# Non-adiabatic mass correction for excited states of molecular hydrogen: improvement for the outer-well $H\bar{H}\ ^1\Sigma_\mathrm{g}^+$ term values

## TL;DR

This paper calculates non-adiabatic mass corrections for excited states of molecular hydrogen, improving theoretical predictions of the outer-well $Har{H} extsuperscript{1}\Sigma_g^+$ state by accounting for vibrational effects near the outer minimum.

## Contribution

It introduces a single-state non-adiabatic approach to evaluate mass corrections for excited hydrogen states, enhancing accuracy of theoretical energy levels.

## Key findings

- Negative mass correction near the outer minimum of the $Har{H}$ state.
- Mass correction accounts for deviations between experimental data and previous theories.
- Qualitative features of mass correction are studied across avoided crossings.

## Abstract

The mass-correction function is evaluated for selected excited states of the hydrogen molecule within a single-state non-adiabatic treatment. Its qualitative features are studied under the avoided crossing of the $EF$ with the $GK$ state and also for the outer well of the $H\bar{H}$ state. For the $H\bar{H}$ state, a negative mass correction is obtained for the vibrational motion near the outer minimum, which accounts for most of the deviation between experiment and earlier theoretical work.