Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems

TL;DR

This paper presents a variational method to solve the no-pair Dirac--Coulomb--Breit equation for two-body systems, providing accurate relativistic energies for systems like positronium and hydrogen, aligning well with QED predictions.

Contribution

It introduces a variational approach to directly solve the no-pair Dirac--Coulomb--Breit equation for two-body systems, bridging relativistic quantum mechanics and QED.

Findings

Excellent agreement with perturbative QED energy expressions

Demonstrates the method's accuracy for various two-body systems

Establishes a reference for relativistic QED computational approaches

Abstract

The sixteen-component, no-pair Dirac--Coulomb--Breit equation, derived from the Bethe--Salpeter equation, is solved in a variational procedure using Gaussian-type basis functions for the example of positronium, muonium, hydrogen atom, and muonic hydrogen. The $\alpha$ fine-structure-constant dependence of the variational energies, through fitting a function of $\alpha^n$ and $\alpha^n\text{ln}\alpha$ terms, shows excellent agreement with the relevant energy expressions of the (perturbative) non-relativistic QED framework, and thereby, establishes a solid reference for the development of a computational relativistic QED approach.