Abstract
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=VC+VS. The regular kerneltSC,l determining thel-th partial wave of the short-range partTSC,l of the T-matrix is the solution of the equationtSC,l=VS,l+VS,lGC,ltSC,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 potentialVS admitting potentials vanishing in the coordinate representation liker−1−ɛ (ɛ>0) in the infinity. The special case of differentiable and analytic potentialsVS,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.
Published Version
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