Abstract
In the representation space approach a useful analytical expression for the integral transform of the Coulomb Green's function by the Hankel function is constructed via Sturmian representation of the bound-state Coulomb Green's function. This integral transform is exploited to construct off-shell Jost solutions for motion in Coulomb and Coulomb plus separable interactions in the maximal reduced form. The expressions for the corresponding off-shell $T$ matrices are also constructed by using a modified relation between the off-shell physical solution and the $T$ matrix that does not involve the potential explicitly. Finally, off-shell $T$ matrices are computed to examine the role of the Coulomb interaction in proton-proton scattering in the ${}^{1}{S}_{0}$ channel.
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