Precision Spectroscopy of the Fine Structure in the and States of the Helium Dimer

With four electrons, He${}_2$ is one of very few molecules for which first-principles quantum-chemical calculations that include the treatment of nonadiabatic, relativistic and quantum-electrodynamics corrections are possible. Precise spectroscopic measurements are needed as references to test these calculations. We report here on a spectroscopic measurement of the $c$ ${}^3{\mathrm{\Sigma }}_g^{+}\leftarrow a$ ${}^3{\mathrm{\Sigma }}_u^{+}$ electronic transition of ${}^4$He${}_2$ at a precision ($\mathrm{\Delta }\nu \mathrm{/}\nu$) of $2.5\times {10}^{-10}$ and with full resolution of the rotational, spin-spin and spin-rotational fine structures. The investigation focuses on transitions to the rotational levels of the $c$ ${}^3{\mathrm{\Sigma }}_g^{+}(v=4)$ state, located energetically above the He$(1$ ${}^1{S}_0)+$He$(2$ ${}^3{S}_1)$ dissociation limit and decaying by tunneling predissociation through a barrier in the $c$ state. The new data include a full map of the energy levels of the $a$ ${}^3{\mathrm{\Sigma }}_u^{+}(v=0)$ and $c$ ${}^3{\mathrm{\Sigma }}_g^{+}(v=4)$ states with rotational quantum numbers $N$ up to 9 and 10, respectively, and full sets of fine-structure intervals in these levels for comparison with first-principles calculations from a parallel investigation [B. Rácsai, P. Jeszenszki, A. Margócsy and E. Matyús, arXiv:2506.23879v1 (2025)]. The new data were combined with data from earlier measurements of the spectrum of the $c-a$ band system of ${}^4$He${}_2$ to derive full sets of molecular constants for the $a$ ${}^3{\mathrm{\Sigma }}_u^{+}(v=0)$ and $c$ ${}^3{\mathrm{\Sigma }}_g^{+}(v=4)$ states with much improved precision over previous experimental results. A pronounced broadening of the linewidths of the transitions to the $c$ ${}^3{\mathrm{\Sigma }}_g^{+}(v=4,N=10)$ fine-structure levels is attributed to tunneling predissociation through a barrier in the potential of the $c$ state and is quantitatively accounted for by calculations of the predissociation widths.