Spectroscopic amplitudes in microscopic three-cluster systems

Abstract

I investigate three-body spectroscopic amplitudes in a microscopic three-cluster model. The total wave functions are described in the resonating group method (RGM) formalism based on cluster wave functions and on relative functions defined in the hyperspherical method. Core excitations are included. I develop a method aimed to determine three-body spectroscopic amplitudes and spectroscopic factors. This technique also provides three-body wave functions where the antisymmetrization is treated approximately. In this way, the various channels are orthogonal to each other and can be used without the antisymmetrization operator. This method is well known in two-cluster systems, and is based on the eigenvalues and the eigenvectors of the antisymmetrization operator. I illustrate the formalism with the $^{6}\mathrm{He}$, $^{11}\mathrm{Li}$, and $^{14}\mathrm{Be}$ nuclei where $^{9}\mathrm{Li}$ and $^{12}\mathrm{Be}$ excited states are taken into account.