Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin

We obtain analytic expressions for the third-order corrections due to the strong interaction Coulomb potential to the S-wave Green function, energy levels and wave functions at the origin for arbitrary principal quantum number n. Together with the known non-Coulomb correction this results in the complete spectrum of S-states up to order alpha(5)(S). The numerical impact of these corrections on the upsilon spectrum and the top quark pair production cross section near threshold is estimated. (c) 2005 Elsevier B.V. All rights reserved.