A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.
Ferraro, E., Messina, A., & Nikitin, A.G. (2010). Exactly solvable relativistic model with the anomalous interaction. PHYSICAL REVIEW A, 81(4), 042108-1-042108-8 [10.1103/PhysRevA.81.042108].