Precision spectroscopy of the hydrogen molecular ions HD$^+$

TL;DR

This paper calculates relativistic and radiative corrections for HD$^+$ molecular ions, improving the precision of transition frequency predictions and independently verifying previous theoretical results.

Contribution

It provides detailed calculations of expectation values and corrections for HD$^+$, reducing numerical uncertainties and confirming prior theoretical work.

Findings

Relativistic and radiative corrections are quantified for HD$^+$.

Numerical uncertainty in key corrections is reduced to sub kHz.

Results verify previous theoretical calculations by Korobov.

Abstract

Expectation values of the Breit operators and the $Q$ terms are calculated for HD$^+$ with the vibrational number $v=0-4$ and the total angular momentum $L=0-4$. Relativistic and radiative corrections to some ro-vibrational transition frequencies are determined. Numerical uncertainty in $R_{\infty}\alpha^2$ order correction is reduced to sub kHz or smaller. Our work provides an independent verification of Korobov's calculations [Phys. Rev. A {\bf74}, 052506 (2006); {\bf77}, 022509 (2008)].