Relativistic corrections of m\alpha^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions

TL;DR

This paper advances high-precision calculations of relativistic corrections to the ro-vibrational spectra of H_2^+ and HD^+ ions, aiding in fundamental constant measurements.

Contribution

It provides the first computation of relativistic corrections at order R_ to the binding energy of these ions.

Findings

Relativistic corrections at order R_ were successfully computed.

The results refine the theoretical models for the ro-vibrational spectra.

These calculations support more precise tests of fundamental constants.

Abstract

The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\infty\alpha^4. In this work we complete calculations of various contributions to the R_\infty\alpha^4 order by computing the relativistic corrections to the binding energy of electron.