Adiabatic Representation for Atomic Dimers and Trimers in Collinear Configuration

We considered collinear models for a trimer of identical atoms with molecular pair interactions and for an atomic dimer scattered by an atom or tunneling through potential barriers. The models are formulated as 2D boundary-value problems in the Jacobi and polar coordinates. In the adiabatic representation the problems are reduced to a system of second-order ordinary differential equations (SODEs) with respect to the radial variable using the expansion of the desired solutions in the set of angular basis functions that depend on the radial variable as a parameter. The efficiency of the elaborated method, algorithms and programs is demonstrated by benchmark calculations of the asymptotic expansions of basis functions, effective potentials, fundamental solutions of the SODEs, and corresponding asymptotic scattering states, as well as the resonance scattering, metastable and bound states.