Splitting of $\Lambda$-doubling in the transition of Hund's coupling cases in sodium molecule

The phenomenon of orbital angular momentum $L$-uncoupling from its internuclear axis is observed in Na$_2$ by using high resolution cw optical-optical double resonance spectroscopy. This $L$-uncoupling removes the degeneracy of $\Lambda$-type doubling. In the case of Na$_2$, however, such $\Lambda$-type doubling only reported in the $B\,^1\Pi_u$ state with large speed of rotation and without significant dependence on the vibrational quantum number $v$. In this study, the splitting of $\Lambda$-doubling in the $4\,^1\Pi_g$ and $5\,^1\Delta_g$ states of Na$_2$ is directly measured under our experimental resolution. This splitting caused by the transition of Hund's coupling from case (a) to case (d) is due to $L$-uncoupling from its internuclear axis. The observed energy levels with $e/f$ parities are assigned and the $\Lambda$-type splitting constants $q_0$, $q_v$ and $\mu$ are globally fitted to a standard deviation of $\sigma$ less than $0.03\,cm^{-1}$.