Asymptotic evaluation of multidimensional integrals for the S matrix in the semiclassical theory of inelastic and reactive molecular collisions

Abstract

The asymptotic evaluation of multidimensional integrals for the S matrix in the semiclassical theory of inelastic and reactive molecular collisions is considered. The n-dimensional integral is assumed to possess two saddle points, whose position depends on a parameter and which may coalesce for a certain value of the parameter. A uniform asymptotic approximation is obtained by evaluating n-1 of the integrals by the ordinary non-uniform method of Chester et al. The resulting uniform asymptotic formulae are generalizations of the results for one dimensional integrals given in a previous paper.