Model-QED-operator approach to relativistic calculations of the nuclear recoil effect in many-electron atoms and ions

TL;DR

This paper introduces a relativistic model-operator method for calculating the nuclear recoil effect in many-electron atoms, improving accuracy beyond the Breit approximation and compatible with existing Dirac-Coulomb-Breit calculations.

Contribution

The paper develops a novel model-operator approach that incorporates relativistic effects and electron correlation for nuclear recoil calculations in many-electron systems.

Findings

The model operator accurately reproduces ab initio QED results.

It extends the capability of relativistic atomic calculations.

The method is easily integrated into existing computational frameworks.

Abstract

A model-operator approach to fully relativistic calculations of the nuclear recoil effect on energy levels in many-electron atomic systems is worked out. The one-electron part of the model operator for treating the normal mass shift beyond the Breit approximation is represented by a sum of semilocal and nonlocal potentials. The latter ones are constructed by employing the diagonal and off-diagonal matrix elements rigorously evaluated for hydrogenlike ions to first order in the electron-to-nucleus mass ratio. The specific mass shift beyond the lowest-order relativistic approximation has a form which can be directly employed in calculations. The capabilities of the method are probed by comparison of its predictions with the results of ab initio QED calculations. The proposed operator can be easily incorporated into any relativistic calculation based on the Dirac-Coulomb-Breit Hamiltonian.