A new (Laguerre) uniform approximation for vibrational transition probabilities

Abstract

A mapping between the exactly soluble forced oscillator and the general vibrationally inelastic scattering problem is shown to yield a new uniform approximation based on generalized Laguerre polynomials. Computations are reported for collinear He-H₂ collisions in which H₂ is represented by harmonic and Morse oscillators. The results show that the Laguerre approximation avoids the known failings of the existing Airy and Bessel uniform approximations.