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arXiv · 2304.12274

Higher-order QED corrections to the hyperfine splitting in $^3$He

Vojtěch Patkóš·Vladimir A. Yerokhin·Krzysztof Pachucki
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Abstract

We present a calculation of the hyperfine splitting of the $2^3S$ state in the $^3$He atom with inclusion of all QED effects up to $\alpha^3E_F$, where $E_F$ is the Fermi splitting. Using the experimental value of the $1S$ hyperfine splitting in $^3$He$^+$, we obtain the theoretical prediction for $^3$He of $\nu_\mathrm{hfs}= -6\,739\,701\,181(41)$ Hz, which is in perfect agreement with the experimental value $-6\,739\,701\,177(16)$ Hz [S. D. Rosner and F. M. Pipkin, Phys. Rev. A ${\bf 1}$, 571 (1970)]. This result constitutes a 40-fold improvement in precision as compared to the previous value and is the most accurate theoretical prediction ever obtained for a non-hydrogenic system.

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Vojtěch Patkóš, Vladimir A. Yerokhin, Krzysztof Pachucki. 2023-04-24. Higher-order QED corrections to the hyperfine splitting in $^3$He. https://doi.org/10.1103/physrevlett.131.183001

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