Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.