A Two Potential Formula and its Application to Proton-Proton Scattering

TL;DR

This paper derives an analytical two-potential formula within scattering theory, enabling improved analysis of proton-proton interactions by incorporating Coulomb and chiral potentials, with applications to phase shift determination.

Contribution

It introduces a novel two-potential formula for on-shell partial wave amplitudes applicable to various long and short-range potentials.

Findings

Derived an analytical two-potential formula for scattering amplitudes.

Applied the formula to proton-proton scattering with chiral potentials.

Analyzed the scales involved in phase shift extraction.

Abstract

Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range Coulomb forces as well as short distance singular potentials. As an example illustrating the use of the formula we analyze the determination of the strong proton-proton scattering s-wave phase shift from the experimentally determined Coulomb phase when the one pion exchange and two pion exchange chiral potentials are taken into account and analyze the relevant scales of the problem.