Relativistic two fermion treatment of hyperfine transitions

TL;DR

This paper develops a fully covariant relativistic model for two interacting fermions, incorporating spin effects and anomalous magnetic moments, to analyze hyperfine transitions and related phenomena like photon emission and Lamb shift.

Contribution

It introduces a novel covariant framework for two-fermion systems that includes spin-spin interactions and anomalous magnetic moments, enabling detailed spectral and transition analyses.

Findings

Calculated the spectrum and eigenfunctions of the two-fermion system.

Analyzed photon emission from hyperfine transitions using relativistic eigenfunctions.

Estimated the Lamb shift in muonic hydrogen considering vacuum polarization effects.

Abstract

A system of two fermions with different masses and interacting by the Coulomb potential is presented in a completely covariant framework. The spin-spin interaction, including the anomalous magnetic moments of the two fermions, is added by means of a Breit term. We solve the resulting fourth order differential system by evaluating the spectrum and the eigenfunctions. The interaction vertex with an external electromagnetic field is then determined. The relativistic eigenfunctions are used to study the photon emission from a hyperfine transition and are checked for the calculation of the Lamb shift due to the electron vacuum polarization in the muonic Hydrogen.