Structure of positive energy states in a deformed mean-field potential

Abstract

We investigate the properties of single-particle resonances in a non-spherical potential by solving the coupled-channels equations for the radial wave functions. We first generalize the box discretization method for positive energy states to a deformed system. As in the spherical case, we find that the discretized energy is stabilized against the box size when a resonance condition is met. Using the wave functions thus obtained, we then discuss the energy and the radial dependences of scattering wave functions in the vicinity of an isolated resonance. In the eigenchannel basis, where the $S$-matrix is diagonal, we propose a generalized expression for the factorization formula for the multi-channel wave function. We find that the factorized wave function agrees well with the exact solution inside the centrifugal barrier when the energy distance from the resonance is less than the resonance width.Comment: 22 pages, 5 eps figures; a figure adde

Particle motion in a deformed potential using a transformed oscillator basis

“…This choice is motivated by the fact that this nucleus is one of the best known one-neutron halo nuclei. Many of its properties can be understood in a simple two-body model, comprising a valence neutron orbiting a 10 Be core. For example, the ground state (1/2 + ) and the only bound excited state (1/2 − ) are reasonably well described by 2s 1/2 and 1p 1/2 single-particle configurations, relative to the 10 Be(g.s.)…”

“…However, recent experimental and theoretical developments indicate that deformation can play a significant role in the structure and dynamics of these proton or neutron rich nuclei, such as halo nuclei containing a deformed core. The description of the continuum states of these systems can still be done using scattering states [10]. For example, the effect of core excitation in the scattering of a two-body halo nucleus has been recently studied in a extension of the CDCC method [11] and, more recently, in the distorted-wave Born approximation (DWBA) model proposed in Refs.…”

Resonant states of deformed nuclei in the complex scaling method

“…In Refs. [35,36], the ACCC method and RSM have been extended to investigate the resonances in axially deformed Woods-Saxon potentials.…”

Study of resonant structures in a deformed mean field by the contour deformation method in momentum space

“…In Ref. [18] a different approach was considered. Their aim was to propose a method to obtain scattering wave functions in the vicinity of a multi-channel resonance on the real axis, then calculate the phase shifts, and investigate whether a resonance condition is met.…”