2C-R4WM spectroscopy of jet cooled NO3

We have generated NO$_3$ from pyrolysis of N$_2$O$_5$ following supersonic free jet expansion, and carried out two color resonant four wave mixing (~2C-R4WM~) spectroscopy of the $\tilde{B}$ $^2E'$ -- $\tilde{X}$ $^2A_2'$ electronic transition. One laser was fixed to pump NO$_3$ to a ro-vibronic level of the $\tilde{B}$ state, and the other laser (~probe~) was scanned across two levels of the $\tilde{X}$ $^2A_2'$ state lying at 1051 and 1492 cm$^{-1}$, the $\nu_1$ ($a_1'$) and $\nu_3$ ($e'$) fundamentals, respectively. The 2C-R4WM spectra have unexpected back-ground signal of NO$_3$ (~stray signal due to experimental set-up is also detected~) similar to laser induced fluorescence (~LIF~) excitation spectrum of the 0-0 band, although the back-ground signal was not expected in considering the 2C-R4WM scheme. Despite the back-ground interference, we have observed two peaks at 1051.61 and 1055.29 cm$^{-1}$ in the $\nu_1$ region of the spectrum, and the frequencies agree with the two bands, 1051.2 and 1055.3 cm$^{-1}$, of our relatively higher resolution dispersed fluorescence spectrum, the former of which has been assigned to the $\nu_1$ fundamental. Band width of both peaks, $\sim$ 0.2 cm$^{-1}$, is broader than twice the experimental spectral-resolution, 0.04 cm$^{-1}$ (~because this experiment is double resonance spectroscopy~), and the 1051.61 cm$^{-1}$ peak is attributed to a $Q$ branch band head (~a line-like $Q$ branch~) of the $\nu_1$ fundamental. The other branches are suspected to be hidden in noise of the back-ground signal. The 1055.29 cm$^{-1}$ peak is also attributed to a $Q$ band head. The $\tilde{B}$ $^2E'_{\frac{1}{2}}$ (~$J' = \frac{3}{2}$, $K' = 1$~) -- $\tilde{X}$ $^2A_2'$ (~$N'' = 1$, $K'' = 0$~) ro-vibronic transition was used as the pump transition. The dump (~probe~) transition to both $a_1'$ and $e'$ vibronic levels are then allowed as perpendicular transition. Accordingly, it cannot be determined from present results whether the 1055.29 cm$^{-1}$ band is attributed to $a_1'$ or $e'$ ($\nu_3$), unfortunately. The 2C-R4WM spectrum of the 1492 cm$^{-1}$ band region shows one $Q$ head at 1499.79 cm$^{-1}$, which is consistent with our dispersed fluorescence spectrum. By considering with the $\nu_3$ + $\nu_4$ - $\nu_4$ hot band\footnote{K.~Kawaguchi $et$ $al.$, $J.$ $Phys.$ $Chem.$ $A$ 117, 13732 (2013) and E.~Hirota, $J.$ $Mol.$ $Spectrosco.$ 310, 99 (2015).}, the present results suggest that both 1055.29 and 1499.79 cm$^{-1}$ levels are $a_1'$ level