Higher-order corrections to spin-spin scalar interactions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>HD</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi mathvariant="normal">H</mml:mi><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:math>
Jean‐Philippe Karr, Mohammad Haidar, Laurent Hilico, Zhen-Xiang Zhong, V. I. Korobov
Abstract
The largest hyperfine interaction coefficients in the hydrogen molecular ion ${\mathrm{HD}}^{+}$, i.e., the electron-proton and electron-deuteron spin-spin scalar interactions, are calculated with estimated uncertainties slightly below 1 ppm. The ${(Z\ensuremath{\alpha})}^{2}{E}_{F}$ relativistic correction for which a detailed derivation is presented, QED corrections up to the order ${\ensuremath{\alpha}}^{3}{ln}^{2}(\ensuremath{\alpha})$ 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 ${\mathrm{H}}_{2}^{+}$, in excellent agreement with rf spectroscopy experiments. In ${\mathrm{HD}}^{+}$, a $4\ensuremath{\sigma}$ difference is found in the hyperfine splitting of the $(v,L)=(0,3)\ensuremath{\rightarrow}(9,3)$ two-photon transition that was recently measured with high precision. The origin of this discrepancy is unknown.