Breakup mechanisms in the 6He+64Zn reaction at near-barrier energies
J. P. Fernández-García, A. Di Pietro, P. Figuera, J. Gómez-Camacho, M. Lattuada, J. Lei, A. M. Moro, M. Rodríguez-Gallardo, V. Scuderi
aa r X i v : . [ nu c l - e x ] J u l Breakup mechanisms in the He+ Zn reaction at near-barrier energies
J. P. Fern´andez-Garc´ıa, ∗ A. Di Pietro, P. Figuera, J. G´omez-Camacho,
M. Lattuada,
3, 4
J. Lei, A. M. Moro, M Rodr´ıguez-Gallardo, and V. Scuderi Departamento de FAMN, Universidad de Sevilla, Apartado 1065, E-41080 Seville, Spain Centro Nacional de Aceleradores, Universidad de Sevilla, Junta de Andaluc´ıa-CSIC, 41092 Sevilla, Spain INFN, Laboratori Nazionali del Sud, via S. Sofia 62, 1-95123 Catania, Italy Dipartamento di Fisica e Astronomia, via S. Sofia 64, I-95123 Catania, Italy Institute of Nuclear and Particle Physics, and Department ofPhysics and Astronomy, Ohio University, Athens, Ohio 45701, USA (Dated: July 20, 2020)New experimental results for the elastic scattering of He on Zn at incident energies of 15.0 and18.0 MeV and He at 17.5 MeV along with results already published at 10.0 and 13.6 MeV, arepresented. Elastic and α experimental cross sections are compared with coupled-reaction-channel,continuum-discretized coupled-channel and a DWBA inclusive-breakup models. The large yield of α particles observed at all measured energies can be explained by considering a non-elastic breakupmechanism. I. INTRODUCTION
The understanding of peripheral heavy-ion collisionprocesses in general, and elastic scattering in particu-lar, is an important part of the overall understandingof heavy-ion reaction dynamics and its dependence onthe structure of the colliding nuclei. Indeed, most reac-tion theories require as a prerequisite for their applicationthe knowledge of the optical potentials derived from theelastic scattering of the particles involved. Despite beinga peripheral process, elastic scattering shows direct evi-dence of the internal structure of the colliding nuclei; oneexample is given by the elastic scattering involving halonuclei as projectiles. Many experimental and theoreti-cal studies of scattering involving halo nuclei on varioustarget masses have been performed so far and completereviews can be found in [1–3]. The dynamics of the elas-tic scattering process has shown many features related tothe peculiar characteristics of these nuclei. The resultsof these studies can be summarized as follows: the lowbinding energy of the halo nuclei enhances the probabilityof breakup; as a consequence, reduced elastic scatteringand large total reaction cross sections, with respect to thecollision induced by the well bound core nucleus on thesame target and E c . m . , are found for all the investigatedsystems.Coupling to nuclear and Coulomb breakup plays a rel-evant role; it modifies the elastic cross section especiallyin the region of interference between the nuclear andCoulomb amplitudes, resulting in a damped Coulomb-nuclear interference peak. The size of the effect dependsupon the B(E1) strength near the threshold of the haloprojectile and upon the charge of the target [4–7].Coupling to transfer has also been found to influenceelastic scattering. The role of coupling of one-neutrontransfer to bound states of the target nucleus has beendiscussed in [2] and it was found to be significant; the ef- ∗ [email protected] fect depends on the detailed nuclear structure of the tar-get nucleus. In the case of He-induced collisions the rel-evance of the two-neutron (2 n ) transfer channel has beenobserved [8, 9]. In [10, 11] the effect of two-neutron trans-fer channels on elastic and α -particle production cross-section was investigated for the reaction He+
Pb andfound to be important. The coupling with these channelsproduce a strong effect on the elastic cross section, givinggood agreement with the data. Moreover, it explains theenergy and angular distribution of the α -particles pro-duced in this reaction.In reactions induced by He, all the aforementioned ef-fects seem to be equally important and need to be consid-ered if a full account of the experimental results is sought.In the present paper new results of elastic scattering datafor the He+ Zn reaction at E beam = 15.0 and 18.0 MeVmeasured with high accuracy are reported as well as theenergy distribution of the α -particles coming from theinclusive breakup of He at the same energies.In order to fully investigate and understand the var-ious aspects of the reaction dynamics of the He two-neutron halo nucleus, the present experimental data,together with results of , He+ Zn already published[9, 12, 13], have been described using different theo-ries. This was necessary since, at present, one the-ory that is able to describe all the experimental observ-ables is not available. Such a complete theoretical anal-ysis has been performed within Optical Model (OM),Continuum-Discretized Coupled-Channel (3-body and 4-body CDCC) and Coupled-Reaction-Channel (CRC) for-malisms. Moreover, the α -particle spectra emitted in thereactions and reported in [9, 13] were theoretically ana-lyzed considering, in addition to the elastic breakup con-tributions calculated with the CDCC method, the con-tribution of non-elastic breakup, computed according tothe formalism proposed in [14], and 2n transfer calculatedwith CRC.The paper is organized as follows: in Sec. II theexperiment is described. In Sec. III the results ofthe different theoretical approaches used are re-ported. In Subsec. III.1 the He+ Zn and He+ Zndata are analyzed under the Optical Model (OM)framework. The subsequent paragraphs report on:Continuum-Discretized Coupled-Channel (Sec. III.2),Coupled-Reaction-Channel (Sec. III.3) and non-elasticbreakup (Sec. III.4) calculations for He+ Zn. Finally,Sec. IV is devoted to summary and conclusions.
II. EXPERIMENTAL DATA AND SET-UP
The experiments , He+ Zn were performed at theCentre de Recherches du Cyclotron at Louvain la Neuve(Belgium) in 2004. A radioactive beam of He at E beam = 15.0 and 18.0 MeV with an average intensity of 3 × pps, and in addition a stable beam of He at E lab = 17.5MeV, were used. In these experiments the fusion exci-tation function as well as the α -particle angular distri-butions were measured and reported in a previous paper[13]. In Fig. 1, a schematic view of the experimentalset-up is shown. The target used was a 530 µ g/cm self-supporting Zn foil; it was tilted at ± ◦ with respectto the y-axis (vertical direction) in order to allow mea-suring at laboratory angles around 90 ◦ . Considering thetarget thickness, the energy at the center of the targetwas E lab = 14.85 and 17.9 MeV for He and 17.4 MeVfor He. Since the target was not rotating around itscenter, but around its bottom-edge, by changing the tar-get angle from +45 ◦ to -45 ◦ , it was possible to changethe target-detector distance and, as a consequence, thedetector angles. This allowed to measure the elastic scat-tering angular distribution in a wider angular range, andto reduce the angular gaps from one detector array to theother.Three arrays of silicon strip detectors consisting ofseven sectors of LEDA-type [15] and two Single-SidedSilicon Strip Detectors (SSSSDs) 50 ×
50 mm were used.The first array consisted of four LEDA sectors, 300 µ mthick, placed in a symmetric configuration with eachsector normal to the beam direction (up, down, left,right) at a distance of about 600 mm or 630 mm from thetarget (depending upon the target angle), covering theoverall laboratory angular range 5 ◦ ≤ θ ≤ ◦ . Such aconfiguration allowed to monitor the beam misalignmentand to normalize the cross-sections to the Rutherfordscattering. Other three LEDA sectors, 500 µ m thick,were angled at 45 ◦ with respect to the beam direction.They were placed close to the target (130 and 160 mmdepending upon the target angle) and were coveringan overall angular range of approximately 18 ◦ ≤ θ ≤ ◦ . This configuration allowed a very large solid anglecoverage. The two SSSSDs detectors were placed around90 ◦ , parallel to the beam axis, and covering the overallangular range 67 ◦ ≤ θ ≤ ◦ . The distance betweenthe detector active area and the target was about85 mm for both SSSSDs. Helium was identified andclearly separated from Hydrogen by the ToF techniqueusing as time reference the RF signal of the cyclotron.Time resolution was insufficient to separate different helium isotopes, therefore the Helium spectrum included α -particles and elastically scattered He.Rutherford scattering on a Au target along with a fullMonte Carlo simulation of the set-up was used to deducethe angle and solid angle of each detector strip. Oncethe geometry of the set-up was deduced for the two an-gular settings of the target, the full angular distributionsof , He+ Zn were obtained by normalizing the elasticscattering data at smaller angles ( θ ≤ ◦ ) to the Ruther-ford cross-section, without further adjustment.A cross-check of the data published in [9, 12] using thenew Monte Carlo code was performed. By applying thenew simulations to deduce the solid angles for the set-upused in [9, 12], a maximum difference of 5% in the experi-mental angular distribution at E lab = 13.5 MeV is found,with respect to those already published in [9, 12]. Thisis within the experimental error bar reported in [9, 12]which accounted for possible systematic errors in the de-termination of the cross-section. In the data from [9, 12]an additional systematic error in the absolute normali-sation, of the order of 5%, could be present as due tolack of data at very small angles where the cross-sectionis Rutherford. FIG. 1. Sketch of the experimental setup with the targettilted at +45 ◦ (a) and -45 ◦ (b). III. THEORETICAL CALCULATIONS
In this section we compare the present experimentaldata as well as the one previously published in [9, 12] withdifferent theoretical calculations in order to understandthe reaction mechanisms governing in the He+ Zn re-action at energies around the Coulomb barrier. First, wepresent an Optical Model (OM) analysis of the He+ Znelastic cross sections. The potentials obtained from thesecalculations will be later used in the few-body calcula-tions performed for the He+ Zn reaction.As a first approach to analyze the He+ Zn data, OMcalculations will be performed in Subsec. III.1. Then, wewill focus on the measured α cross sections. Since thesedata are inclusive with respect to the (unobserved) neu-trons, they contain in general two distinct contributions,namely, (i) the elastic breakup (EBU), in which the pro-jectile fragments “survive” after the collision and the tar-get remains in its ground state, and (ii) the non-elasticbreakup (NEB), which includes any process in which the α particles “survive” whereas the dissociated neutronsinteract non-elastically with the target nucleus (i.e. tar-get excitation and neutron transfer or absorption). TheEBU can be taken into account by the CDCC calcula-tions, while the CRC calculations account for EBU andNEB components approximately. Finally, an alternativecalculation for the NEB part is presented, in which theclosed-form method of Refs. [14, 16] is employed. Thesame di-neutron model of He ( α +2n)[17] will be used inCDCC, CRC and NEB calculations. III.1. Optical Model calculations
The experimental data of the reaction He+ Zn at17.4 MeV have been analyzed with the OM method, us-ing the microscopic S˜ao Paulo Potential (SPP) [18] forthe real part of the potential. For the imaginary part, thesame geometry was adopted, renormalized by the factor N i = 0.78 from Ref. [19]. In Fig. 2, the calculated elasticscattering angular distributions are compared with thepresent experimental data and those of Refs. [9, 12]. Con-sidering the uncertainty in the normalization discussed inSec. II, the calculated elastic scattering angular distri-bution is in reasonable agreement with the experimentaldata. Therefore, from now on we will consider the SPPfor the interaction He+ Zn.
TABLE I. Parameters of the derivative imaginary Woods-Saxon potential for the He+ Zn reactions, where the re-duced radius is fixed at r d =1.2 fm. The volume part of theoptical model is given by S˜ao Paulo potential. See text fordetails.Energy (MeV) W d (MeV) a d (fm)9.8 3.23 1.0013.5 2.87 1.1014.85 2.46 0.9217.90 1.91 0.91 In reactions induced by halo nuclei (such as He [20], Be [6] or Li [21]) it is useful to consider an opticalmodel prescription composed by two terms: one takesinto account the scattering of the core with the target θ c.m. (deg)0.20.40.60.811.21.4 ( d σ / d Ω ) / ( d σ R / d Ω ) He+ Zn E lab = 13.2 MeV He+ Zn E lab = 17.4 MeVSPP
FIG. 2. Elastic scattering angular distributions of α + Znreaction. The red circles are the experimental data at 17.4MeV, while the yellow squares represent the experimentaldata at 13.2 MeV of Ref. [9, 12]. The solid lines are the OMcalculations. by means of a volume part whereas the other representsthe long-range effects produced by the nuclear halo andis conveniently parametrized using a surface potential.Thus, the He+ Zn potential is parametrized accordingto the following expression. U opt ( R ) = U bare ( R ) + i W d ( R ) , (1)where the “bare” potential U bare is approximated by theinteraction α + Zn obtained before and W d is the surfacepart represented by a derivative imaginary Woods-Saxonpotential.The volume term and the reduced radius of the surfacepart ( r d = 1.2 fm) are kept fixed, while the imaginarydepth ( w d ) and the diffuseness ( a d ) are allowed to vary inorder to reproduce the elastic scattering data at the fourreaction energies. The OM fits have been performed withthe routine SFRESCO , which is part of the
FRESCO coupled-channels code [22]. The parameters obtained are shownin Table I and the calculated elastic scattering angulardistributions are compared with the experimental datain Fig. 3. As expected, a large value of the imaginarydiffuseness ( a d ≈ III.2. CDCC calculations
The He experimental data have also been com-pared with CDCC calculations. Because of the three-body structure of He, we employ the four-body CDCCmethod. However, since it is our aim to compute also the α energy and angular distribution, and the calculation ofthese observables has not yet been implemented in thefour-body CDCC method, we have also performed three-body CDCC calculations, assuming a two-body structurefor He ( α +2 n ). Within the three-body CDCC frame- ( d σ / d Ω ) / ( d σ R / d Ω ) E lab =9.8MeVOM E lab =13.5 MeV θ c.m. (deg)0.51 ( d σ / d Ω ) / ( d σ R / d Ω ) E lab =14.85 MeV θ c.m. (deg) E lab =17.90 MeV FIG. 3. Experimental elastic scattering angular distribu-tions of He+ Zn reaction at the incident energies of 9.8,13.5, 14.85 and 17.9 MeV (symbols). Optical model calcu-lations are shown as continuous line. work, the breakup of the projectile is treated as an in-elastic process, where the two valence neutrons can be ex-cited to unbound states of the He-2 n system. Since tar-get excited states are not considered explicitly, the com-puted cross sections correspond to the elastic breakup(EBU) part defined earlier. To describe the He states,the improved di-neutron model of Ref. [17] has been used.In this model, the 2 n + He interaction is parametrizedwith a Woods-Saxon potential with a radius R = 1.9 fmand diffuseness a = 0.25 fm. For ℓ = 0, the depth ofthe potential is adjusted to give an effective two-neutronseparation energy of 1.6 MeV, which was chosen to repro-duce the tail and rms radius of the 2 n + He wave func-tion, as predicted by a realistic three-body calculation of He. For the ℓ = 2 continuum, the potential depth wasadjusted to reproduce the 2 + resonance at the excitationenergy of 1.8 MeV above the ground state.The CDCC calculations require also the fragment-target optical potentials. For the He- Zn interaction weconsidered the SPP of Subsec. III.1, whereas the Zn-2 n potential was calculated using the following single-foldingmodel: U ( R ) = Z ρ ( r nn )[ U n ( ~R + ~r nn U n ( ~R − ~r nn d~r nn , (2)where ~R is the Zn-2 n relative coordinate, U n is theneutron-target optical potential, which we adopted fromRef. [23], and ρ ( r nn ) is the density probability alongthe ~r nn coordinate calculated within the He three-bodymodel of Ref. [24]. The He continuum was discretizedusing the standard binning method, including He-2 n rel-ative angular momenta up to ℓ max = 4 and excitationenergies up to 8 MeV with respect the two-neutron sepa-ration threshold. The coupled equations were integratednumerically up to 100 fm, and for total angular momentaup to J = 80. These calculations were performed usingthe code FRESCO [22].In Fig. 4, we compare the elastic scattering data withCDCC calculations. The solid lines are the full CDCC ( d σ / d Ω ) / ( d σ R / d Ω ) CRC4b-CDCC 3b-CDCCone-channel0 30 60 90 120 150 θ c.m. (deg)0.51 ( d σ / d Ω ) / ( d σ R / d Ω ) θ c.m. (deg)E lab =9.8 MeV E lab =13.5 MeVE lab =17.90 MeVE lab =14.85 MeV FIG. 4. Elastic scattering angular distributions of He+ Znreaction at the incident energies of 9.8, 13.5, 14.85 and 17.9MeV. The dashed and dashed-dotted lines are the 4b- and3b-CDCC calculations, respectively. The solid line is theCRC calculation, which takes into account the coupling tothe 2 n -transfer channels (section III.3). The dotted lines arethe one-channel calculations, which ignore the coupling tothe continuum states. calculations, while the dotted lines represent the single-channel calculations, where the coupling to the con-tinuum states is not considered. As it was found inRefs. [10, 20], the inclusion of coupling to breakup chan-nels produces a suppression of the Coulomb nuclear in-terference peak. The full CDCC calculations reproducereasonably the overall set of experimental data.In order to assess the accuracy of the di-neutron modelof the 3b-CDCC calculations, the elastic scattering an-gular distributions have been also compared with four-body CDCC calculations using the formalism developedin Ref. [24]. To discretize the three-body continuum weuse the transformed harmonic oscillator (THO) method[25]. Here we use the same structure model for thethree-body system He( α + n + n ) as in Ref. [24]. TheHamiltonian includes two-body potentials plus an effec-tive three-body potential. The He ground-state wavefunction ( j = 0 + ) needed to construct the THO basis isgenerated as explained in Ref. [24]. The parameters ofthe three-body interaction are adjusted to reproduce theground-state separation energy and matter radius. Thecalculated binding energy is 0.952 MeV and the rms ra-dius 2.46 fm (assuming a rms radius of 1.47 fm for the α particle). The fragment-target interactions were rep-resented by optical potentials that reproduce the elasticscattering at the appropriate energy. The n + Zn poten-tial was taken from the global parametrization of Kon-ing and Delaroche [23]. For the α + Zn potential, wetook the optical potential obtained in the Subsec. III.1.Both Coulomb and nuclear potentials are included. Thecoupled-channels equations were solved using the code
FRESCO [22], with the coupling potentials supplied ex-ternally. We included in the calculation the states withangular momentum j = 0 + , 1 − , and 2 + . To get conver-gence a THO basis with 86 states and truncated at themaximum energy value of 8 MeV was needed. The cou-pled equations were solved up to J = 40 for 10 MeV and J = 60 for the rest of energies, and for projectile-targetseparations up to a matching radius of 100 fm.The calculated elastic angular distributions are com-pared with the data in Fig. 4. The results are very closeto those obtained with the 3-body CDCC calculations,which gives additional support to the use of the 3-bodyCDCC method to compute the breakup cross sections.The calculated α cross sections, provided by the 3-body CDCC calculations, are compared in Fig. 5 withthe experimental data. A significant underestimation isobserved, which is taken as an indication that the mea-sured α single cross sections cannot be explained by aelastic breakup mechanism, at least in the angular rangecovered by the data.In summary, although the elastic scattering can be re-produced by the CDCC calculations, showing the im-portance of including the coupling to breakup channels,the angular distribution of α particles coming from thebreakup of He cannot be described only by a elasticbreakup mechanism and, therefore, other breakup mech-anisms need to be considered.
III.3. CRC calculations
The failure of the CDCC calculations to reproducethe α cross sections indicates that these fragments aremostly produced via non-elastic breakup (NEB) mecha-nisms. The evaluation of these NEB contributions facesthe difficulty that many processes can actually contributeto it, such as one- and two-neutron transfer, complete andincomplete fusion and non-capture breakup accompaniedby target excitation, as found in [13]. Following previ-ous analyses of other He reactions [11], an approximateway of evaluating the total inclusive cross section (i.e.EBU+NEB) consists in a transfer-like mechanism pop-ulating a set of doorway states of the 2 n -target system.Within the extreme di-neutron model adopted in the 3-body CDCC calculations, we consider here a two-neutronmodel populating a set of 2 n + Zn states. These statesare generated according to the procedure described inRef. [11]. In the present calculations, partial waves upto ℓ f = 5 for the Zn-2 n relative motion were consid-ered. The states above the two-neutron breakup thresh-old were discretized using 2 MeV bins up to 10 MeV. Forenergies below the threshold, six states spaced by 2 MeVfor each relative angular momentum ℓ f were considered.The same 2 n - Zn and He- Zn potentials used in theCDCC calculations were considered. In order to avoid adouble counting of the effects of channel couplings, theentrance channel, He+ Zn, has to be described by abare potential. For that, in this work we have used anOM potential composed by the sum of the SPP [26] andthe Coulomb dipole polarization potential [27]. In theSPP, we assumed the two-parameter Fermi (2pF) distri-bution with a matter diffuseness of 0.50 [26] and 0.56 fm,for the the Zn and He matter density, respectively. In addition, and in order to simulate the fusion conditions,a short-range Woods-Saxon imaginary potential with pa-rameters W = 50 MeV, r = 1 . a = 0.1 fm wasconsidered.Transfer couplings were iterated beyond the first order,until convergence of the elastic and transfer observableswas achieved, thus performing a CRC (coupled-reactionchannels) calculation.In Figs. 5 and 6, the calculated angular and energy dis-tributions of the He fragments emitted in the He+ Zncollisions are represented. A reasonable agreement be-tween the CRC calculations and the experimental data isobserved, indicating that the two-neutron transfer mech-anism is a major contributor to the inclusive cross sec-tion. In the next subsection, we present further calcula-tions for the NEB contribution based on an alternativeformalism.
III.4. Non-Elastic breakup calculations
The CRC calculations presented in the previous sub-section assume a transfer-like mechanism leading to a setof single-particle configurations built on top of the targetground state. These states can be interpreted as door-way states preceding more complicated configurations,involving admixtures with target excitations. As such,the method can be regarded as an approximate way ofincluding both EBU and NEB contributions [28].A more rigorous method to evaluate NEB cross sec-tions was proposed in the 1980s by Ichimura, Austern andVincent (IAV) [14, 29], and has recently been revisitedand successfully applied to several inclusive breakup re-actions [16, 30, 31]. The model is based on a participant-spectator description of the reaction and makes use ofthe Feshbach projection technique. It was originally de-veloped for processes of the form a + A → b + B , where a = b + x is a two-body projectile, and B is any finalstate (bound or unbound) of the x + A system. In thismodel, the double differential cross section, as a functionof the energy and angle of the detected fragment ( b ), isgiven by: d σdE b d Ω b (cid:12)(cid:12)(cid:12)(cid:12) NEB = − ~ v a ρ b ( E b ) h ϕ x ( ~k b ) | Im[ U xA ] | ϕ x ( ~k b )) i , (3)where ρ b ( E b ) = k b µ b / [(2 π ) ~ ], U xA is the optical poten-tial describing x + A elastic scattering, and ϕ x ( ~k c , ~r xA ) isthe wave function describing the evolution of the x parti-cle after dissociating from the projectile, when the core isscattered with momentum ~k b and the target remains inits ground state. This function is obtained as a solutionof the inhomogeneous equation( E x − K x − U xA ) ϕ x ( ~k b , ~r x ) = h ~r x χ ( − ) b ( ~k b ) | V post | Ψ b i , (4)where E x = E − E b , χ ( − ) b ( ~k b , ~r bB ) is the distorted-wavedescribing the scattering of the outgoing b fragment withrespect to the B ≡ x + A system, obtained with some d σ α / d Ω ( m b / s r) d σ α / d Ω ( m b / s r) d σ α / d Ω ( m b / s r) θ lab (deg)10100 d σ α / d Ω ( m b / s r) E lab =9.8 MeVE lab =13.5 MeVE lab =14.85 MeVE lab =17.90 MeV FIG. 5. Angular distributions of the He fragments, in thelaboratory frame, for the reaction He+ Zn at energies of9.8, 13.5, 14.85 and 17.9 MeV. The dotted red lines representthe CRC calculations considering the 2n transfer reaction,while the dashed green lines are the CDCC calculations,which consider the elastic breakup of the projectile. Thenon-elastic breakup calculations based on the IAV modelare represented by solid blue lines. optical potential U bB , and V post ≡ V xb + U bA − U bB isthe post-form transition operator. This equation is to besolved with outgoing boundary conditions. In addition,for simplicity, DWBA approximation is applied to thethree-body wave function, i.e., | Ψ b i = | χ (+) a φ a i , where χ (+) a is the distorted wave describing a + A elastic scatter-ing and φ a is the projectile ground state wave function.Although the model is not directly applicable to He,due of its three-body structure, we apply it anyway, con-sidering one limiting scenario, in which the α core is thespectator and the two valence neutrons interact inelasti-cally with the target as a whole. We present the resultsof these two kinds of calculations in Figs. 5 and 6.The calculated NEB angular distributions reproducerather well the shape of the data, whereas the magnitude α (MeV)010203040Exp. data3b-CDCCCRCIAV model θ =100º-110ºE lab =17.90 MeV0 5 10 15 20E α (MeV)0246810 d σ / d E ( m b / M e V ) d σ / d E ( m b / M e V ) E lab =14.85 MeV θ =40º-50º θ =80º-90º θ =68.5º - 71.5º θ =100º-110º FIG. 6. Energy distributions of the He fragments, in thelaboratory frame, for the reaction He+ Zn at energies of17.9 (right panel) and 14.85 MeV (left panel) in the angu-lar range of 40-50 ◦ , 80-90 ◦ and 100-110 ◦ for the 17.9 MeVand 100-110 ◦ and the strip cover 70 ± ◦ for the 14.85MeV. The dotted red lines represent the CRC calculationsconsidering the 2n transfer reaction, while the dashed greenlines are the CDCC calculations, which consider the elasticbreakup of the projectile. The non-elastic breakup calcula-tions based on the IAV model are represented by the solidblue lines. is somewhat overestimated. Despite this disagreement,which might be due to the crude structure model or tothe DWBA approximation itself, we can conclude that,at the four measured energies, the non-elastic breakup ofthe projectile is the dominant breakup mode. θ c.m. (deg)00.30.60.91.2 ( d σ / d Ω ) / ( d σ R / d Ω ) E lab =14.85 MeVOM 1OM 2 θ lab (deg)10 d σ α / d Ω ( m b / s r) E lab =14.85 MeVIAV model (OM 1)IAV model (OM 2) FIG. 7. (left) Elastic scattering angular distributions of He+ Zn reaction at the incident energy of 14.85 MeV.(right) Angular distributions of the He fragments, in thelaboratory frame, for the reaction He+ Zn at incidentenergy of 14.85 MeV.
Since some ambiguities of the breakup cross-section ob-tained from DWBA calculations have been observed fromdifferent potentials which reproduce the entrance chan-nel in Refs. [32–36], we have calculated the NEB angulardistributions with two different potentials at 14.85 MeV.One is the optical model potential from Table I (OM1), which reproduces better the experimental data interms of χ , and the second optical model (OM 2) hasbeen forced to reproduce the experimental data in thevicinity of the rainbow peak, yielding: v =5.71 MeV, r =0.99 fm, a =1.99 fm, w =0.25 MeV, r i =1.86 fm and a i =0.99 fm (see LHS of Fig. 7). The calculated breakupcross sections (shown in the RHS of Fig. 7), indicate asignificant sensitivity of the NEB results with respectto the entrance channel optical model potential. There-fore, improvement on theoretical NEB model is necessaryfor a complete understanding of reaction involving two-neutron halo nuclei. IV. SUMMARY AND CONCLUSIONS
In this work we have presented new experimental datafor the reaction He+ Zn at middle-target energies of14.85 and 17.9 MeV. In order to understand the dynam-ics of the reaction, the measured elastic angular distri-butions, together with the data previously published in[9, 12] have been compared with different theoretical cal-culations. As a start, optical model calculations basedon the S˜ao Paulo potential, were performed. In orderto reproduce the experimental data, a derivative imagi-nary Woods-Saxon potential with a large value of the dif-fuseness parameter were needed, in accord with previousfindings for other He-induced reactions on medium-massand heavy targets [4]. This is a clear indication of thepresence of long-range absorption, and this is confirmedby three-body and four-body CDCC calculations, whichshow the need to include coupling to the continuum in or-der to reproduce the experimental elastic scattering data.However, the α cross sections provided by these three-body CDCC calculations are found to largely underesti-mate the data, indicating that the majority of observed α particles are not produced by an elastic breakup mech-anism. In order to pin down their origin, additional cal-culations have been performed and compared with themeasured angular and energy distributions.In order to investigate the role of transfer, CRCcalculations were performed. They consider a two-neutron transfer mechanism populating bound and un-bound states of the target nucleus. These calculationsbetter reproduce the shape and magnitude of the angu-lar distributions of the α particles, although some under-estimation is still observed. One should bear in mind,however, that this two-neutron transfer mechanism, al-though it may be reasonable for the 2 n -halo structureof He, it provides a very crude description of the fi-nal 2 n + Zn states, which depends significantly on thechoice of 2 n + Zn energy levels.Finally, we consider the DWBA version of the inclu- sive breakup mechanism of Ichimura, Austern and Vin-cent (IAV). These calculations account for the non-elasticbreakup processes in which the neutrons interact non-elastically with the target. Calculations based on thismodel reproduce very well the shape of the α distribu-tions, although they overestimate somewhat the mea-sured cross sections. Despite the remaining disagreementin the magnitude, which might be a consequence of thesimplified two-body description of the He projectile or ofthe DWBA assumption itself, these calculations clearlyindicate that most of the measured α yield stem fromnon-elastic breakup mechanisms, involving the transferor absorption of the valence neutrons by the target nu-cleus. In order to better reproduce the breakup data,some improvements would be necessary such as: i) theextension of the IAV model beyond the DWBA approx-imation and ii) the use a three-body model of the Heprojectile in the IAV model.We outline the main conclusions of this work:(i) He nucleus, as other halo nuclei, can be stronglypolarized during the scattering. Hence, an impor-tant effect of coupling to the continuum is foundin the elastic scattering, that can be described ei-ther with full 4b-CDCC or with di-neutron based3b-CDCC calculations. These effects, which werestudied in heavier targets, are now investigated ina medium-mass target Zn, where both Coulomband nuclear forces play a role.(ii) The elastic break-up mechanism, as described byCDCC, fails completely to describe the yield ofalpha particles coming out of the reaction. CRCcalculations, based on a model in which the di-neutron is transferred to some states in the target,close to the continuum, can explain partly the al-pha particle produced. However, this explanationis not completely satisfactory, as these CRC calcu-lations depends significantly on the choice of thesedi-neutron-target states to which the di-neutron istransferred.(iii) The IAV non-elastic breakup mechanism for the di-neutron removal, which is completely determinedby the optical potentials, is able to describe thescattering energy dependence of the alpha particleyield, the angular dependence and the energy dis-tributions of these alpha particles. Although themechanism overestimates the alpha particle yield(which is not surprising, given that we assume a di-neutron model), the results are relevant to correlatethe elastic scattering and the inclusive break-up ofhalo nuclei.
ACKNOWLEDGMENTS
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Reichart, H. Ja-sicek, H. Oberhummer, P. Riehs, R. Wagner, andW. Pfeifer, Phys. Rev. C , 1626 (1978). α (MeV)010203040Exp. data3b-CDCCCRCIAV model θ =100º-110ºE lab =17.90 MeV0 5 10 15 20E α (MeV)0246810 d σ / d E ( m b / M e V ) d σ / d E ( m b / M e V ) E lab =14.85 MeV θ =40º-50º θ =80º-90º θ =68.5º - 71.5º θ =100º-110º d σ α / d Ω ( m b / s r) d σ α / d Ω ( m b / s r) d σ α / d Ω ( m b / s r) θ lab (deg)10100 d σ α / d Ω ( m b / s r) E lab =9.8 MeVE lab =13.5 MeVE lab =14.85 MeVE lab =17.90 MeV θ c.m. (deg)0.20.40.60.811.21.4 ( d σ / d Ω ) / ( d σ R / d Ω ) He+ Zn E lab = 13.2 MeV He+ Zn E lab = 17.4 MeVOM ( d σ / d Ω ) / ( d σ R / d Ω ) CRC4b-CDCC 3b-CDCCone-channel0 30 60 90 120 150 θ c.m. (deg)0.51 ( d σ / d Ω ) / ( d σ R / d Ω ) θ c.m. E lab =9.8 MeVE lablab