Analytical solution of the integral equation for partial wave Coulomb t-matrices at excited-state energy

TL;DR

This paper derives new analytical expressions for partial wave Coulomb t-matrices at excited-state energies, enhancing understanding of Coulomb interactions in quantum systems.

Contribution

It presents the first analytical solutions for partial wave Coulomb t-matrices at excited bound state energies, using symmetry properties in a four-dimensional Euclidean space.

Findings

Derived analytical expressions for s-, p-, and d-wave t-matrices for like-charged particles.

Obtained the d-wave t-matrix expression for unlike-charged particles at the first excited state.

Enhanced analytical tools for studying Coulomb interactions at excited energies.

Abstract

Starting from the integral representation of the three-dimensional Coulomb transition matrix elaborated by us formerly with the use of specific symmetry of the interaction in a four-dimensional Euclidean space introduced by Fock, the possibility of the analytical solving of the integral equation for the partial wave transition matrices at the excited bound state energy has been studied. New analytical expressions for the partial s-, p- and d-wave Coulomb t-matrices for like-charged particles and the expression for the partial d-wave t-matrix for unlike-charged particles at the energy of the first excited bound state have been derived.