The short distance behaviour of the anomalous magnetic moment of the electron

The effective anomalous magnetic moment of the electron vanishes at short distances because the electrodynamic form factor F₂(q²) vanishes for q² --> ∞. The effective potential due to the interaction between the anomalous magnetic moment and the Coulomb field of a nucleus only diverges logarithmically at short distances, and not, as might naively be expected, quadratically. There are no other bound states of an electron in a Coulomb field than the well-known atomic states. In particular, there is no room for high mass resonances emulating the ψ as suggested by Barut and Kraus.