Amplification of coupling for Yukawa potentials

TL;DR

This paper investigates how the coupling in Yukawa potentials can be amplified when considering the Dirac equation, revealing complex effects beyond traditional non-relativistic bounds.

Contribution

It introduces a numerical study of the Dirac equation with Yukawa potentials to explore the amplification of coupling effects suggested by Darwin term arguments.

Findings

Amplification of coupling effects observed in Dirac equation solutions

Traditional bounds on bound states are modified by relativistic effects

Numerical results support the complex interplay between potential parameters

Abstract

It is well known that Yukawa potentials permit bound states in the Schrodinger equation only if the ratio of the exchanged mass to bound mass is below a critical multiple of the coupling constant. However, arguments suggested by the Darwin term imply a more complex situation. By numerically studying the Dirac equation with a Yukawa potential we investigate this amplification effect.