The critical role of negative-energy states in the Land\'{e} $g$-factor of lithium-like ions

TL;DR

This paper presents relativistic calculations of the Landé g-factor in lithium-like ions, highlighting the significant impact of negative-energy states on the interelectronic-interaction correction across different states and nuclear charges.

Contribution

It introduces a comprehensive method combining coupled-cluster and perturbation theory to accurately account for negative-energy states in g-factor calculations.

Findings

Negative-energy states contribute up to 30% of the total correction at Z=20 for 2p_{1/2} state.

The approach achieves agreement within 0.1% of previous high-precision calculations.

Negative-energy contributions vary significantly with atomic state and nuclear charge.

Abstract

We report relativistic many-body calculations of the interelectronic-interaction correction to the Land\'{e} $g$-factor of the $2s_{1/2}$, $2p_{1/2}$, $2p_{3/2}$, and $3s_{1/2}$ states in lithium-like ions with nuclear charge $Z = 4-20$. Starting from the Dirac-Coulomb-Breit Hamiltonian, we treat positive-energy contributions using the coupled-cluster method with single and double excitations and include negative-energy contributions through third-order perturbation theory. We observe that negative-energy states give a state-dependent correction whose magnitude and sign vary with both Z and the state; for $2p_{1/2}$, the correction from the negative-energy states reaches 30\% of the total interelectronic-interaction contribution at $Z = 20$. Agreement with previous high-precision calculations is better than $0.1\%$, confirming the reliability of the present approach. This work may serve as a valuable reference for future precise calculations of $g$-factors for many-electron atomic systems.