Three-states model for calculating the $X$-$X$ rovibrational transition intensities in hydroxyl radical

The best available line list of OH [Brooke et al. (2016)] contains the high-quality line frequencies, yet the line intensities need refinement because the model function used to interpolate the RKR potential and to extrapolate it into the repulsion region was not analytic [Medvedev et al. Mol. Phys. (2024)], and also because the coupling between the ground $X^2\Pi$ and first excited $A^2\Sigma^+$ electronic states was treated by the perturbation theory. In this paper, we performed ab initio calculations of all necessary molecular functions at $r=0.4$-8.0 bohr, and then we construct fully analytic model functions entering the Hamiltonian. The model functions were fitted to both the \ai\ data and the available experimental data on the line positions and energy levels, the relative line intensities, and the transition dipole moments derived from the measured permanent dipoles. The system of three coupled Schr\"odinger equations for two multiplet components of the $X$ state plus the $A$ state was solved to calculate the energy levels and the line intensities. The new set of the \EinA\ permits to decrease the scatter of the logarithmic populations of the ro-vibrational levels derived from the observed radiation fluxes [Noll et al. (2020)], to achieve better agreement with the measured relative intensities, and to obtain significant differences in the intensities of the $\Lambda$ doublets for large $v$ and $J$ as observed by Noll et al. The $X$-$A$ coupling fully modifies the Q-line intensities at high $J$ by removing the well-known $J^{-2}$ dependence. A new line list is constructed where the transition frequencies are from Brooke \etal\ and the \EinA\ are from the present study. However, not all the problems with the intensities were resolved, presumably due to the neglect of the interaction with the $^4\Sigma^-,^2\Sigma^-$ and $^4\Pi$ repulsive electronic terms.