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, based on an angular-momentum basis transformation, to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important ${{\mathrm{He}}_2}^{+}$ ion in the $X$ ${}^2{\mathrm{\Sigma }}_u^{+}$ state. The fine-structure splittings of the $v^{+}=0$, $N^{+}=1$, 3, and 5 levels of ${{\mathrm{He}}_2}^{+}$ are 7.96(14), 17.91(32), and 28.0(6) MHz, respectively. The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of ${\mathrm{He}}_2$ from the $a{}^3{\mathrm{\Sigma }}_u^{+}$ metastable state.

• Received 13 October 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.043001