Partial-wave Coulomb t-matrices for like-charged particles at ground-state energy

We study a special case at which the analytical solution of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix for likely charged particles at negative energy is possible. With the use of the Fock’s method of the stereographic projection of the momentum space onto the four-dimensional unit sphere, the analytical expressions for s-, p- and d-wave partial Coulomb transition matrices for repulsively interacting particles at bound-state energy have been derived.