Partial waves of a general off-shell two-body Coulomb-like T-matrix

On the basis of the Gell-Mann — Goldberger two-potential formalism we investigate the partial waves of an off-shell two-body T-matrix in the case of a general Coulomb-like potentialV=V_C+V_S. The regular kernelt_SC,l determining thel-th partial wave of the short-range partT_SC,l of the T-matrix is the solution of the equationt_SC,l=V_S,l+V_S,lG_C,lt_SC,l. The Lippmann-Schwinger operator of this equation formed by the short-range part of the potential and the pure Coulomb Green's operator is shown to be compact under very general assumptions on the potentialV_S admitting potentials vanishing in the coordinate representation liker^–1– (>0) in the infinity. The special case of differentiable and analytic potentialsV_S,l(p,p) is considered in particular. The results are used to discuss in full generality the on-shell singularities of Coulomb-like T-matrices and wave functions and to investigate the singular integrals that occur in the Faddeev equations for Coulomb-like interactions.