Partial-wave Coulomb transition matrices for attractive interaction by Fock's method

TL;DR

This paper uses Fock's stereographic projection method to analytically solve the Lippmann-Schwinger equation for partial wave Coulomb transition matrices at the ground state, providing new simple formulas for p-, d-, and f-waves.

Contribution

It introduces an analytical approach based on Fock's method to derive explicit formulas for Coulomb transition matrices at the ground state energy, extending to excited states.

Findings

Derived simple analytical expressions for p-, d-, and f-wave transition matrices.

Demonstrated the method's applicability at the ground bound state energy.

Potential extension to excited bound states energies.

Abstract

Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states. Keywords: Partial wave Coulomb transition matrix; Lippmann-Schwinger equation; Fock method; Analytical solution PACS Nos. 03.65.-w; 03.65.Nk; 34.20.Cf