Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD$^+$

TL;DR

This paper enhances the theoretical precision of hyperfine interaction coefficients in HD$^+$ by calculating higher-order relativistic and radiative corrections, revealing some deviations from recent spectroscopic measurements.

Contribution

It provides the first detailed calculation of relativistic and radiative corrections at the $meta^6$ and $meta^7 ext{ln}(eta)$ orders for HD$^+$ hyperfine coefficients, improving accuracy significantly.

Findings

Theoretical accuracy improved by over an order of magnitude.

Deviations observed between theory and recent experiments.

Good agreement with previous results for H$_2^+$.

Abstract

Improved values of hyperfine coefficients related to the electronic spin-orbit and electron-nucleus spin-spin tensor interactions in the HD$^+$ molecular ion are obtained through numerical calculation of relativistic corrections at the $m\alpha^6$ order and radiative corrections at the $m\alpha^7\ln(\alpha)$ order. The theoretical accuracy is improved by more than one order of magnitude. Some deviations with recent high-precision ro-vibrational spectroscopy experiments are observed, in contrast with the good agreement obtained in H$_2^+$.