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

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.