Coulomb transition matrix with fractional values of interaction parameter

TL;DR

This paper analytically solves the Coulomb transition matrix for fractional interaction parameters using Fock symmetry, providing explicit expressions for specific fractional values.

Contribution

It introduces analytical solutions for the Coulomb transition matrix at fractional interaction parameters, expanding understanding beyond integer cases.

Findings

Explicit analytical expressions for Coulomb transition matrix at fractional parameters

Solutions derived using Fock symmetry in four-dimensional momentum space

Applicable to negative energy cases in Coulomb interactions

Abstract

Leaning upon the specific Fock symmetry of the Coulomb interaction potential in the four-dimensional momentum space we perform the analytical solution of the Lippman-Schwinger equation for the Coulomb transition matrix in the case of negative energy at fraction values of the interaction parameter. Analytical expressions for the three dimensional and partial Coulomb transition matrix with simplest factional values of the interaction parameter are obtained.