb and (2) 208Pb(8He,7He →6He +n)209Pb. For reaction 2, the arrow marks the center of the energy distribution of 6He arising from the decay of the 7He 3/2−ground-state resonance; see text for further details. but this is not expected to be significant. The shapes of the extracted inclusive angular distributions and distorted wave Born approximation (DWBA) calculations provide a posteriori justification for these conclusions. The energy spectrum of events gated on 4He from several pixels around θlab =94.5◦ added together is given in Fig. 1(b).InFig.2, we show similar plots for events gated on 6He. In Fig. 3, we present the elastic scattering data for an incident 8He energy of 16 MeV, together with the previously published data at 22 MeV [1]. The solid curves represent optical model fits to the data. The 22-MeV curve employs the potential parameters from Table Iof Ref. [6]. These also give a reasonable description of the data at 16 MeV but the best fit, displayed on Fig. 3as the solid red curve, was obtained by increasing the imaginary well depth W to 50.0 MeV. The dashed red curve denotes the 16-MeV elastic scattering angular distribution calculated using the same optical potential parameters as at 22 MeV. There is a small but noticeable difference in the angular distribution calculated with these parameters compared to the best fit, 20 40 60 80 100 120 140 160 θc.m. (deg) 10-2 10-1 100 Ratio to Rutherford FIG. 3. Angular distributions for the 8He +208Pb elastic scattering at 16 MeV (open circles) and 22 MeV [1] (filled circles). The solid curves denote optical model fits to the data; see text for details. The dashed curve denotes the 16-MeV elastic scattering angular distribution calculated using the same optical potential parameters as at 22 MeV. leading to an ∼8% increase in χ2and a ∼24% decrease in total reaction cross section (σR) compared to the best-fit values. The σRextracted from the optical model fits are given in Table I. The uncertainties represent the effect of varying Wsuch that χ2increased by 10% compared to the minimum values. Ratios of the number of 6He to 8He and 4He to 8He detected, the latter excluding the 4He at low energies arising from fusion evaporation, were formed for each pixel and the results converted into laboratory frame absolute cross sections by multiplying by the appropriate elastic scattering cross-section angular distributions obtained from the optical model fits to the elastic scattering data, suitably transformed to the laboratory frame. The resulting angular distributions are plotted in Fig. 4. Errors are purely statistical. It is apparent that TABLE I. Integrated cross sections for 6He (σ6He)and4He (σ4He) production obtained from fits to the experimental angular distributions shown in Fig. 4. Also given are the total reaction cross sections from the optical model fits to the elastic scattering data plotted on Fig. 3(σR) and total 1n-stripping cross sections (σ1n) from the DWBA calculations described in Sec. III, while σFus = σR−(σ6He +σ4He) represents an upper limit on the fusion cross section. Elab (MeV) σ1n(mb) σ6He (mb) σ4He (mb) σR(mb) σFus (mb) 16 90 ±3 203+10 −28 26 ±5 254 ±60 25+61 −66 22 292 ±61 871 ±31 393+10 −33 1529 ±40 265+52 −60 034615-3 G. MARQUÍNEZ-DURÁN et al. PHYSICAL REVIEW C 98, 034615 (2018) 0 10 20 30 40 30 60 90 120 150 180 θ lab (deg) 0 50 100 150 dσ/dΩ (mb/sr) (a) (b) FIG. 4. Laboratory frame angular distributions of total 6He (filled circles) and 4He (open circles) yields at 16 (a) and 22 MeV (b). The solid curves represent fits to the data while the dashed curves and gray shaded areas denote the results of 208Pb(8He,7He)209Pb singleneutron stripping DWBA calculations including the uncertainties due to the use of different distorting potentials in the exit channels (see text for details). the shapes of the angular distributions (with the exception of the 4He yield at 16 MeV where the statistics are too low to determine accurately the shape) are characteristic of transfer reactions. However, it will be noted that the angular distributions displayed in Fig. 4are confined to angles θlab >∼40◦ whereas the measurements extend down to θlab =20◦, as seen in Figs. 1and 2. This cutoff was imposed by the angular resolution of the pixels of the GLORIA array. At forward angles (in this case, for angles θlab 40◦) the elastic scattering cross section varies too rapidly as a function of angle over the range subtended by a pixel for a reliable absolute cross section to be extracted from the 6He to 8He and 4He to 8He ratios (the ratios themselves are, of course, unaffected by this problem). At larger angles, the variation of the elastic scattering cross section as a function of angle is slow enough not to cause a problem. This does mean that we are, unfortunately, unable to make any quantitative deductions concerning the contribution of breakup to the 6He and 4He yields. The solid curves on Fig. 4represent fits to the experimental angular distributions. At 16 MeV, the 6He yield was fitted with a third-order Legendre polynomial which reproduces the shape very well. The 4He yield was simply fitted by two straight line segments, 0 mb/sr for angles 0◦<θ lab <50◦and 2.5 mb/sr for 50◦<θ lab <180◦.At22MeV,the6He yield was well reproduced by the sum of two Lorentzian peaks while the 4He yield was well described by a single Lorentzian. The integrated cross sections obtained from these fits are given in Table I. The uncertainties were estimated by scaling the fits to give χ2values 20% greater than the minimum values. The asymmetric errors on some values reflect the scatter in the points, emphasized somewhat by this procedure. III. DISCUSSION In Tables II and III,wegivetheQvalues for the various direct reaction processes that can yield 4He and 6He nuclei in the exit channel, respectively, together with the optimum Q values for the A(a,b)Btransfer processes calculated according to the Brink matching rules [7,8]: Qopt =(ZbZB−ZaZA)e2/R −1 2mv2,(1) where the charge on nucleus iis denoted by Zie, the relative velocity of the two nuclei in the region of interaction (separated by distance R)byv, and the mass of the transferred particle by m. For transfers of neutron(s), the first term is zero so Qopt will always be negative in these cases. The relative velocity vmay be calculated as [9] v=[2(Ec.m.−EB)/μ]1/2,(2) where EBand μare the Coulomb barrier and reduced mass of the projectile-target system, respectively. We took a Coulomb barrier of 18 MeV, similar to the empirical result of Ref. [10] for the 6He +208Pb system, when calculating the relative velocity of the 8He +208Pb nuclei. The Qopt values given are for an incident 8He energy of 22 MeV. Tables II and III indicate that the 4He production is the most complicated of the two, since more processes may, in principle, contribute. However, Fig. 1(a) suggests that the 4He arising from breakup are well separated from those produced by transfer events. Three-body kinematics calculations with the code PAKINE3[11] support this suggestion, indicating that at the angles where we have extracted the angular distributions the contribution to the 4He yield from breakup should be negligible. The three numbered arrows on Fig. 1(b) mark the energies of 4He ejectiles corresponding to Qopt for the following reactions: (1) 208Pb(8He,4He)212Pb, (2) 208Pb(8He,5He →4He +n)211Pb, and (3) 208Pb(8He,6He∗ 1.8→4He +2n)210Pb. For reactions 2 and 3, the markers are positioned at the centers of the range of allowed 4He energies from the decay of the 3/2−ground-state resonance of 5He and the 1.8-MeV 2+resonance of 6He, respectively, calculated with PAKINE3. These distributions are approximately ±3.0 and ±3.7 MeV wide, respectively. The possibility of Coulomb postacceleration was neglected. These kinematic considerations are consistent with the shape of the angular distribution in Fig. 4, indicating a dominant contribution from transfer reactions to the 4He production mechanism. We may make one further deduction concerning the 4He production. Despite being the best matched of the three transfer processes that yield 4He in the exit channel, the 208Pb(8He,6He∗ 1.8→4He +2n)210Pb reaction is unlikely to 034615-4 INTERACTION OF 8He WITH 208Pb AT NEAR- … PHYSICAL REVIEW C 98, 034615 (2018) TABLE II. Qvalues for the various processes that can lead to the production of 4He nuclei in the interaction of a 8He beam with a 208Pb target. Optimum Qvalues, Qopt, calculated according to the Brink [7,8] matching rules are also given for the transfer reactions. Reaction Q(MeV) Qopt (MeV) 208Pb(8He,4He)212Pb +14.99 −1.7 208Pb(8He,5He →4He +n)211Pb +9.12 −1.2 208Pb(8He,6He∗ 1.8→4He +2n)210Pb +5.20 −0.8 208Pb(8He,8He∗→4He +4n)208Pb −3.11 208Pb(8He,8He∗→(6He∗ 1.8→4He +2n)+2n)208Pb −3.94 contribute significantly due to the small spectroscopic factor for the 8He |6He∗ 1.8+2noverlap [13]. Coupled channel Born approximation (CCBA) calculations including direct transfer to both the 0+ground state and 1.8-MeV 2+excited state of 6He and the inelastic coupling between them bears this out, predicting negligible cross sections for hypothetical states in 210Pb at excitation energies such that the reaction Qvalue is close to Qopt. We may thus infer that the main production mechanisms for 4He are the 4nand 3nstripping reactions, preferentially populating states in the residual 212Pb and 211Pb nuclei at excitation energies centered at about 17 and 10 MeV, respectively. However, it is not possible to infer anything about the details of the mechanism, i.e., whether the reactions proceed as direct, one-step transfers or sequential transfer of, e.g., two dineutron-like clusters in the case of the 4nstripping. For the 6He production, Fig. 2(a) suggests that 6He arising from breakup are also well separated from those produced by transfers, and three-body kinematics calculations again support this, indicating that any breakup contribution to the extracted 6He angular distributions should be negligible, breakup being essentially confined to forward angles. The numbered arrows on Fig. 2(b) mark the energies of 6He ejectiles corresponding to Qopt for the following reactions: (1) 208Pb(8He,6He)210Pb and (2) 208Pb(8He,7He →6He + n)209Pb. For reaction 2, the marker is positioned at the center of the range of allowed 6He energies from the decay of the 7He 3/2−ground-state resonance, again calculated with PAKINE3. The distribution is approximately ±2.0 MeV wide. We can make some further deductions concerning the 6He production, although these will necessarily be more or less model dependent. The 1nstripping can be calculated rather accurately using the DWBA since the necessary spectroscopic factors are known and the reaction is well Qmatched and thus most likely to be a one-step transfer process. Such TABLE III. Qvalues for the various processes that can lead to the production of 6He nuclei in the interaction of a 8He beam with a208Pb target. Optimum Qvalues, Qopt, calculated according to the Brink [7,8] matching rules are also given for the transfer reactions. Reaction Q(MeV) Qopt (MeV) 208Pb(8He,6He)210Pb +7.00 −0.8 208Pb(8He,7He →6He +n)209Pb +1.40 −0.4 208Pb(8He,8He∗→6He +2n)208Pb −2.14 calculations were therefore performed using the code FRESCO [12], with 8He |7He +nand 209Pb |208Pb +noverlaps taken from Refs. [13] and [14], respectively. The following states in 209Pb were included: 0.0 MeV 9/2+,0.78MeV 11/2+, 1.42 MeV 15/2−,1.57MeV5/2+,2.03MeV1/2+, 2.49 MeV 7/2+, and 2.54 MeV 3/2+. The entrance channel optical potentials were taken from Table Iof Ref. [6], with the imaginary well depth at 16 MeV increased to 50 MeV, as described in Sec. II. Since the exit channel potential is unknown, involving as it does the unbound 7He nucleus, the effect of employing several different choices was investigated: (1) the same parameters as in the entrance channel, (2) the global 6Li parameters of Cook [15], (3) the global 7Li parameters of Cook [15], and (4) the 16 and 22 MeV 6He +208Pb parameters of Ref. [16] for the calculations at incident 8He energies of 16 and 22 MeV, respectively. It was found that the cross sections calculated using these exit channel potentials all lie between two extreme values at both energies, those calculated with the entrance channel parameters (the smallest) and those calculated with the global 6Li parameters of Ref. [15] (the largest). The summed angular distributions for the calculations using these parameters, transformed into the laboratory reference frame, are plotted on Fig. 4as the dashed lines with the gray areas denoting the degree of uncertainty. Note that the angular distributions are for the 7He particle, although given the large difference in mass between the 6He and neutron fragments produced by its decay the 6He distribution should not differ significantly. Monte Carlo calculations of the 6He angular distribution, similar to those performed in Ref. [17] for the single-neutron stripping and pickup reactions in the 7Be +58Ni system, using the calculated 7He angular distributions as input confirm this. The mean values of the summed integrated cross sections are given in Table Iwith uncertainties indicating the range covered by the use of the different exit channel potentials. We thus see that 44+3 −6% and 33 ±7% of the total 6He production cross section may be attributed to 1nstripping at 8He incident energies of 16 and 22 MeV, respectively, the proportion diminishing slightly (within the uncertainty) as the beam energy is increased above the Coulomb barrier. The remaining cross section must come almost exclusively from 2nstripping since, as Fig. 2(b) shows, breakup may be ruled out as a significant contributor on purely kinematic grounds. It is also possible to estimate an upper limit for the total fusion cross section by subtracting the integrated 6He and 4He cross sections from the total reaction cross section extracted from the optical model fits to the elastic scattering angular 034615-5 G. MARQUÍNEZ-DURÁN et al. PHYSICAL REVIEW C 98, 034615 (2018) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Ec.m./EB 100 101 102 103 σ (mb) FIG. 5. Excitation functions of the fusion (filled circles) and neutron transfer (filled triangles) cross sections for the 8He +197Au system [4] compared with the present results for the upper limit on fusion (open circle) and combined 4He and 6He cross sections (open triangles) for the 8He +208Pb system. distributions. Other contributions to the total reaction cross section should be small, DWBA estimates of the cross sections for inelastic scattering to the 2.60-MeV 3−, 3.09-MeV 5−, and 4.18-MeV 2+states of 208Pb being negligible, for example. The resulting values are given in Table I. However, the uncertainty in the value at 16 MeV is such that we cannot make any meaningful deduction concerning the fusion cross section at this energy. We may compare our results for the 8He +208Pb system with those obtained by Lemasson et al. [3,4]for8He +197Au. The measured fusion and transfer excitation functions of Ref. [4] are plotted in Fig. 5, together with the upper limits on fusion and the sum of the 4He and 6He yields from this work as a function of Ec.m./EB, where EBis the nominal Coulomb barrier (EB=19.84 MeV for 8He +197Au and EB= 20.37 MeV for 8He +208Pb). In this comparison, we have used the nominal barriers since only their difference (due to the different targets) is important here. The upper limit on the fusion cross section at 22 MeV is in good agreement with the data of Lemasson et al. [4]. The sum of the 4He and 6He production cross sections agrees reasonably well with the trend of the transfer cross-section data of Ref. [4], being approximately 25% larger at both 16 and 22 MeV. This could reflect a larger 1n-stripping cross section for the 208Pb target due to the fragmentation of the single-neutron levels in 198Au. Lemasson et al. [3] also give model-independent lower limits on the ratio of 2nto 1ntransfer cross sections, their only assumption being that any contributions to the observed 198Au, 199Au, and 198mAu residue cross sections from 3nand 4ntransfers could be neglected. We may carry out a similar exercise, although the result is necessarily model dependent since it relies on the DWBA calculations for the 1nstripping cross sections. We further make the assumption, based on our inferences concerning the 4He production, that 2nstripping only contributes significantly to the 6He cross section so that σ2n=σ6He −σ1n. We obtain values of σ2n/σ1n=1.26+0.12 −0.31 and 1.98 ±0.48 at 8He incident energies of 16 and 22 MeV, respectively, considerably larger than the results of Ref. [3] which range from about 0.1 to 0.3 but nevertheless compatible with them since they are lower limits. However, the rather large difference between our values and those of Lemasson et al. could indicate that either their assumption that contributions from 3nand 4ntransfers could be neglected or our assumptions regarding 2ntransfer require revision. Only full coincidence measurements, unfortunately not possible with currently available 8He beam intensities, will be able to provide a definitive answer. Our results for the σ2n/σ1nratio may also be compared with similar values obtained with 6He beams incident on heavy targets at energies close to the Coulomb barrier. A series of αneutron coincidence measurements carried out at the TwinSol facility of the University of Notre Dame for the 6He +209Bi system [18–20]gaveavalueofσ2n/σ1n=2.58 ±0.77 for a beam energy of 22 MeV. Standyło et al. [21] obtained a value of about 1.4 for the same ratio in the 6He +206Pb system at an incident 6He energy of 18 MeV, although like the present result for 8He +208Pb this is also model dependent. Both 6He values are fully compatible with our 8He results. IV. CONCLUSIONS The inclusive 4He and 6He yields were measured for the 8He +208Pb system at 8He incident energies of 16 and 22 MeV. Employing a combination of kinematics and model calculations it was possible to draw some model-dependent but nevertheless reasonably robust conclusions as to the production mechanisms. It is clear from the discussion in the previous section that breakup can only make a small contribution to the inclusive 4He and 6He cross sections in this system at near-barrier energies. First, any breakup events seem to be kinematically rather well separated from those due to transfer processes. Second, the shapes of the angular distributions (and their evolution with increasing beam energy) are consistent with those of transfer reactions. Finally, the upper limit on the fusion cross section at 22 MeV obtained by subtracting the integrated 4He and 6He cross sections from the total reaction cross section extracted from an optical model fit to the elastic scattering data leaves little or no room for a significant breakup cross section when compared to the measured fusion cross sections for the 8He +197Au system [4]. The σ2n/σ1nratios obtained from our analysis, while model dependent since they rely on calculated values for σ1n,are compatible with the model-independent lower limits obtained by Lemasson et al. [3]forthe8He +197Au system. They are also compatible with the results for the 6He +209Bi [18–20] and 6He +206Pb [21] systems. This is consistent with the intriguing possibility that the structure of 8He may be represented as a 4He core plus two dineutron-like clusters arranged on opposite sides of the core, somewhat similar to the model proposed by Nesterov et al. [22]. Given that the matching 034615-6 INTERACTION OF 8He WITH 208Pb AT NEAR- … PHYSICAL REVIEW C 98, 034615 (2018) conditions for 1nand 2nstripping are similar for 6He and 8He (they are somewhat better matched for 8He) the cross sections should roughly scale according to the spectroscopic factors. In this simple picture, the spectroscopic factors for 1n and 2nstripping for 8He would both be twice those for 6He, since the probability of stripping either a single neutron or a dineutron-like cluster is twice as large for 8He as it is for 6He. The σ2n/σ1nratio would then be the same for both projectiles, as is apparently the case. However, the reality is presumably more complicated since while the empirical spectroscopic factors for the 8He |7He +nand 6He |5He +noverlaps do differ by approximately a factor of 2 [23], those for the 8He |6He +2nand 6He |4He +2nare about the same [23]. The apparent similarity of the σ2n/σ1nratios for the two isotopes could possibly be explained by an increased importance of two-step neutron stripping for 8He, but this remains to be confirmed. Also, the uncertainties in the transfer cross sections are at present still too large to draw firm conclusions. Nevertheless, it is clear that for 8He incident on a208Pb target the breakup cross section must be considerably smaller than the values obtained for the 6He +206Pb (151 mb at 18 MeV, calculated [21]) or 6He +209Bi (205 ±65 mb at 22.5 MeV, measured [20]) systems. Definitive conclusions will have to await the availability of more intense 8He beams than those currently available to allow multiple αor 6He plus neutron coincidence measurements although, as this work has shown, much can be inferred from inclusive charged-particle measurements by making physically reasonable assumptions. ACKNOWLEDGMENTS The authors would like to thank the staff of the GANIL accelerator facility for providing the high-quality 8He beam. This work was supported in part by Grants No. FPA-2010- 22131-CO2-01 (FINURA) and No. FPA2013-47327-C2-1-R from the Spanish Ministry of Economy and Competitiveness, UNAM-PAPIIT IA103218 (Mexico); Grant No. N202 033637 from the Ministry of Science and Higher Education of Poland; the National Science Centre of Poland under Contracts No. 2013/08/M/ST2/00257 (LEA-COPIGAL) and No. 2014/14/M/ST2/00738 (COPIN-INFN Collaboration); and Grant No. EUI2009-04163432 (EUROGENESIS) from the European Science Foundation. [1] G. Marquínez-Durán, I. Martel, A. M. Sánchez-Benítez, L. Acosta, R. Berjillos, J. Dueñas, K. Rusek, N. Keeley, M. A. G. Alvarez, M. J. G. Borge et al.,Phys.Rev.C94,064618 (2016). [2] Z. Podolyák, P. M Walker, H. Mach, G. de France, G. Sletten, F. Azaiez, J. M. Casandjian, B. Cederwall, D. M. Cullen, Zs. Dombrádi et al.,Nucl. Instrum. Methods Phys. Res. A 511,354 (2003). [3] A. Lemasson, A. Navin, M. Rejmund, N. Keeley, V. Zelevinsky, S. Bhattacharyya, A. Shrivastava, D. Bazin, D. Beaumel, Y. Blumenfeld et al.,Phys. Lett. B 697,454 (2011). [4] A. Lemasson, A. Shrivastava, A. Navin, M. Rejmund, N. Keeley, V. Zelevinsky, S. Bhattacharyya, A. Chatterjee, G. de France, B. Jacquot et al.,Phys.Rev.Lett.103,232701 (2009). [5] G. Marquínez-Durán, L. Acosta, R. Berjillos, J. A. Dueñas, J. A. Labrador, K. Rusek, A. M. Sánchez-Benítez, and I. Martel, Nucl. Instrum. Methods Phys. Res. A 755,69 (2014). [6] G. Marquínez-Durán, N. Keeley, K. W. Kemper, R. S. Mackintosh, I. Martel, K. Rusek, and A. M. Sánchez-Benítez, Phys. Rev. C 95,024602 (2017). [7] D. M. Brink, Phys. Lett. B 40,37 (1972). [8] J. L. C. Ford, Jr., K. S. Toth, G. R. Satchler, D. C. Hensley, L. W. Owen, R. M. DeVries, R. M. Gaedke, P. J. Riley, and S. T. Thornton, Phys. Rev. C 10,1429 (1974). [9] C. Olmer, M. Mermaz, M. Buenerd, C. K. Gelbke, D. L. Hendrie, J. Mahoney, D. K. Scott, M. H. Macfarlane, and S. C. Pieper, Phys. Rev. C 18,205 (1978). [10] K. Rusek, N. Alamanos, N. Keeley, V. Lapoux, and A. Pakou, Phys. Rev. C 70,014603 (2004). [11] P. A. Assimakopoulos, Comput. Phys. Commun. 10,385 (1975). [12] I. J. Thompson, Comput. Phys. Rep. 7,167 (1988). [13] N. Keeley, F. Skaza, V. Lapoux, N. Alamanos, F. Auger, D. Beaumel, E. Becheva, Y. Blumenfeld, F. Delaunay, A. Drouart et al.,Phys. Lett. B 646,222 (2007). [14] D. G. Kovar, N. Stein, and C. K. Bockelman, Nucl. Phys. A 231, 266 (1974). [15] J. Cook, Nucl. Phys. A 388,153 (1982). [16] A. M. Sánchez-Benítez, D. Escrig, M. A. G. Álvarez, M. V. Andrés, C. Angulo, M. J. G. Borge, J. Cabrera, S. Cherubini, P. Demaret, J. M. Espino et al.,Nucl. Phys. A 803,30 (2008). [17] M. Mazzocco, D. Torresi, D. Pierroutsakou, N. Keeley, L. Acosta, A. Boiano, C. Boiano, T. Glodariu, A. Guglielmetti, M. La Commara et al.,Phys.Rev.C92,024615 (2015). [18] J. P. Bychowski, P. A. DeYoung, B. B. Hilldore, J. D. Hinnefeld, A. Vida, F. D. Becchetti, J. Lupton, T. W. O’Donnell, J. J. Kolata,G.Rogachevet al.,Phys. Lett. B 596,26 (2004). [19] P. A. DeYoung, P. J. Mears, J. J. Kolata, E. F. Aguilera, F. D. Becchetti, Y. Chen, M. Cloughesy, H. Griffin, C. Guess, J. D. Hinnefeld et al.,Phys.Rev.C71,051601(R) (2005). [20] J. J. Kolata, H. Amro, F. D. Becchetti, J. A. Brown, P. A. DeYoung, M. Hencheck, J. D. Hinnefeld, G. F. Peaslee, A. L. Fritsch, C. Hall et al.,Phys.Rev.C75,031302(R) (2007). [21] Ł. Standylo, L. Acosta, C. Angulo, R. Berjillos, J. A. Duenas, M. S. Golovkov, N. Keeley, T. Keutgen, I. Martel, M. Mazzocco et al.,Phys. Rev. C 87,064603 (2013). [22] A. V. Nesterov, V. S. Vasilevsky, and O. F. Chernov, Phys. At. Nucl. 64,1409 (2001). [23] N. Keeley, N. Alamanos, K. W. Kemper, and K. Rusek, Prog. Part. Nucl. Phys. 63,396 (2009). 034615-7