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Article Dans Une Revue Physical Review A Année : 2020

Higher-order corrections to spin-spin scalar interactions in HD$^+$ and H$_2^+$

Résumé

The largest hyperfine interaction coefficients in the hydrogen molecular ion HD$^+$, i.e. the electron-proton and electron-deuteron spin-spin scalar interactions, are calculated with estimated uncertainties slightly below 1~ppm. The $(Z\alpha)^2 E_F$ relativistic correction, for which a detailed derivation is presented, QED corrections up to the order $\alpha^3 \ln^2 (\alpha)$ along with an estimate of higher-order terms, and nuclear structure corrections are taken into account. Improved results are also given for the electron-proton interaction coefficient in H$_2^+$, in excellent agreement with RF spectroscopy experiments. In HD$^+$, a 4$\sigma$ difference is found in the hyperfine splitting of the $(v,L)=(0,3) \to (9,3)$ two-photon transition that was recently measured with high precision. The origin of this discrepancy is unknown.
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Dates et versions

hal-02991514 , version 1 (06-11-2020)

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Jean-Philippe Karr, Mohammad Haidar, Laurent Hilico, Zhen-Xiang Zhong, Vladimir Korobov. Higher-order corrections to spin-spin scalar interactions in HD$^+$ and H$_2^+$. Physical Review A, 2020, 102 (5), pp.052827. ⟨10.1103/PhysRevA.102.052827⟩. ⟨hal-02991514⟩
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