The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, 6 He+

The structure of the three-body Borromean nucleus 6 He is approximated by a two-body di-neutron cluster model. The binding energy of the 2n-α system is determined to obtain a correct description of the 2n-α coordinate, as given by a realistic three-body model calculation. The model is applied to describe the breakup effects in elastic scattering of 6 He on several targets, for which experimental data exist. We show that an adequate description of the di-neutron-core degree of freedom permits a fairly accurate description of the elastic scattering of 6 He on different targets.A. M. MORO et al. PHYSICAL REVIEW C 75, 064607 (2007)

The effect of core excitation in the elastic scattering and breakup of a two-body halo nucleus on a stable target nucleus is studied. The structure of the weakly bound projectile is described in the weak-coupling limit, assuming a particle-rotor model. The eigenfunctions and the associated eigenvalues are obtained by diagonalizing this Hamiltonian in a square-integrable basis (pseudostates). For the radial coordinate between the particle and the core, a transformed harmonic oscillator (THO) basis is used. For the reaction dynamics, an extension of the continuum-discretized coupled-channels (CDCC) method, which takes into account dynamic core excitation and de-excitation due to the presence of noncentral parts in the core-target interaction, is adapted to be used along with a pseudostates (PS) basis.

The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations.

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...

Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here, the method is generalized to study three-body systems. To test the goodness of the formalism and establish its applicability and limitations, the capture reaction rate for the nucleosynthesis of the Borromean nucleus 6 He ( 4 He + n + n) is addressed. Results are compared with previous publications and with calculations based on actual three-body continuum wave functions, which can be generated for this simple case. The obtained results encourage the application to other Borromean nuclei of astrophysical interest such as 9 Be and 12 C, for which actual three-body continuum calculations are very involved.

The relation of the recently proposed E͑5͒ critical point symmetry with the interacting boson model is investigated. The large-N limit of the interacting boson model at the critical point in the transition from U(5) to O (6) The study of phase transitions is one of the most exciting topics in physics. Recently the concept of critical point symmetry has been proposed by Iachello [1]. These kinds of symmetries apply when a quantal system undergoes transitions between traditional dynamical symmetries. In Ref.[1] the particular case of the Bohr Hamiltonian [2] in nuclear physics was worked out. In this case, in the situation in which the potential energy surface in the ␤-␥ plane is ␥ independent and the dependence in the ␤ degree of freedom can be modeled by an infinite square well, the so-called E͑5͒ symmetry appears. This situation is expected to be realized in actual nuclei when they undergo a transition from spherical to ␥-unstable deformed shapes. The E͑5͒ symmetry is obtained within the formalism based on the Bohr Hamiltonian, but it has also been used in connection with the interacting boson model (IBM) [3]. Although this is not the form it was originally proposed [1], it has been in fact argued that moving from the spherical to the ␥-unstable deformed case within the IBM one should reobtain, at the critical point in the transition, the predictions of the E͑5͒ symmetry. This correspondence is supposed to be valid in the limit of large number N of bosons, but the calculations with the IBM should provide predictions for finite N as stated in Ref. [4]. In this paper, on one hand we calculate exactly the large-N limit of the IBM at the critical point in the transition from U(5) (spherical case) to O(6) (deformed ␥-unstable case). On the other hand, we solve the Bohr differential equation for a ␤ 4 potential. Both calculations lead to the same results and are not close to those obtained by solving the Bohr equation for an infinite square well [E͑5͒ symmetry]. We also show with two schematic examples that the corrections arising from the finite number of bosons are important. With this in mind, the IBM calculations still provide a tool for including corrections due to the finite number of bosons.In Ref.[1] the Bohr Hamiltonian is considered for the case of a ␥ independent potential, described by an infinite square well in the ␤ variable. In that case, the Hamiltonian is separable in both variables and if we set ⌿͑␤, ␥, i ͒ = f͑␤͒⌽͑␥, i ͒, ͑1͒where i stands for the three Euler angles, the Schrödinger equation can be split in two equations. [7][8][9] which allows to associate to it a geometrical shape in terms of the deformation variables ͑␤,␥͒. The basic idea of this formalism is to consider that the pure quadrupole states are globally described by a boson condensate of the form ͉g;N, ␤, ␥͘ = 1where the basic boson is given bywhich depends on the ␤ and ␥ shape variables. The energy surface is defined aswhere Ĥ is the IBM Hamiltonian. Here we are interested in the case in which the Hamiltonian undergoes a transitio...

A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d + 58 Ni at 80 MeV, 6 Li + 40 Ca at 156 MeV, and 6 He + 208 Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.