Tensorial form and matrix elements of the relativistic nuclear recoil operator

TL;DR

This paper derives the tensorial form of the relativistic nuclear recoil operator within a specific approximation, demonstrating its importance for accurate isotope shift calculations in multiconfiguration Dirac-Hartree-Fock methods.

Contribution

It introduces a tensorial form of the relativistic nuclear recoil operator at lowest-order relativistic approximation, facilitating more accurate isotope shift computations.

Findings

Relativistic corrections are essential for reliable isotope shift values.

The tensorial form enables improved calculations in multiconfiguration Dirac-Hartree-Fock framework.

Illustrated calculations for Li-, B-, and C-like ions support the method's effectiveness.

Abstract

Within the lowest-order relativistic approximation ($\sim v^2/c^2$) and to first order in $m_e/M$, the tensorial form of the relativistic corrections of the nuclear recoil Hamiltonian is derived, opening interesting perspectives for calculating isotope shifts in the multiconfiguration Dirac-Hartree-Fock framework. Their calculation is illustrated for selected Li-, B- and C-like ions. The present work underlines the fact that the relativistic corrections to the nuclear recoil are definitively necessary for getting reliable isotope shift values.