Coulomb problem with short-range interaction: an exactly solvable model

Nonrelativistic Coulomb problem with short-range interaction is considered. As a model of a strong potential Vsub(s)(r), the delta-function type interaction on a sphere r=r0 is chosen. Exact solutions of the Schroedinger equation are obtained for the states with arbitrary angular momentum as well as explicit analytic expressions for scattering lengths, effective radii etc. Comparison of the exact solutions with approximate formulas found earlier for arbitrary short-range potentials Vsub(s)(r) makes it possible to determine regions of the validity of these approximations