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

Abstract

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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Cited by in corpus (9)

• Generation of rotational ground state HD${}^{+}$ ions in an ion trap using a resonance-enhanced threshold photoionization process
• Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H${}_2^{+}$
• A comparative study of LQU and LQFI in general qubit-qutrit axially symmetric states
• Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD${}^{+}$
• Ab initio QED calculations in diatomic quasimolecules
• Quantum control of a single ${\mathrm{H}}_2^{+}$ molecular ion
• Precision spectroscopy of the hydrogen molecular ions: present status of theory and experiment
• Quantum correlations in general qubit-qudit axially symmetric states
• Spin-orbit interaction in the HD${}^{+}$ ion