Spin-orbit coupling of the NaK $3^{3}\Pi$ and $3^{1}\Pi$ states: Determination of the coupling constant and observation of quantum interference effects

We have studied the mutually perturbing $3^{3}\Pi_{\Omega = 0}(v = 32, J = 19) \sim 3^{1}\Pi_{\Omega = 1}(v = 6, J = 19)$ levels of NaK that are coupled together by the spin-orbit interaction. This coupling is nominally forbidden by the $\Delta \Omega = 0$ selection rule for spin-orbit perturbations. However $3^{3}\Pi$ levels labeled by different values of $\Omega$ are mixed by rotational coupling; i.e. the $3^{3}\Pi _{\Omega }$ levels are best described by a coupling scheme intermediate between Hund's cases (a) and (b). Thus the $3^{1}\Pi_{\Omega = 1}$ level couples to the $3^{3}\Pi_{\Omega = 0}$ level via the small admixture of $3^{3}\Pi_{\Omega = 1}$ character in the latter. The $3^{3}\Pi_{\Omega = 0}(v = 32, J = 19) \sim 3^{1}\Pi_{\Omega = 1}(v = 6, J = 19)$ $f$ symmetry pair is of particular interest since it appears to be very close to a 50-50 mixture of triplet and singlet character, and the splitting between these levels provides a direct measure of the $3^{3}\Pi \sim 3^{1}\Pi$ spin-orbit coupling constant. Excitation spectra of the $3^{3}\Pi_{\Omega =0}(v = 32, J = 19) \sim 3^{1}\Pi_{\Omega = 1}(v = 6, J = 19)$ $e$ symmetry pair through the mixed ``window'' levels $1(b)^{3}\Pi_{\Omega = 0}(v = 17, J = 18, 20) \sim 2(A)^{1}\Sigma^{+}(v = 18, J = 18, 20)$ display dramatic quantum interference effects associated with ``singlet'' and ``triplet'' excitation channels. Complete cancellation for one or the other of the two upper states is observed for excitation from the predominantly triplet members of the window level pairs.