A single reflection approximation for heavy-ion potential scattering

A multiple reflection expansion is introduced for the amplitude or wave function pertaining to a definite partial wave in which each term corresponds to a wave undergoing an ever increasing number of reflections in the potential region. The two leading terms in the expansion corresponding to one reflection from the origin and from intervals of rapid change in the local wave number, provide an excellent approximation for phase shifts and wave functions over a wide range of energies and partial waves for real and complex potentials except for real wells, when "pockets" exist in the effective potentials. The small parameter associated with the expansion is identified to be βV/E with β≈O( 1 10). The WKB and variable-phase approximation for real wells are obtained in well defined limits of our expressions.