Av. Bogdanov et al., QUASI-CLASSICAL ANALYTICAL APPROXIMATION OF THE S-MATRIX FOR THE 3-PARTICLE COLLINEAR REARRANGEMENT REACTION, Theoretical and mathematical physics, 107(2), 1996, pp. 609-619
In the framework of the quasi-classical method of the Fock-Leontovich
parabolic equation, the collinear problem of the three-particle rearra
ngement reaction is reduced to the quantum problem of a one-dimensiona
l harmonic oscillator with a variable frequency in an external force f
ield. This allows one to express the S-matrix elements responsible for
the rearrangement channel via the known analytical functions of the o
scillator model, using the parameters of the potential surface of a li
near configuration of three particles.