Taylor approximation to treat nonlocality in scattering processes

TL;DR

This paper introduces a Taylor approximation method to efficiently solve nonlocal scattering equations, achieving high accuracy and computational speedup over previous iterative approaches for neutron scattering observables.

Contribution

The work develops a Taylor approximation-based approach to solve nonlocal scattering equations, significantly improving computational efficiency while maintaining high accuracy compared to iterative methods.

Findings

Achieves a 10-fold speed increase over previous iterative schemes.

Provides neutron scattering observables within 8% accuracy of iterative methods.

Proposes an improved Taylor scheme that yields indistinguishable results from iterative solutions.

Abstract

Study of scattering process in the nonlocal interaction framework leads to an integro-differential equation. The purpose of the present work is to develop an efficient approach to solve this integro-differential equation with high degree of precision. The method developed here employs Taylor approximation for the radial wave function which converts the integro-differential equation in to a readily solvable second-order homogeneous differential equation. This scheme is found to be computationally efficient by a factor of 10 when compared to the iterative scheme developed in J.~Phys.~G~Nucl.~Part.~Phys.~{\bf 45},~015106~(2018). The calculated observables for neutron scattering off $^{24}$Mg, $^{40}$Ca, $^{100}$Mo and $^{208}$Pb with energies up to 10 MeV are found to be within at most 8$\%$ of those obtained with the iterative scheme. Further, we propose an improvement over the Taylor scheme that brings the observables so close to the results obtained by iterative scheme that they are visually indistinguishable. This is achieved without any appreciable change in the run time.