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

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 $Zα$ (where $Z$ is the nuclear charge number and $α$ is the fine-structure constant). We also extend the known results for the $Zα$ expansion of the QED screening correction by deriving the leading logarithmic contribution of order $α^5\lnα$ and obtaining approximate results for the $α^5$ and $α^6$ 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.

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