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.

References in corpus (5)

• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Proton structure corrections to electronic and muonic hydrogen hyperfine splitting
• Electron self-energy in the presence of magnetic field: hyperfine splitting and g factor
• Relativistic corrections of mα^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion
• Hyperfine structure in the H${}_2^{+}$ and HD${}^{+}$ molecular ions at $m{\alpha }^6$ order

Cited by in corpus (4)

• Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H${}_2^{+}$
• Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD${}^{+}$
• Ab initio QED calculations in diatomic quasimolecules
• Spin-orbit interaction in the HD${}^{+}$ ion