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

摘要

We report a new resummation procedure for the partial wave series (PWS)representation of the scattering amplitude, when a basis set of Legendrepolynomials is used for the expansion. The effect of the resummation is toremove from the PWS the factor containing alpha and beta. The resummedscattering amplitude is then exactly decomposed into the sum of a nearside (N)subamplitude and a farside (F) subamplitude. We make two applications of the NFresummed theory: to elastic angular scattering in a strongly absorptivecollision 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 ofstructure in the angular scattering for suitable choices of alpha, beta and r.