Solution of the Dirac equation with non-minimal coupling to noncentral three-vector potential

We introduce non-minimal coupling to three-vector potential in the 3+1 dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic energy spectrum and spinor wavefunctions are obtained for the case where the radial component of the vector potential is proportional to 1/r. The non-minimal coupling presented in this work is a generalization of that which was introduced by Moshinsky and Szczepaniak in the Dirac-Oscillator problem.