Study of proton-proton Scattering using Phase Function Method

TL;DR

This paper applies the phase function method to study proton-proton scattering, successfully calculating phase shifts and cross-sections that align with realistic potentials, making it suitable for undergraduate education.

Contribution

It demonstrates the use of the phase function method with the Malfliet-Tjon potential to accurately model pp scattering, offering an accessible approach for students.

Findings

Interaction potential matches Argonne V18 for 1S0 state

Phase shifts and cross-sections agree with experimental data

Method is suitable for undergraduate teaching

Abstract

Background: The study of np and pp scattering, central to understanding nuclear force, remains an optional topic in many undergraduate nuclear physics curriculum. Purpose: The main thrust of this paper is to study pp scattering using the phase function method to obtain the observed S-wave phase shifts and cross-sections at various energies. Methods: The pp interaction has been modeled by choosing the Malfliet-Tjon potential for the nuclear part along with the screened Coulomb potential. The phase equation has been solved to obtain scattering phase shifts using the fourth-order RK method (RK-4). Results: The interaction potential obtained from optimized parameters matches well with the realistic Argonne V18 potential for 1S0 state of pp scattering and the scattering phase shifts as well as the cross-section for energies ranging from 1-350 MeV are in good agreement with expected data. Conclusion: Introducing the phase function method for S-wave (l=0) could bring this interesting study of nucleon-nucleon scattering to the undergraduate classroom.