SPARSE: Scattering Poles and Amplitudes from Radial Schr\"odinger Equations

TL;DR

This paper presents an algorithm that numerically solves radial Schrödinger equations to compute scattering poles and amplitudes, enhancing the analysis of inelastic particle scattering with spin.

Contribution

It introduces a finite difference method-based algorithm for solving radial Schrödinger equations and calculating scattering parameters from the $K$-matrix.

Findings

Accurately computes scattering poles and amplitudes.

Provides a numerical approach for inelastic scattering with spin.

Uses boundary conditions at origin and large radius.

Abstract

We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations is approximated as an ordinary linear nonhomogeneous system using the finite difference method. Dirichlet boundary conditions are imposed at the origin and at an arbitrary large radius. The $K$-matrix for physical energies is calculated from the numerical solutions of the system by comparison to the analytical real solutions at large distances. Scattering poles and amplitudes are calculated from the physical $K$-matrix.