# Relativistic quantum dynamics of scalar bosons under a full vector Coulomb interaction

## TL;DR

This paper investigates the relativistic quantum behavior of scalar bosons under a comprehensive vector Coulomb interaction, revealing the importance of coupling components for scattering and bound states within the Duffin-Kemmer-Petiau framework.

## Contribution

It provides a detailed analysis of scalar boson dynamics with full vector couplings, including the Coulomb phase shift and bound-state spectrum, highlighting the role of nonminimal and minimal couplings.

## Key findings

- Space component of nonminimal coupling is essential for exact scattering amplitude.
- Rutherford cross section vanishes without the time component of minimal coupling.
- Bound states depend on the couplings and show no pair production, with an accidental degeneracy for specific coupling mixes.

## Abstract

The relativistic quantum dynamics of scalar bosons in the background of a full vector coupling (minimal plus nonminimal vector couplings) is explored in the context of the Duffin-Kemmer-Petiau formalism. The Coulomb phase shift is determined for a general mixing of couplings and it is shown that the space component of the nonminimal coupling is a {\it sine qua non} condition for the exact closed-form scattering amplitude. It follows that the Rutherford cross section vanishes in the absence of the time component of the minimal coupling. Bound-state solutions obtained from the poles of the partial scattering amplitude show that the time component of the minimal coupling plays an essential role. The bound-state solutions depend on the nonminimal coupling and the spectrum consists of particles or antiparticles depending on the sign of the time component of the minimal coupling without chance for pair production even in the presence of strong couplings. It is also shown that an accidental degeneracy appears for a particular mixing of couplings.