Partial wave off-shell Coulomb amplitudes at excited-state energy

Abstract

Based on the integral representation of the three-dimensional Coulomb transition matrix elaborated by us formerly with the use of specific symmetry of the interaction in the four-dimensional Euclidean space introduced by Fock, the possibility of analytical solution 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.