A new treatment of nonlocality in scattering process

TL;DR

This paper introduces a novel, highly accurate method to solve nonlocal scattering equations by transforming the integro-differential equation into a local form, enabling better analysis of nuclear scattering data.

Contribution

The work presents a new approach using the mean value theorem to convert nonlocal scattering equations into a local form, applicable to any nonlocal potential kernel.

Findings

Accurately calculates neutron scattering cross sections for various nuclei.

Method shows good agreement with experimental data in low-energy scattering.

Produces energy-independent local potentials with angular momentum dependence.

Abstract

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 Schroedinger equation is usually handled by approximating r,r'-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 has high accuracy and is 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 good accord with the experiments.