Three-body continuum states in a microscopic cluster model

Abstract

We propose a microscopic approach to three-body continuum states in the hyperspherical formalism. The $A$-nucleon wave functions are defined in the generator coordinate method, based on a three-cluster approximation of the system. We develop a semianalytical treatment of the matrix elements, limited to $s$ clusters. This allows a fast calculation, as well as a direct interpretation of the wave functions, in terms of nucleon exchanges. We apply the method to the $\ensuremath{\alpha}+n+n$ three-body phase shifts and confirm the existence of broad structures in the ${0}^{+}$ and ${1}^{\ensuremath{-}}$ partial waves at low energies.