Relativistic corrections of order $m\alpha^6$: singular operators and regularization

TL;DR

This paper derives finite operators for relativistic corrections of order mα^6 in hydrogen-like systems, analyzing singular operators and discussing regularization methods beyond the adiabatic approximation.

Contribution

It provides a detailed derivation of finite operators for relativistic corrections at order mα^6, including analysis of singular operators and regularization techniques.

Findings

Derived finite operators for relativistic corrections of order mα^6.

Analyzed singular operators and discussed regularization methods.

Extended the formalism beyond the adiabatic approximation.

Abstract

The finite operators are derived for the nonrecoil (leading order in the $(m/M)$ expansion) relativistic corrections in hydrogen-like atoms and ions at orders $m\alpha^6$ in the two- and three-body formalism beyond the adiabatic approximation. Singular operators that appear in the derivation are analysed, and various regularization methods are discussed.