Computing Scattering Cross Sections For Spherically Symmetric Potentials

TL;DR

This paper demonstrates how to use open-source Scilab and Xcos to compute scattering phase shifts for spherically symmetric potentials by solving the Schrödinger equation numerically, aiding students and instructors.

Contribution

It introduces a practical method for calculating scattering phase shifts using Scilab and Xcos, making complex differential equations accessible for educational purposes.

Findings

Effective numerical solution of Riccati equations for scattering

Integration of Scilab and Xcos for modeling quantum scattering

Educational approach for teaching scattering calculations

Abstract

This paper introduces students and instructors to the use of Scilab for calculating phase shifts from phenomenological potentials in nuclear, atomic, and molecular scattering, beginning with a Riccati-type nonlinear differential equation derived from the time-independent Schr$\ddot{\text{o}}$dinger equation. For spherically symmetric potentials, this equation can be easily solved using Xcos, a Scilab toolbox. \cite{PRC}\cite{bobby} Scilab is open source software that is used for numerical computations and can be freely downloaded for Windows, Linux and Mac OS.\cite{scilab} Xcos is a Scilab toolbox dedicated to the modeling and simulation of hybrid dynamic systems \cite{rachna}. Xcos provides users with the ability to model complex dynamical systems using a block diagram editor (GUI based), offering a step-by-step procedure for learning to solve complex differential equations interactively.