  We show that the point spectrum of the standard Coulomb-Dirac operator H_0 is
the limit of the point spectrum of the Dirac operator with anomalous magnetic
moment H_a as the anomaly parameter tends to 0. For negative angular momentum
quantum number kappa, this holds for all Coulomb coupling constants c for which
H_0 has a distinguished self-adjoint realisation. For positive kappa, however,
there are some exceptional values for c, and in general an index shift between
the eigenvalues of H_0 and the limits of eigenvalues of H_a appears,
accompanied with additional oscillations of the eigenfunctions of H_a very
close to the origin.
