Excluding the very shallow potential minimum of the electronic ground state, all bound electronic states of ${\mathrm{He}}_2$ have Rydberg character. Their potential-energy functions are very similar to the potential-energy functions of the ${\mathrm{He}}_2{}^{+}$ states to which the Rydberg series converge. Photoionization and electron-impact ionization of the metastable $a{}^3{\mathrm{\Sigma }}_u{}^{+}$ state of ${\mathrm{He}}_2$ are thus characterized by diagonal Franck-Condon factors and only provide access to low vibrational levels of the ${\mathrm{He}}_2{}^{+} X^{+}{}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic ground state. For this reason, hardly any experimental information is available on the excited vibrational levels of ${\mathrm{He}}_2{}^{+}$. We report on a measurement, by high-resolution photoelectron spectroscopy, of 17 vibrational levels of the $X^{+}{}^2{\mathrm{\Sigma }}_u{}^{+}$ state of ${}^4{\mathrm{He}}_2{}^{+}$, with vibrational quantum number $v^{+}$ ranging 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 $c{}^3{\mathrm{\Sigma }}_g{}^{+}$ state, which has vibrational wave functions extending to large internuclear distance by quantum-mechanical tunneling through the potential barrier. Combining these new results with data available on the lowest ($v^{+}=0–2$) and highest ($v^{+}=22,23$) vibrational levels of ${}^4{\mathrm{He}}_2{}^{+}$, we derive a full map of the rovibrational level structure of ${\mathrm{He}}_2{}^{+}$ and use it to determine, in a least-squares fit, an empirical effective potential-energy function that describes all experimental data within their uncertainties. This potential-energy function is used to calculate the positions of the 409 bound rovibrational levels and the positions and widths of the 74 shape resonances of the $X^{+}{}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic ground state of ${}^4{\mathrm{He}}_2{}^{+}$. The dissociation energy of ${\mathrm{He}}_2{}^{+}$ is determined to be $D_{\mathrm{e}}=19956.10\left(10\right) {\mathrm{cm}}^{-1}[D_0{(}^4{\mathrm{He}}_2{}^{+})=19101.29\left(10\right){\mathrm{cm}}^{-1}]$.

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• Atomic & molecular structure
• Electronic structure of atoms & molecules
• Potential energy surfaces
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• Rotational states
• Scattering of atoms, molecules, clusters & ions
• Single- and few-photon ionization & excitation
• Vibrational states
• Ions
• Molecules
• Rydberg atoms & molecules
• Optical spectroscopy
• Photoionization