Self-energy screening effects in the $g$ factor of Li-like ions

Abstract

We report an investigation of the self-energy screening effects for the $g$ factor of the ground state of Li-like ions. The leading screening contribution of the relative order $1/Z$ is calculated to all orders in the binding nuclear strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). We also extend the known results for the $Z\alpha$ expansion of the QED screening correction by deriving the leading logarithmic contribution of order ${\alpha }^5\ln \alpha$ and obtaining approximate results for the ${\alpha }^5$ and ${\alpha }^6$ contributions. The comparison of the two approaches yields a stringent check of consistency of the two calculations and allows us to obtain improved estimations of the higher-order screening effects.

arXiv commentSeveral misprints are corrected in ver.3; Sec. VI is updated in ver.2

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• $g$ Factor of Boron-like Tin
• Testing inter-electronic interaction in lithium-like tin
• QED effects in quadratic Zeeman splitting in highly charged hydrogen-like ions
• $g$ factor of the $2p_j$ excited states in lithium-like ions
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation
• Insight into the prospective evaluation of third-order interelectronic corrections on Li-like ions