Model of the passing of the $s$-term through the parabolic boundary of the continuum

An exactly solvable (by means of a computer) model of inelastic processes in a system of two atomic particles that form a stable molecule and a weakly bound $s$-electron is discussed. In it, one can describe a system with a stable molecular ion, as well as a system in which there is no such ion. The results of some numerical calculations are given.