Three-body continuum discretization in a basis of transformed harmonic oscillator states

Abstract

Data for scattering of 6 He from 197 Au, 208 Pb, and 209 Bi targets at low energies were consistently analyzed by use of the continuum-discretized coupled-channels method and the dineutron model of the projectile. A very good description of the experimental data was obtained with the strength of the dipole couplings reduced by 50%. We find that the dipole couplings are responsible for the suppression of the Coulomb rainbow and that the quadrupole couplings must be included in the calculations in order to obtain good agreement with the elastic-scattering data at more backward angles. The continuum-discretized coupled-channel (CDCC) method, developed originally to study the effect of deuteron breakup on the process of elastic scattering [1], plays an important role in the study of reactions with weakly bound light nuclei. So far the method has been limited to the three-body systems, allowing the study of interactions of a projectile consisting of two clusters with a target nucleus. Some efforts have been reported recently to extend it to the four-body systems [2][3][4] so that the scattering of 6 He, the nucleus known to have a three-body α + n + n structure, could be studied. However, these approaches are not applicable yet for the processes taking place in the vicinity of the Coulomb barrier because they do not account for the four-body Coulomb breakup of the projectile.Therefore low-energy 6 He elastic-scattering data have been analyzed so far by use of the limited model of this nucleus, with the two neutrons outside the α-particle core coupled to a single particle, a dineutron ( 2 n), [5,6] Au target measured at the Cyclotron Research Centre in Louvain-laNeuve open the possibility for more detailed studies of the applicability of such a simplified approach. The experiment at Louvain-la-Neuve was part of a campaign (by the PH-114 collaboration [8,9]) in which scattering of 6 He by different targets was investigated; details are given in Ref. [10]. In this report we present results of CDCC calculations limited to the three-body systems for these data sets.The calculations follow closely the procedure of Keeley et al. [6]. The two-body α + 2 n model of 6 He was employed, with the spin of the dineutron cluster set to zero. The potential binding the two clusters was of Woods-Saxon form, with the set II parameters listed in Table I of Ref. [11]. All the interactions were derived from empirical optical-model potentials describing elastic scattering of α particles and deuterons from the gold and lead targets [12,13] by use of the single-folding technique. The calculations were performed by means of the computer code FRESCO, version frxp18 [14].The continuum of the α + 2 n cluster states was truncated at relative momentum k = 0.6 fm −1 and discretized into bins of k = 0.1 fm −1 . The relative angular momentum of the cluster states was limited to the values L = 0,1,2. For the L = 2 states the binning scheme was modified because of the presence of the resonant state at an excitation energy of 0.825 MeV above the brea...

Coupled-channel effects in elastic scattering and near-barrier fusion induced by weakly bound nuclei and exotic halo nuclei

“…The CDCC formalism, with continuum-continuum couplings taken into account, is probably one of the most reliable methods available nowadays to study reactions induced by weakly bound nuclei and exotic halo nuclei, although many of the latter have added complications like core excitation and three-body structure that are only now being incorporated within the formalism [35,36,37,38,39,40]. One really needs to investigate such processes within the dynamics of the interaction at the Coulomb barrier with loosely bound halo nuclei.…”

“…Studies have been initiated in this direction by several groups [35,36,37,38,39,40] to investigate reactions induced by an exotic "Borromean" ( 6 He) nucleus, which is known to have a strong dipole excitation mode [41], and the single neutron halo nucleus 11 Be, where collective excitation of the 10 Be core is expected to be important.…”

Analytical transformed harmonic oscillator basis for continuum discretized coupled channels calculations

“…Although the method has been recently extended to three-body projectiles [23,34], in this paper we restrict ourselves to the two-body case.…”

Four-body continuum-discretized coupled-channels calculations

“…This method has been shown to be useful for describing the two-body continuum in both structure [17,18,20] and scattering [21][22][23] problems. In a recent work [24] the THO method was generalized to describe continuum states of three-body systems, based on expansion in hyperspherical harmonics (HH) [25]. In particular the method was applied to the Borromean nucleus 6 He, for which several strength functions, including the dipole and quadrupole Coulomb transition strengths, were calculated.…”