Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment

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.