Nearside-farside theory of differential cross sections : resummation of a partial wave series involving Legendre polynomials

Abstract

We report a new resummation procedure for the partial wave series (PWS) representation of the scattering amplitude, when a basis set of Legendre polynomials is used for the expansion. The effect of the resummation is to remove from the PWS the factor containing alpha and beta. The resummed scattering amplitude is then exactly decomposed into the sum of a nearside (N) subamplitude and a farside (F) subamplitude. We make two applications of the NF resummed theory: to elastic angular scattering in a strongly absorptive collision and to a state-to-state differential cross section for the I + HI > IH + I reaction. In both applications, we can understand the physical origin of structure in the angular scattering for suitable choices of alpha, beta and r.