ECAMP 15

Precise spectroscopic measurements in small molecular systems such as He$_2$ and He$_2^+$ are of interest as benchmark for high-accuracy ab-initio quantum-chemical calculations in few-electron molecules [1-3].
In the case of He$_2^+$, only the lowest ($v^+=0-2$) [4-5] and highest ($v^+=22-23$) [6] vibrational levels of the X$^+$ $^2\Sigma_u^+$ electronic ground state have been characterized experimentally.
We describe methods to access and study all vibrational states of He$_2^+$ X$^+$ $^2\Sigma_u^+$ from $v^+=0$ to $v^+=19$ using a multi-steps excitation scheme.
The approach involves the production of a supersonic beam of He$_2$ in the long-lived metastable a $^3\Sigma_u^+(v=0-2)$ states using a cryogenic pulsed valve coupled to an electric discharge [7].
A pulsed laser promotes the system to a selected excited rovibrational level of the c $^3\Sigma_g^+$ electronic state with $v'$ and $N'$ in the range $3-4$ and $0-18$, respectively.
These states either decay radiatively to vibrationally excited levels of the a $^3\Sigma_u^+$ state or by quantum mechanical tunneling through a barrier in the c-state potential.
A second laser is then employed to induce transitions from these vibrationally excited a $^3\Sigma_u^+(v)$ metastable states to vibrationally excited He$_2^+$ X$^+$ $^2\Sigma_u^+(v^+)$ states with $v^+\leq 5$.
High-resolution photoelectron spectra of these ionizing transitions are recorded using the technique of pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy.
To study even higher vibrational levels of He$_2^+$, the second laser is used to directly photoionize the selected intermediate c $^3\Sigma_g^+(v', N')$ states and record PFI-ZEKE photoelectron spectra of the X$^+$ $^2\Sigma_u^+(v^+, N^+)$ levels.
With these excitation schemes, spectra of X$^+$ $^2\Sigma_u^+(v^+, N^+)$ rovibrational levels of He$_2^+$ could be measured for the first time up to the $v^+=19$ rovibrational level.
These new results will be compared with the predictions of ab-initio quantum-chemical calculations and are used to determine an empirical potential-energy function for the X$^+$ $^2\Sigma_u^+$ ground electronic state of He$_2^+$ that reproduces all experimental data within their experimental uncertainties.

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[2] D. Ferenc, V. I. Korobov, and E. Matyus, Phys. Rev. Lett., {125}, 213001 (2020).

[3] J. Gebala, M. Przybytek, M. Gronowski, and M. Tomza, Phys. Rev. A, {108}, 052821 (2023).

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[7] M. Motsch, P. Jansen, J. A. Agner, H. Schmutz, and F. Merkt, Phys. Rev. A, {89}, 043420 (2014).