Dirac eigenvalues for a softcore Coulomb potential in d dimensions

TL;DR

This paper derives analytical lower bounds for the Dirac energy spectrum of a fermion in a softcore Coulomb potential across multiple dimensions, validated by numerical comparisons.

Contribution

It introduces a novel application of envelope theory to obtain bounds on Dirac eigenvalues for a generalized softcore Coulomb potential.

Findings

Analytic lower bounds closely match numerical eigenvalues.

Envelope theory effectively bounds Dirac spectra in higher dimensions.

Results extend understanding of relativistic quantum systems with softcore potentials.

Abstract

A single fermion is bound by a softcore central Coulomb potential V(r) = -v/(r^q + b^q)^(1/q), v>0, b>0, q \ge 1, in d>1 spatial dimensions. Envelope theory is used to construct analytic lower bounds for the discrete Dirac energy spectrum. The results are compared to accurate eigenvalues obtained numerically.