  A special class of Dirac-Pauli equations with time-like vector potentials of
external field is investigated. A new exactly solvable relativistic model
describing anomalous interaction of a neutral Dirac fermion with a
cylindrically symmetric external e.m. 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
non-relativistic approximation the considered model is reduced to the
integrable Pron'ko-Stroganov model.
