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

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.