Relativistic Coulomb scattering of spinless bosons

TL;DR

This paper provides an exact analysis of relativistic Coulomb scattering of spinless bosons, revealing conditions for simplified scattering formulas, suppression effects, and bound-state solutions with implications for spin and pseudospin symmetries.

Contribution

It derives exact closed-form scattering amplitudes and bound states for spinless bosons with mixed vector and scalar Coulomb potentials, including suppression phenomena and symmetry considerations.

Findings

Partial wave series reduces to Rutherford formula under specific potential conditions.

Strong suppression of scattering amplitude occurs when vector and scalar potentials are equal.

Exact bound-state solutions are obtained from complex poles of the scattering amplitude.

Abstract

The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb fields is analyzed in detail with an arbitrary mixing of vector and scalar couplings. It is shown that the partial wave series reduces the scattering amplitude to the closed Rutherford formula exactly when the vector and scalar potentials have the same magnitude, and as an approximation for weak fields. The behavior of the scattering amplitude near the conditions that furnish its closed form is also discussed. Strong suppressions of the scattering amplitude when the vector and scalar potentials have the same magnitude are observed either for particles or antiparticles with low incident momentum. We point out that such strong suppressions might be relevant in the analysis of the scattering of fermions near the conditions for the spin and pseudospin symmetries. From the complex poles of the partial scattering amplitude the exact closed form of bound-state solutions for both particles and antiparticles with different scenarios for the coupling constants are obtained. Perturbative breaking of the accidental degeneracy appearing in a pair of special cases is related to the nonconservation of the Runge-Lenz vector.