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 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 ln α 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.

g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment

“…Here, we note that even though in the case of the original Furry picture the higher-order effects are generally more significant than those in the extended Furry picture, the corresponding uncertainty suggested in Ref. [40] is twice smaller than in Ref. [28].…”

“…However, the theoretical value from Ref. [40] disagrees by about 5.2σ with experiment and, therefore, the g-factor "puzzle" has only got worse. Just recently, Yerokhin et al accomplished an independent evaluation of the two-photon-exchange contribution [42] and presented new results for Li-like silicon and calcium.…”

“…The major difficulty of Li-like systems in comparison to the H-like ones consists in the manyelectron contributions. The recent progress in the manyelectron QED calculations includes the evaluation of the screened QED diagrams [36][37][38][39][40], the two-photon-exchange diagrams [25,39,41,42], and various higher-order effects [28,43,44]. The nuclear recoil effect in Li-like ions was addressed recently in Refs.…”

“…In attempt to resolve this discrepancy, an independent eval-uation of the screened QED diagrams was undertaken by Yerokhin et al [40]. In contrast to Ref.…”

“…The higher-order effects were evaluated within the nonrelativistic quantum electrodynamics (NRQED) approach to the leading order in αZ. As a result, a new theoretical value for 28 Si 11+ was obtained: g th,2020 = 2.000 889 896 3 (15) [40]. For both g th,2019 and g th,2020 , the theoretical error bar is determined by the numerical uncertainty of the calculated contributions and by estimating the unknown higher-order many-electron QED effects.…”