An analytically solvable model to test the hyperspherical Sturmian approach for break up processes

Abstract

An analytically solvable model for three particles break up processes is presented. The scattering process is represented by a non-homogeneous Schrödinger equation where the driven term is given by a Yukawa-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. A closed form solution is derived in hyperspherical coordinates (ρ,α). This leads to an analytic expression for the transition amplitude associated to the scattering process. This model is used to test calculations performed within the frame of an hyperspherical Sturmian approach.