Highly accurate eigenvalues for the distorted Coulomb potential

We consider the eigenvalue problem for the radial Schroedinger equation with potentials of the form V(r) = S(r)/r + R(r) where S(r) and R(r) are well behaved functions which tend to some (not necessarily equal) constants when r → 0 and r → ∞. Formulae given by Abramowitz and Stegun, corresponding to the pure Coulomb case, are here generalized for this distorted case. We also present a complete procedure for the numerical solution of the problem. Our procedure is robust, very economic and particularly suited for very large n. Numerical illustration for n up to 2000 are given. (authors)