# Precision measurement of the rotational energy-level structure of the three-electron molecule He$_2^+$

## TL;DR

This study precisely measured the rotational energy levels of the He₂⁺ molecule's ground state, revealing discrepancies with recent ab initio calculations that grow with higher rotational states.

## Contribution

The paper provides highly accurate experimental rotational energy levels of He₂⁺ and compares them with theoretical calculations, highlighting significant deviations at higher rotational quantum numbers.

## Key findings

- Measured rotational levels with 8 x 10⁻⁴ cm⁻¹ accuracy.
- Discrepancies between experimental data and ab initio calculations increase with N⁺.
- Differences reach up to 0.07 cm⁻¹ at N⁺=19.

## Abstract

The term values of all rotational levels of the $^4$He${_2}^+\,X^+\,^2\Sigma_u^+\,(\nu^+=0)$ ground vibronic state with rotational quantum number $N^+\le 19$ have been determined with an accuracy of 8 x 10$^{-4}$ cm$^{-1}$ ($\sim{25}$ MHz) by MQDT-assisted Rydberg spectroscopy of metastable He$_2^*$. Comparison of these term values with term values recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309 (2012)] reveal discrepancies that rapidly increase with increasing rotational quantum number and reach values of 0.07 cm$^{-1}$ ($\sim{2.1}$ GHz) at $N^+=19$.