Relativistic recoil corrections of order \boldmath$m(Z\alpha)^6(m/M)$: Hydrogen-like atom and hydrogen molecular ion

TL;DR

This paper derives finite operators for relativistic recoil corrections of order m(Zα)^6(m/M) in hydrogen-like atoms and ions, providing formulas suitable for numerical calculations beyond the adiabatic approximation.

Contribution

It introduces a new derivation of recoil correction operators at order m(Zα)^6(m/M) for two- and three-body systems, extending previous approximations.

Findings

Derived finite operators for recoil corrections

Formulas suitable for numerical evaluation

Beyond adiabatic approximation results

Abstract

The finite operators are derived for the recoil $m\alpha^6(m/M)$ order relativistic corrections (to spin-averaged energy levels) in hydrogen-like atoms and ions in the two- and three-body formalism beyond the adiabatic approximation. Results are presented in a form suitable for numerical evaluation.