DETERMINATION OF THE SPIN-ROTATION FINE STRUCTURE OF He2+

Measuring spin-rotation intervals in molecular cations is challenging, particularly so when the ions do not have electric-dipole-allowed rovibrational transitions. We present a method to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states\footnote{P. Jansen, L. Semeria, and F. Merkt, \textit{Phys. Rev. Lett.} \textbf{120}, 043001 (2018).}. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important He${_2}^+$ ion in the X$^+$ $^2\Sigma_\text{u}^+$ ground electronic state. The interaction that is responsible for the level structure in the high Rydberg states of He$_2$ that were probed in our experiment is the $n$-independent spin-rotation interaction of the ion core. As a consequence, the fine-structure splittings in He${_2}^+$ can be related to the fine-structure of the Rydberg states by applying an angular-momentum basis transformation from Hund's case (e[b]) to Hund's case (d). The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of He$_2$ from the a $^3\Sigma_\text{u}^+$ metastable state. Metastable helium molecules are produced by striking a discharge in a pulsed expansion of neat helium gas\footnote{M. Motsch, P. Jansen, J.A. Agner, H. Schmutz, and F. Merkt, \textit{Phys. Rev. A} \textbf{89}, 043420 (2014).}. Cooling the valve body to a temperature of 10\,K and using continuous-wave excitation results in an observed Doppler-limited linewidth of 25\,MHz. The fine structure of Rydberg states of He$_2$ is determined from strict selection rules by comparing the observed splitting of the Rydberg spectrum with the spin-rotational intervals of the initial metastable state. The fine-structure splittings of the $v^+=0$, $N^+=1, 3,$ and 5 levels of He${_2}^+$ are 7.96(14)MHz, 17.91(32)\,MHz and 28.0(6)\,MHz, respectively