Ⅰ. INTRODUCTION
The blue system, or the $ C^2\Pi $$ X^2\Pi $ transition of silver oxide (AgO) has been studied by several groups [16]. The blue system was originally named as the $ A $$ X $ system, and it was renamed as the $ C $$ X $ system by Bauschlicher et al. [6] following ab initio calculations. The first rotational analysis of the $ C^2\Pi $$ X^2\Pi $ transition was performed by Uhler [1], resulting in determination of the spectroscopic constants for $ C^2\Pi $ $ v' $ = 0/1 states. After that, Griffiths and Barrow [2] studied the $ C^2\Pi $$ X^2\Pi $ emission spectrum and obtained both vibrational and rotational constants for the $ C^2\Pi $ state of the $ ^{107} $Ag$ ^{16} $O isotopologue. The experiment also shows that the $ C^2\Pi $ state only has a shallow potential minimum. Supported by isotope shifts, Vujisić et al. [3] reported the improved $ ^{107} $Ag$ ^{16} $O and the new $ ^{107} $Ag$ ^{18} $O vibrational constants for the $ C^2\Pi $ state. Later, through a reanalysis of the $ C^2\Pi $$ X^2\Pi $(0, 0/1) band spectra recorded by Uhler [1], Brien et al. [5] obtained more accurate spectroscopic constants for the $ C^2\Pi $ $ v' $ = 0 state of $ ^{107} $Ag$ ^{16} $O isotopologue.
Considering the fact that the natural abundance ratio of silver isotopes is about 1:1, both $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O molecules should be produced simultaneously in previous experiments where isotopically pure silver samples were not used. However, limited by the experimental resolution, rotational constants have not been obtained for the $ C^2\Pi $ state of $ ^{109} $Ag$ ^{16} $O. In this work, we reinvestigated the $ C^2\Pi $$ X^2\Pi $(0, 0) band by using a narrowband laser source [7]. The spectral resolution ($ \sim $0.02 cm$ ^{1} $) allows us to resolve the rotational structures for both $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O isotopologues. From a detailed analysis of the experimental data, accurate rotational constants of the $ C^2\Pi $ $ v' $ = 0 state have been determined for both $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O isotopologues.
Ⅱ. EXPERIMENTS
The experiment is performed in our supersonic jet laser induced fluorescence (LIF) setup that has been described in detail elsewhere [zhang_highresolution_2017, zhang_rotationally_2018]. In brief, AgO molecules are produced by discharging a gas mixture ($ \sim $5%O$ _2 $/Ar) between the tips of two silver needles. The needles are made from a bulk silver with natural isotopic abundances, i.e. $ ^{107} $Ag:$ ^{109} $Ag = 1.08:1, allowing for simultaneous production of $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O in the experiment. The discharge occurs at the beginning part of the supersonic jet expansion. The AgO molecules produced in the discharge plasma are then cooled down by supersonic expansion. At a distance of $ \sim $30 mm downstream away from the electrodes, the molecule beam is crossed perpendicularly by a laser beam. Fluorescent emissions from laser excited AgO molecules are collected by a lens system and detected by a photomultiplier tube (PMT).
To resolve the rotational structures of the two $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O isotopologues, a homemade single longitude mode optical parametric oscillator (SLMOPO) is used to record the LIF spectra [7]. The SLMOPO employs a grazingincidencegrating Littmantype cavity as the oscillator and a KTP (KTiOPO$ _4 $) crystal as the nonlinear frequency conversion medium, and is pumped by a pulsed singlefrequency 532 nm laser beam. The signal output of the OPO can be operated in the 700$  $1030 nm range, with an estimated bandwidth of $ \sim $0.004 cm$ ^{1} $. Further details and full performance of this OPO system can be seen in Ref.[7]. In the present experiment, the signal output of the OPO is frequency doubled in a KDP (KD$ _2 $PO$ _4 $) crystal to obtain the tunable radiation in the 405$  $415 nm region, with an estimated bandwidth of $ \sim $0.006 cm$ ^{1} $. During the experiment running, the frequency of the OPO signal output is calibrated online by a wavelength meter (High Finesse, WS7). The absolute frequency accuracy of extracted individual line positions from the recorded spectral is found to be $ \sim $0.006 cm$ ^{1} $.
Ⅲ. RESULTS AND DISCUSSION
According to the reported band origin of $ ^{107} $Ag$ ^{16} $O $ C^2\Pi $$ X^2\Pi $(0, 0) band [2, 5], our experiment was performed in a frequency region of 24200$  $24420 cm$ ^{1} $. Due to the spinorbit coupling in both $ C^2\Pi $ and $ X^2\Pi $ states, the (0, 0) band consists of two subbands. FIG. 1 and FIG. 2 show the recorded spectra of the two spinorbit subbands of $ C^2\Pi_{1/2} $$ X^2\Pi_{1/2} $ and $ C^2\Pi_{3/2} $$ X^2\Pi_{3/2} $ at around 24240.2 cm$ ^{1} $ and 24412.3 cm$ ^{1} $, respectively. These estimated band origins are in good agreement with the values reported in Refs.[15]. The spectral resolution is found to be $ \sim $0.02 cm$ ^{1} $, which is dominated by the Doppler linewidth originating from the residual velocity distribution of AgO molecules in the supersonic jet expansion. At this spectral resolution, most rotational transition lines of both $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O isotopologues are well resolved, leaving the most dense part of the spectra, namely the Rbranch head of $ C^2\Pi_{1/2} $$ X^2\Pi_{1/2} $, to be partly resolved. Each spinorbit subband consists of strong P and Rbranches, and a relatively weak Qbranch, which is characteristic for a typical $ \Pi $$ \Pi $ transition. The Rbranch can be easily recognized by its clear band head profile while the P and Qbranches extend to the red side. With a close look at the high resolution spectrum, each subband exhibits two Rbranch band heads with an energy interval of $ \sim $0.1 cm$ ^{1} $. In addition, two components with nearly equal intensities are also observed in P and Qbranches. The comparable intensities are consistent with the natural abundance ratio of $ ^{107} $Ag$ ^{16} $O to $ ^{109} $Ag$ ^{16} $O ($ \sim $1:1). Furthermore, the component in the lower energy side is readily recognized as the (0, 0) band of $ ^{107} $Ag$ ^{16} $O based on the previously reported spectroscopic constants [2, 5]. Therefore, the other component is assigned as the (0, 0) band of $ ^{109} $Ag$ ^{16} $O isotopologue.
It can also be seen from FIG. 1 and FIG. 2 that the rotational structure of the $ C^2\Pi_{3/2} $$ X^2\Pi_{3/2} $ subband is much simpler than that of the $ C^2\Pi_{1/2} $$ X^2\Pi_{1/2} $ one. For the $ C^2\Pi_{3/2} $$ X^2\Pi_{3/2} $ subband (FIG. 2), individual $ J $lines contain two components and the energy intervals within them are $ J $independent. As pointed above, these two components arise from $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O isotope shift. For the $ C^2\Pi_{1/2} $$ X^2\Pi_{1/2} $ subband (FIG. 1), in addition to the isotope shift, the $ \Lambda $doubling is also observed. As expected, the energy intervals within the two $ \Lambda $doubling components should be $ J $dependent, that is, become larger as the $ J $ increases. Because the $ \Lambda $doubling effect is much smaller in $ \Omega $ = 3/2 components of both $ C^2\Pi $ and $ X^2\Pi $ states [4, 10], the $ \Lambda $doubling could not be resolved for the $ C^2\Pi_{3/2} $$ X^2\Pi_{3/2} $ subband in present study. These behaviors are also observed in previous study [2].
Based on the reported spectroscopic constants for both $ C^2\Pi $ and $ X^2\Pi $ states of $ ^{107} $Ag$ ^{16} $O isotopologue, rotational assignments of individual transition lines are straightforward. For the $ ^{109} $Ag$ ^{16} $O isotopologue, as the starting point, a set of constants are calculated firstly using isotope relations of rotational constants [11]. After that, using these calculated constants and rotational combination differences in the ground state $ X^2\Pi $, the lines arising from the $ ^{109} $Ag$ ^{16} $O isotopologue are also assigned. The assignments for both $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O isotopologues and the line positions extracted from the observed spectra are summarized in supplementary materials. A least square fit of the line positions is performed in the Pgopher software [12] to obtain accurate spectroscopic constants. For the $ C^2\Pi $ and $ X^2\Pi $ states, a standard effective Hamiltonian [13] is used as the following:
$ \begin{eqnarray} \hat{\textbf{H}} = B\hat{\textbf{N}}^{2}  D\hat{\textbf{N}}^{4} + A\hat{L}_{Z}\hat{S}_{Z} + \dfrac{A_{D}}{2}[\hat{\textbf{N}}^{2} , \, \hat{L}_{Z}\hat{S}_{Z}]_{+} \\ \dfrac{p}{2}(\hat{N}_{+}\hat{S}_{+} + \hat{N}_{}\hat{S}_{}) + \dfrac{q}{2}({\hat N_ + ^2 + \hat N_  ^2} )\quad \end{eqnarray} $

(1) 
where the first two terms represent the rotation operator, the middle two terms describe the spinorbit operator, and the last two terms represent the $ \Lambda $doubling effect in a $ ^{2}\Pi $ state. In Eq.(1), $ B $ is the rotational constant, $ D $ is the centrifugal distortion constant, $ A $ is the spinorbit coupling constant, $ A_D $ the centrifugal distortion of the spinorbit coupling effect, $ p $ and $ q $ are the $ \Lambda $doubling constants.
In the fits, the spectroscopic constants for $ X^2\Pi $ $ v $ = 0 state are fixed to the values reported in Ref.[10], while the $ C^2\Pi $ $ v $ = 0 state constants are set to the variable parameters. In order to obtain more accurate molecular constants, some partly resolved Rbranch lines and very weak Qbranch lines are weighted by two standard deviations (see the detailed line list in supplementary materials). In total, 364 observed lines are included in the fit. The rms of the fit is $ \sim $ 0.003 cm$ ^{1} $(weighted, unweighted average error is 0.004 cm$ ^{1} $). The calculated line positions and observationcalculation (oc) deviations for individual transition lines are also summarized in supplementary materials. The resulting $ C^2\Pi $ $ v $ = 0 state constants for both $ ^{109} $Ag$ ^{16} $O and $ ^{107} $Ag$ ^{16} $O are summarized in Table Ⅰ. The $ ^{109} $Ag$ ^{16} $O constants are reported for the first time. The $ ^{107} $Ag$ ^{16} $O constants are also improved in precision compared to previously reported values [2, 5], due to the fact that the spectrum in literature could be more or less contaminated by unresolved isotopologues.
Table Ⅰ
Spectroscopic constants for the $ C^2\Pi $ $ v' $ = 0 state of AgO.
The determined spinorbit coupling constant for the $ C^2\Pi $ state is $ A $ = $  $97.1 cm$ ^{1} $, which is significantly smaller than that for $ X^2\Pi $ ($ A $ = $  $269.3 cm$ ^{1} $) and $ D^2\Pi $ ($ A $ = $  $226.3 cm$ ^{1} $) states [5]. The difference indicates that the nature of the spinorbit coupling effect in $ C^2\Pi $ is probably different from that in $ C^2\Pi $ and $ D^2\Pi $ states. According to discussions in Refs.[4, 6, 10], the $ X^2\Pi $ state correlates to two ground state atoms Ag(4d$ ^{10} $5s$ ^{1} $, $ ^{2} $S)+O(2p$ ^4 $, $ ^{3} $P) and has significantly ionic characters Ag$ ^+ $(4d$ ^{10} $)+O$ ^{} $(2p$ ^5 $) and Ag$ ^+ $(4d$ ^{9} $5s$ ^{1} $)+O$ ^{} $(2p$ ^5 $). The $ D^2\Pi $ correlates to the ground state O(2p$ ^4 $, $ ^{3} $P) atom and excited state Ag(4d$ ^{9} $5s$ ^{2} $, $ ^{2} $P or $ ^{2} $D) atom. The spinorbit constants for the atoms are O(2p$ ^4 $, $ \zeta $ = $  $151 cm$ ^{1} $), O$ ^{} $(2p$ ^5 $, $ \zeta $ = $  $121 cm$ ^{1} $) and Ag(4d$ ^{9} $5s$ ^{2} $, $ \zeta $ = $  $1767 cm$ ^{1} $) [helene_lefebvrebrion_spectra_2004]. By comparing the molecular spinorbit coupling constants with the atomic ones, we can easily conclude that both phole on the O (or O$ ^ $) atom and dhole on the Ag atom account for the large spinorbit coupling in $ X^2\Pi $ and $ D^2\Pi $ states [5, 10]. In contrast, the spinorbit coupling effect in the $ C^2\Pi $ state differs. Theoretical study [6] shows that the $ C^2\Pi $ state correlates to the Ag(4d$ ^{10} $5s$ ^{1} $, $ ^{2} $S)+O(2p$ ^4 $, $ ^{1} $D) dissociation limit, in which neither the O nor Ag atom could make contributions to the molecular spinorbit coupling. If this holds strictly, the $ C^2\Pi $ state is expected free of spinorbit splitting. However, the experiments (this work and Ref.[5]) do observe spinorbit splitting in the $ C^2\Pi $ state. Therefore, the observed spinorbit splitting must be caused by mixing with other states. By examining the nearby electronic states, the candidates are probably the repulsive $ ^{4}\Sigma^{} $ and $ ^{4}\Pi $ states, which correlate to the dissociation limit of the ground state atoms Ag(4d$ ^{10} $5s$ ^{1} $, $ ^{2} $S)+O(2p$ ^4 $, $ ^{3} $P) [6]. As the spinorbit splitting in O(2p$ ^4 $, $ ^{3}P $) is $  $158 cm$ ^{1} $, it is reasonable that $ C^2\Pi $ state gains a splitting of $  $97 cm$ ^{1} $ by partly mixing with this (these) state(s). This idea could be supported by previous studies [1, 2], where Uhler [1] observed predissociation in both $ \Omega $ = 1/2 and $ \Omega $ = 3/2 components of $ C^2\Pi $ $ v' $ = 1 level. It is suggested that the predissociation is caused by interaction with a $ ^{4}\Sigma^{} $ or $ ^{4}\Pi $ state because they do have the $ \Omega $ = 3/2 component [2]. The interactions between $ C^2\Pi $ state and these repulsive states can be well understood by further theoretical studies.
Ⅳ. CONCLUSION
We present a high resolution spectroscopic study on the $ C^2\Pi $$ X^2\Pi $ transition (0, 0) band of both $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O isotopologues. The spectrum of $ ^{109} $Ag$ ^{16} $O is reported for the first time. From rotational analysis, accurate molecular constants have been determined for both $ ^{107} $Ag$ ^{16} $O and $ ^{109} $Ag$ ^{16} $O. The spinorbit splitting of $ C^2\Pi $ state is suggested to be caused by interacting with the repulsive $ ^{4}\Sigma^{} $ or $ ^{4}\Pi $ state, which correlates to the two ground state atoms Ag(4d$ ^{10} $5s$ ^{1} $, $ ^{2} $S)+O(2p$ ^4 $, $ ^{3} $P).
Supplementary materials: The list of transition lines, rotational assignments, and oc deviations obtained from the fits are given.
Ⅴ. ACKNOWLEDGEMENTS
This work was supported by the the National Natural Science foundation of China (No.21773221 and No.21727804), the National Key R&D Program of China (2017YFA0303502), , and the Fundamental Research Funds for the Central Universities of China (No.WK2340000078).