  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.
