Coulomb problem with short-range interaction: exactly solvable model

This paper considers the nonrelativistic Coulomb problem with short-range interaction. The strong potential is modeled by a delta-function interaction on a sphere r = r0. Exact solutions to the Schroedinger equation are obtained for states with arbitrary angular momentum together with explicit analytic expressions for the scattering lengths, effective ranges, etc. The comparison of the exact solutions with the approximate formulas established earlier for arbitrary short-range potential makes it possible to determine the limits of applicability of these approximations