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arXiv · 2604.25515

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

Chang-Xian Song·Yong-Bo Tang
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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.

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Chang-Xian Song, Yong-Bo Tang. 2026-04-28. The critical role of negative-energy states in the Land\'{e} $g$-factor of lithium-like ions. https://arxiv.org/abs/2604.25515

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