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

We show that the point spectrum of the standard Coulomb–Dirac operator H0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment Ha as the anomaly parameter tends to 0. For negative angular momentum quantum number (kappa), this holds for all Coulomb coupling constants c for which H0 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 H0 and the limits of eigenvalues of Ha appears, accompanied with additional oscillations of the eigenfunctions of Ha very close to the origin.