Uniform semiclassical IVR treatment of the S-matrix

A new, uniform, semiclassical, initial value representation expression is obtained for the S-matrix in the case of collinear collisions. The derivation is based on an asymptotic analysis (for large inter-fragment distances) of a uniform semiclassical integral expression for the time independent scattering wave function. Although this derivation specifically treats the case of the collision of an atom with a harmonic diatom, the final expression is generalized to arbitrary collinear collisions. The various properties of the expression and its relation to existing semiclassical methods are discussed. Numerical tests are performed for the well-known Secrest–Johnson system. Among other important advantages, the present treatment is a well-defined, uniform, semiclassical approximation that is capable of good accuracy and high computational efficiency, requiring a relatively small number of classical trajectories to obtain converged S-matrix elements for a given energy and initial state.

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