Observation of b$_2$ symmetry vibrational levels of the SO$_2$ $\tilde{\mbox{C}}$ $^1$B$_2$ state: Vibrational level staggering, Coriolis interactions, and rotation-vibration constants

The $\mathrm{\tilde{C}}$ $^1$B$_2$ state of SO$_2$ has a double-minimum potential in the antisymmetric stretch coordinate, such that the minimum energy geometry has nonequivalent SO bond lengths. However, low-lying levels with odd quanta of antisymmetric stretch (b$_2$ vibrational symmetry) have not previously been observed because transitions into these levels from the zero-point level of the $\mathrm{\tilde{X}}$ state are vibronically forbidden. We use IR-UV double resonance to observe the b$_2$ vibrational levels of the $\mathrm{\tilde{C}}$ state below 1600 cm$^{-1}$ of vibrational excitation. This enables a direct characterization of the vibrational level staggering that results from the double-minimum potential. In addition, it allows us to deperturb the strong $c$-axis Coriolis interactions between levels of a$_1$ and b$_2$ vibrational symmetry, and to determine accurately the vibrational dependence of the rotational constants in the distorted $\mathrm{\tilde{C}}$ electronic state.