Pure Coulomb tensor interaction in the Dirac equation

In this work we compute bound solutions for particles and antiparticles of the Dirac equation for a pure tensor radial Coulomb potential plus a constant. We find that the binding depends on the sign of the tensor constant potential, and allows only bound solutions for a certain sign and magnitude of the $\ensuremath{\kappa}$ quantum number, which is related to the spin-orbit coupling in the Dirac equation. This relation is reversed for antiparticle solutions. On the other hand, the Coulomb tensor potential, although not binding, changes the range of $\ensuremath{\kappa}$ values for which there are bound solutions.