Three-body scattering model: diatomic homonuclear molecule and atom in collinear configuration

Three-body model comprising a diatomic homonuclear molecule and an atom, the solutions of which are necessary for modelling interactions of three-body systems with laser radiation and spectroscopy, is formulated in the collinear configuration of the adiabatic representation. The mapping of the relevant 2D boundary-value problems (BVPs) in the Jacobi coordinates and in polar (hyperspherical) coordinates is reduced to a 1D BVP for a system of coupled second-order ordinary differential equations (ODEs) by means of the Kantorovich expansion in basis functions of one of the two independent variables, depending on the other independent variable parametrically. The efficiency of the proposed approach and software is demonstrated by benchmark calculations of the discrete spectrum of Be 3 trimer in the collinear configuration.