Leading order relativistic corrections to the ro-vibrational spectrum of $\mbox{H}^+_2$ and $\mbox{HD}^+$ molecular ions

Abstract

High-precision variational calculations of the operators for the relativistic corrections in the leading $m{\alpha }^4$ order are presented. The ro-vibrational states in the range of the total orbital angular momentum $L=0-4$ and vibrational quantum number $v=0-10$ for the $\mbox{H}_2^+$ and $\mbox{HD}^+$ molecular ions are considered. We estimate that about ten significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of $10^{-12}$ relative uncertainty.

8 pages, 3 tables, submitted to Phys. Rev. A