Higher-order corrections to spin-spin scalar interactions in HD+ and H2+
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 (Zα)2 EF relativistic correction, for which a detailed derivation is presented, QED corrections up to the order α3 2 (α) 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 H2+, in excellent agreement with RF spectroscopy experiments. In HD+, a 4σ difference is found in the hyperfine splitting of the (v,L)=(0,3) (9,3) two-photon transition that was recently measured with high precision. The origin of this discrepancy is unknown.