Highly accurate eigenvalues for the distorted Coulomb potential

We consider the eigenvalue problem for the radial Schrodinger 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-->infinity. Formulas (14.4.5)-(14.4.8) of Abramowitz and Stegun [Handbook of Mathematical Functions, 8th ed. (Dover, New York, 1972)], 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 illustrations for n up to 2000 are given.