Exceptional coupling constants for the Coulomb–Dirac operator with anomalous magnetic moment

It was recently shown that the point spectrum of the separated Coulomb–Dirac operator H 0 ( k ) is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H a ( k ) as the anomaly parameter tends to 0; this spectral stability holds for all Coulomb coupling constants c for which H 0 ( k ) has a distinguished self-adjoint extension if the angular momentum quantum number k is negative, but for positive k there are certain exceptional values for c. Here we obtain an explicit formula for these exceptional values. In particular, it implies spectral stability for the three-dimensional Coulomb–Dirac operator if | c | < 1 , covering all physically relevant cases.