Coulomb Effects in Low Energy Proton-Proton Scattering

TL;DR

This paper develops a non-perturbative approach using effective field theory to calculate Coulomb corrections in low-energy proton-proton scattering, revealing modifications to scattering relations and implications for hadronic atoms.

Contribution

It introduces a method to incorporate Coulomb effects non-perturbatively in effective field theory, including derivative interactions, and modifies the Blatt-Jackson relation.

Findings

Coulomb corrections are calculated non-perturbatively for proton-proton scattering.

The modified Blatt-Jackson relation is recovered with Coulomb effects included.

Effective range remains unaffected by Coulomb interactions at this order.

Abstract

Using a recently developed effective field theory for the interactions of nucleons at non-relativistic energies, we calculate non-perturbatively Coulomb corrections to proton-proton scattering. Including the dimension-eight derivative interaction in the PDS regularization scheme, we recover a modified form of the Blatt-Jackson relation between the scattering lengths. The effective range receives no corrections from the Coulomb interactions to this order. Also the case of scattering in channels where the Coulomb force is attractive, is considered. This is of importance for hadronic atoms.