Perturbative evaluation of the eigenvalues of the Herbst hamiltonian

We reconsider the well--known and long debated problem of the calculation of the eigenvalues of the Herbst hamiltonian 2\sqrt{ p^2 +m^2} - \kappa / r. We give a formulation of the problem which allows for the first time a perturbative evaluation of the eigenvalues for any n and l and in principle up to any order in \kappa via standard Kato perturbation theory. We present the evaluation of the energy of the n=1 and n=2 states up to \kappa^6 confirming the result previously obtained by Le Yaouanc et al. with a completely different technique. Moreover we give the n=2, l=1 level which is new. Discussion of the results and comparison with previous findings are given in the end.