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

摘要

It was recently shown that the point spectrum of the separated Coulomb–Dirac operator H0(k) is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment Ha(k) as the anomaly parameter tends to 0; this spectral stability holds for all Coulomb coupling constants c for which H0(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.