Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H$_2^+$

Abstract

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spinspin tensor interactions in hydrogen molecular ions. The mα 7 ln(α)-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the mα 6 -order relativistic correction, for the case of H + 2 . The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.