Precision Spectroscopy of the Fine Structure in the $\boldsymbol{a\;{}^3Σ_u^+(v=0)}$ and $\boldsymbol{c\;{}^3Σ_g^+(v=4)}$ 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 $c$ $^3Σ_g^+\leftarrow a$ $^3Σ_u^+$ electronic transition of $^4$He$_2$ at a precision ($Δν/ν$) 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 $c$ $^3Σ_g^+(v=4)$ state, located energetically above the He$(1$ $^1S_0) + $He$(2$ $^3S_1)$ 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 $a$ $^3Σ_u^+(v=0)$ and $c$ $^3Σ_g^+(v=4)$ 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 $a$ $^3Σ_u^+(v=0)$ and $c$ $^3Σ_g^+(v=4)$ states with much improved precision over previous experimental results. A pronounced broadening of the linewidths of the transitions to the $c$ $^3Σ_g^+(v=4,N=10)$ 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.