Study of the Klein--Gordon equation for a hydrogenic model of dyons

TL;DR

This paper extends the hydrogen atom model to include dyons using the Klein--Gordon equation, deriving analytical solutions and analyzing the energy spectrum and charge density, revealing stronger interactions than standard atoms.

Contribution

It generalizes the hydrogen atom model to relativistic dyons and provides analytical solutions using special functions, highlighting differences in interaction strength.

Findings

Dyon atom exhibits greater charge interaction than standard hydrogen.

Analytical solutions expressed via Whittaker functions and Jacobi polynomials.

Comparison shows smaller nucleus-charge distance in dyon atom.

Abstract

This article presents the generalization of a zero spin hydrogen atom to a relativistic atomic model of hydrogen with dyons using the Klein--Gordon equation. The derivation of the Klein--Gordon equation for the particle of relative motion is shown. In addition, the analytical solutions of the equation are calculated in terms of Whittaker functions and Jacobi weighted polynomials. The discrete spectrum of energy, and the charge density of the orbiting dyon are presented. For a system of positive magnetic and electric charges in the nucleus and negative charges for the orbiting particle, and considering the first allowed values of $N$ and $l$, it was found that the dyon atom acts with a greater force of interaction between the charges of the nucleus and the secondary particle compared to the standard atom. It was obtained by comparing the distance between the nucleus and charge density concentrations from the dyon atom with the relativistic pionic atom.