# Pure Coulomb tensor interaction in the Dirac equation

## TL;DR

This paper analyzes bound solutions of the Dirac equation with a pure tensor Coulomb potential, revealing how the potential's sign and magnitude influence particle and anti-particle binding, and how it affects the quantum number range for bound states.

## Contribution

It provides a detailed computation of bound states in the Dirac equation with a tensor Coulomb potential, highlighting the dependence on potential sign and quantum number, which was not previously characterized.

## Key findings

- Binding depends on the sign of the tensor potential.
- Bound solutions exist only for specific signs and magnitudes of the quantum number.
- The tensor potential alters the range of quantum numbers for bound states.

## Abstract

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