Quasi classical analytical approximation to the $S$-matrix of collinear rearrangement reaction

Collinear problem of three-particle rearrangement reaction in the framework of the quasi classical method of Fock–Leontovich parabolic equation is reduced to the quantum problem of the one-dimensional harmonic oscillator with variable frequency in an external force field. This allows one to express the $S$-matrix elements responsible for the rearrangement channel via analytical solution of the oscillator model by using the parameters of the linear configuration of the three particles.