Determination of the Spin-Rotation Fine Structure of He_{2}^{+}.

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 He-2(+) ion in the X (2)Sigma(+)(u) state. The fine-structure splittings of the v(+) = 0, N+ = 1, 3, and 5 levels of 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 He-2 from the a (3)Sigma(+)(u) metastable state.