Calculation of the reaction cross section from a rate constant by the method of steepest-descent

The reaction cross section of a bimolecular reaction has been calculated from the corresponding rate constant by the inverse Laplace transform. In carrying out the inverse Laplace transform, the method of steepest-descent has been used. As applications, the reaction cross sections for the rate constant of k(T) = k' T(n)e(-E0/kT) and for the rate constant of the absolute reaction rate theory have been calculated. The computation of the energy density function associated with the definition of the weighted-average cross section has also been discussed.