RE-ANALYSIS OF THE SPIN-ORBIT PERTURBATION FOR THE PHILLIPS SYSTEM AND THE BALLIK-RAMSAY SYSTEM OF THE SPECTRA OF C$_{2}$

Author Institution: Graduate School of Natural Science and Technology Okayama University, 3-1-1 Tsushima-Naka, Okayama 700-8530, JapanThe Phillips system and the Ballik-Ramsay system of the spectra of C$_{2}$ have been studied extensively before, and the energy difference between the ground $X^{1}\Sigma^{+}_{g}$ state and the first triplet $a^{3}\Pi_{u}$ state has been determined by analyzing the spin-orbit interaction between the $X^{1}\Sigma^{+}_{g}$ and $b^{3}\Sigma^{-}_{g}$ states. However, the analysis was carried out previously for the individual vibronic bands, and the perturbation parameters $<v|H_{SO}|v^{\prime}>$ of the spin-orbit interaction determined for the different vibronic states lead to the very different values of $A_{so}^{bX}$., 19 (1979).}$^,$, 1838 (1988).} In the present study, we re-analyzed the previous spectral data$^{a,}$, 250 (1988). }$^,$, 340 (2004).} by using the overlap integrals (Franck-Condon factors) and r-centroids between the vibronic states of $X^{1}\Sigma^{+}_{g}$ and $b^{3}\Sigma^{-}_{g}$ calculated from the RKR potential and by fitting all the vibronic states simultaneously. A new set of molecular parameters was obtained, including the single-valued spin-orbit interaction constant $A_{so}^{bX}=3.067(9)$ cm$^{-1}$ and the energy difference $\Delta E=719.84(6)$ cm$^{-1}$ between the $X^{1}\Sigma^{+}_{g}$ and $a^{3}\Pi_{u}$ states, the latter of which is about 1.5 cm$^{-1}$ larger than the previously determined value.$^{a}$ This new result may guide for searching the forbidden transitions between the singlet and triplet states of C$_{2}$