Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable $\mathbf{^4}$He$\mathbf{{_2}}$ and the First Rotational Interval of $\mathbf{^4}$He$\mathbf{{_2}^+}$

TL;DR

This study precisely measures the ionization energy of metastable helium molecules and the rotational interval of helium molecular ions using advanced laser spectroscopy and quantum defect theory, providing benchmarks for theoretical calculations.

Contribution

The paper reports the first high-precision measurements of the ionization energy and rotational interval of helium molecules and ions, using frequency-comb-calibrated spectroscopy and quantum defect extrapolation.

Findings

Ionization energy of He₂ (a³Σu⁺) is 34301.207002(23) cm⁻¹.

Rotational interval of He₂⁺ (X⁺²Σu⁺) is 70.937589(23) cm⁻¹.

Measurements agree with and benchmark ab initio calculations.

Abstract

Molecular helium represents a benchmark system for testing $\textit{ab initio}$ calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the $a\,^3\Sigma_u^+$ state of He$_2$, corresponding to the energy interval between the $a\,^3\Sigma_u^+$ ($v''=0$, $N''=1$) state of He$_2$ and the $X^+\,^2\Sigma_u^+$ ($v^+=0$, $N^+=1$) state of He${_2}^+$, and of the lowest rotational interval of He${_2}^+$. These measurements rely on the excitation of metastable He$_2$ molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a counter-propagating-laser-beam setup. The observed Rydberg states were extrapolated to their series limit using multichannel quantum-defect theory. The ionization energy of He$_2$ ($a\,^3\Sigma_u^+$) and the lowest rotational interval of He${_2}^+$ ($X^+\,^2\Sigma_u^+$) are 34301.207002(23)$\pm 0.000037_{\mathrm{sys}}$ cm$^{-1}$ and 70.937589(23)$\pm 0.000060_{\mathrm{sys}}$ cm$^{-1}$, respectively.