Characterization of the electronic ground state of He$_2^+$ by high-resolution photoelectron spectroscopy

TL;DR

This study uses high-resolution photoelectron spectroscopy to map the vibrational and rovibrational structure of He₂⁺, providing detailed energy levels, shape resonances, and an empirical potential-energy function for its electronic ground state.

Contribution

It reports the first comprehensive measurement of 17 vibrational levels of He₂⁺'s ground state, covering over 95% of the potential well, and derives an empirical potential-energy function fitting all experimental data.

Findings

Mapped 17 vibrational levels of He₂⁺'s ground state

Determined the dissociation energy D_e of He₂⁺ as 19,956.10 cm⁻¹

Identified 74 shape resonances in the rovibrational spectrum

Abstract

Excluding the very shallow potential minimum of the electronic ground state, all bound electronic states of He$_2$ have Rydberg character. Their potential-energy functions are similar to those of the He$_2^+$ states to which the Rydberg series converge. Photoionization and electron-impact ionization of the metastable $a~^3\Sigma_u^+$ state of He$_2$ are thus characterized by diagonal Franck-Condon factors and only provide access to low vibrational levels of the He$_2^+$ $X^+$ $^2\Sigma_u^+$ electronic ground state. For this reason, little experimental information is available on the excited vibrational levels of He$_2^+$. We report a measurement, by high-resolution photoelectron spectroscopy, of 17 vibrational levels of the $X^+$ $^2\Sigma_u^+$ state of $^4$He$_2^+$, with vibrational quantum number $v^+$ from 3 to 19 and covering more than 95% of the potential well. To access these states, we exploit a hump in the potential-energy function of the $c~^3\Sigma_g^+$ state, whose vibrational wavefunctions extend to large internuclear distance by quantum-mechanical tunneling through the potential barrier. Combining these results with data on the lowest ($v^+=0-2$) and highest ($v^+=22, 23$) vibrational levels of $^4$He$_2^+$, we derive a full map of the rovibrational structure of He$_2^+$ and, in a least-squares fit, an empirical effective potential-energy function that describes all experimental data within uncertainties. This function yields the positions of the 409 bound rovibrational levels and the positions and widths of the 74 shape resonances of the $X^+$ $^2\Sigma_u^+$ state of $^4$He$_2^+$. The dissociation energy of He$_2^+$ is $D{\rm e}=19,956.10(10)$ cm$^{-1}$ [$D_0(^4{\rm He}_2^+)=19,101.29(10)$ cm$^{-1}$].