Rovibrational computations for the He$_2$ a $^3\Sigma_\mathrm{u}^+$ state including non-adiabatic, relativistic, and QED corrections

TL;DR

This paper presents highly precise rovibrational energy calculations for the He$_2$ molecule's $^3\Sigma_ ext{u}^+$ state, incorporating advanced corrections to match experimental data with exceptional accuracy.

Contribution

It introduces a potential energy curve with sub-ppm accuracy including relativistic and QED effects, enabling precise rovibrational level predictions.

Findings

Computed rovibrational intervals agree with experimental data.

Achieved sub-ppm accuracy in potential energy curve.

Successfully included non-adiabatic, relativistic, and QED corrections.

Abstract

A potential energy curve (PEC) accurate to a fraction of 1 ppm ($1:10^6$) is computed for the $^3\Sigma_\mathrm{u}^+$ state of He$_2$ endowed with relativistic and QED corrections. The nuclear Schr\"odinger equation is solved on this PEC with diagonal Born-Oppenheimer and non-adiabatic mass corrections to obtain highly accurate rotational-vibrational levels. The computed rovibrational intervals and fine-structure splittings, spanning over several orders of magnitude in energy, are found to be in remarkable agreement with available high-resolution spectroscopy data.