A new treatment of nonlocality in scattering process

Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,$r^{\prime }$-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off ¹²C, ⁵⁶Fe and ¹⁰⁰Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments. (paper)