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\newcommand{\cm}{\mbox{cm$^{-1}$}}
\newcommand{\AX}{\mbox{$\textrm{A}^{2}\Pi_{i}-\textrm{X}^{2}\Sigma^{+}$}}
\newcommand{\A}{\mbox{$\textrm{A}^{2}\Pi_{i}$}}
\newcommand{\Av}{\mbox{$\textrm{A}^{2}\Pi_{i}$(\emph{v} = 0)}}
\newcommand{\X}{\mbox{$\textrm{X}^{2}\Sigma^{+}$}}
\newcommand{\Xv}{\mbox{$\textrm{X}^{2}\Sigma^{+}$(\emph{v} = 10)}}
\newcommand{\COplus}{\mbox{$^{12}\textrm{C}^{17}\textrm{O}^+$}}


\newcommand{\BX}{\mbox{$\textrm{B}^{2}\Sigma^+-\textrm{X}^{2}\Sigma^{+}$}}
\newcommand{\B}{\mbox{$\textrm{B}^{2}\Sigma^{+}$}}




\title{FIRST ANALYSIS OF THE $0 - \nu''$ PROGRESSION OF THE COMET-TAIL SYSTEM \AX\ IN THE \mbox{$^{12}$C$^{17}$O$^+$} CATION.}

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\author{\FirstName I.~\LastName PIOTROWSKA, \FirstName W.~\LastName SZAJNA, \FirstName S.~\LastName RYZNER, \FirstName A.~\LastName STASIK, \FirstName A.~ \LastName PARA, \FirstName P.~ \LastName KOLEK, \FirstName R.~\LastName K\c{E}PA, \underline{\FirstName R. \LastName HAKALLA}}
\address{Materials Spectroscopy Laboratory, Institute of Physics, University of Rzesz\'{o}w, Pigonia 1 Street, 35-310 Rzesz\'{o}w, Poland}

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\author{\FirstName M.I. \LastName MALICKA}
\address{The Faculty of Mathematics and Applied Physics, Rzesz\'{o}w University of Technology, Powsta\'{n}c\'{o}w Warszawy 8 Street, 35-959 Rzesz\'{o}w, Poland}


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\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
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The $0 - \nu''$ progression of the Comet-Tail \AX\ system, where $\nu'' = (0,1,2,3)$, was recorded for the first time in the \COplus\ isotopologue. Using a high-resolution Fourier-transform spectrometer, more than 1500 emission lines were measured in the region of 12,880 - 20,500 \cm. 

A deperturbation analysis was performed using the PGOPHER program.\footnote{\href{http://dx.doi.org/10.1016/j.jqsrt.2016.04.010}{doi:10.1016/j.jqsrt.2016.04.010}, C. M. Western, PGOPHER: a program for simulating rotational, vibrational and electronic spectra, \textit{Journal of Quantitative Spectroscopy and Radiative Transfer}, \textbf{186}, 221-242, (2017).} As a result, deperturbed molecular parameters of the \Av\ and X(\emph{v} = 0,1,2,3) levels and the \Av\ $\sim$ \Xv\ perturbation parameter of a complex (spin-orbit, spin-electronic and rotation-electronic) character were determined. 

The values of the ro-vibronic terms of the \Av\ level were also calculated and the percentage $^2\Pi$ character of the \Av\ and \Xv\ levels was examined. This work is a continuation of the studies on the \A\ state in the \COplus\ isotopologue made by our team.\footnote{\href{http://dx.doi.org/10.1016/j.jqsrt.2022.108268}{doi:10.1016/j.jqsrt.2022.108268}, I. Piotrowska, R. Hakalla, W. Szajna, R. K\c{e}pa, First observation of the Comet-Tail \AX\ system in the \COplus\ cation, \textit{Journal of Quantitative Spectroscopy and Radiative Transfer}, \textbf{289}, 108268, (2022).}


%The first recording of the ... progression of the Comet-Tail \AX\ system, where ..., in the \CO\ molecule was performed. Using a high-resolution Fourier-transform spectrometer, more than 1500 emission lines were measured in the region of 12 880 – 20 500 \cm\. A deperturbation analysis was performed using the PGOPHER program.\footnote{\href{http://dx.doi.org/10.1016/j.jqsrt.2016.04.010}{doi:10.1016/j.jqsrt.2016.04.010}, C. M. Western, PGOPHER: a program for simulating rotational, vibrational and
%electronic spectra, \textit{Journal of Quantitative Spectroscopy and Radiative Transfer}, \textbf{186}, 221-242, (2017).} 

%As a result, deperturbed molecular parameters of the \Av\ and X(v = 0,1,2,3) levels and the A(v = 0) ~ X(v = 10) perturbation parameter of a complex, spin-orbit, spin-electronic and rotation-electronic ($\textit{\textbf{L}}-$uncoupling) character were determined. 

%The values of the ro-vibronic terms of the \Av\ level were also calculated and the percentage $^2\Pi$ character of the \Av\ and \Xv\ levels was examined. This work is a continuation of the studies on the \A\ state in the \CO\ isotopologue, made by our team.

%\footnote{\href{http://dx.doi.org/10.1016/j.jqsrt.2022.108268}{doi:10.1016/j.jqsrt.2022.108268}, I. Piotrowska, R. Hakalla, W. Szajna, R. K\c{e}pa, First observation of the Comet-Tail \AX\ system in the \COplus\ cation, \textit{Journal of Quantitative Spectroscopy and Radiative Transfer}, \textbf{289}, 108268, (2022).}



%The \B~$(\nu=1)$ level of \COplus\ was investigated using the high-resolution, emission spectra obtained via Fourier-transform spectroscopy of the strongest $(1-2)$ and $(1-3)$ bands of the First Negative (\BX) system\footnote{\href{https://doi.org/10.1016/j.jms.2003.10.007}{doi:10.1016/j.jms.2003.10.007}, W. Szajna, R. K\c{e}pa, M. Zachwieja, The first negative \mbox{($\textrm{B}^{2}\Sigma^+-\textrm{X}^{2}\Sigma^{+}$)} system of \textrm{CO}$^+$: excitation of higher vibrational levels, J. Mol. Spectrosc., 223, 125-131 (2004)}$^,$\footnote{\href{https://link.springer.com/article/10.1140/epjd/e2004-00060-0}{doi:10.1140/epjd/e2004-00060-0}, W. Szajna, R. K\c{e}pa, M. Zachwieja, Reinvestigation of the \mbox{$\textrm{B}^{2}\Sigma^+-\textrm{X}^{2}\Sigma^{+}$} system in the CO$^+$, Eur. Phys J. D, 30, 49-55 (2004).}.

%The \textrm{B-X, CO}$^+$ bands were recorded with an instrumental resolution of 0.04~\cm\ and the best signal-to-noise ratio ca. 50:1.
%For obtaining spectra of the \COplus\ isotopologue an air-cooled hollow-cathode (HC) lamp, filled with \textrm{$^{12}$C$^{16}$O}$_2$ and trace amount of Ne, was used. The spectrum was calibrated using measurements of the atomic lines of Fe \footnote{\href{https://opg.optica.org/viewmedia.cfm?r=1&rwjcode=josab&uri=josab-8-10-2028&html=true}{doi:10.1364/JOSAB.8.002028}, G. Nave, R.C.M. Learner, A.P. Thorne, C.J. Harris, Precision Fe I and Fe II wavelengths in the ultraviolet spectrum of the iron-neon hollow-cathode lamp, J. Opt. Soc. Am. B, 8, 2028-2041, (1991).} impurity present in the spectra. The absolute accuracy of the calibration is estimated to be better than 0.0050~\cm.

%The present data were elaborated with the PGOPHER program\footnote{\href{https://www.sciencedirect.com/science/article/pii/S0022407316300437?via\%3Dihub}{doi:10.1016/j.jqsrt.2016.04.010}, C. Western, PGOPHER: A program for simulating rotational, vibrational and electronic spectra, J. Quant. Spectrosc. Radiat. Transfer, 186, 221-242 (2017).} and wide set of molecular constants for the \B, $\nu=1$ and \X, $\nu=2,3$ and levels was obtained.This work results were compared with the recent ones presented by Ventura et al.\footnote{\href{https://doi.org/10.1016/j.jqsrt.2020.107312}{doi:10.1016/j.jqsrt.2020.107312}, L.R. Ventura, R.S. da Silva, M.Y. Balleser, C.E. Fellows, Revisiting \textrm{$^{12}$C$^{16}$O}$^+$ first negative system: An experimental and theoretical study, J. Quant. Spectrosc. Radiat. Transfer, 256, 107312 (2020).}, and the discussed by the authors band origin values were carefully checked and verified. Moreover, a very week irregularities with the positions of the lines connected with \B,~$\nu=1, N=21$ levels were discovered.

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