Partial-wave Coulomb t-matrices for like-charged particles at ground-state energy

TL;DR

This paper derives analytical expressions for partial-wave Coulomb transition matrices for like-charged particles at bound-state energy using Fock's stereographic projection method, providing exact solutions for specific cases.

Contribution

It introduces a novel analytical approach to solve the Lippmann-Schwinger equation for Coulomb interactions at negative energy, specifically for like-charged particles.

Findings

Derived explicit formulas for s-, p-, and d-wave Coulomb transition matrices.

Provided analytical solutions at bound-state energy for repulsive Coulomb interactions.

Enhanced understanding of Coulomb scattering at negative energies.

Abstract

We study a special case at which the analytical solution of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix for likely charged particles at negative energy is possible. With the use of the Fock's method of the stereographic projection of the momentum space onto the four-dimensional unit sphere, the analytical expressions for s-, p- and d-wave partial Coulomb transition matrices for repulsively interacting particles at bound-state energy have been derived.