Second-order hyperfine correction to H, D, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math> energy levels
Krzysztof Pachucki, Vojtěch Patkóš, V. A. Yerokhin
Abstract
The complete second-order hyperfine-interaction correction is calculated for centroid energy levels of H, D, and $^{3}\mathrm{He}$ atoms. For $^{3}\mathrm{He}$, the corrections of $\ensuremath{-}2.075\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$ and $\ensuremath{-}0.305\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$ beyond the leading hyperfine-mixing contribution are obtained for the $2\phantom{\rule{0.16em}{0ex}}^{1}S$ and $2\phantom{\rule{0.16em}{0ex}}^{3}S$ states, respectively. These results shift the nuclear charge radii difference derived from the $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ isotope shift and largely resolve the previously reported disagreement between the muonic and electronic helium determinations [van der Werf et al., arXiv:2306.02333; Schuhmann et al., arXiv:2305.11679].