Effects of the form of potential on the behavior of the two-particle scattering amplitude outside the energy surface. [Pade approximation, Neumann--Liouville series]

This study is a continuation of previous work in which some methods of solving a linear Lippman-Schwinger integral equation for the scattering amplitude for positive energy were discussed; it was shown that it is convenient to use a numerical method in the Pade approximation to analyze the physical features of the two-particle scattering amplitude, and therefore one applies that approximation to the behavior of the solution of the integral Lippman--Schwinger equation in order to examine the two-particle scattering amplitude outside the energy surface in relation to the form of the scattering potential. This method enables one to obtain a solution to the linear Lippman-Schwinger equation via Neumann-Liouville series. (JFP)