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.