## Abstract

The theory of rotationally inelastic collisions between orbitally degenerate diatomic molecules and open-shell atoms is developed. Because of the orbital degeneracy two or more electronic potential energy surfaces are involved. Matrix elements of the interaction Hamiltonian are given, hyperfine coupling in the diatomic molecule also being included. From these it is apparent that the parity of the initial $\Lambda $-doublet level will influence the inelastic scattering cross section for poles of interaction $\lambda $ such that $\lambda \geq 2\Lambda $. An expression is developed for state-to-state cross sections using the restricted distorted wave Born approximation. A set of branching coefficients is defined which allows the representation of the parity dependence of the cross section in a simple parametric form. The theory is applied to collisional pumping as an excitation mechanism for interstellar maser action of OH and CH through the inversion of $\Lambda $-doublet populations. H atoms, H$_{2}$, He, H$^{+}$ and H$_{3}^{+}$ are considered as collision partners. Branching coefficients are tabulated for a variety of excitations from the rotational ground states. The sense of the parity dependence of the cross sections arises from the gross features of the interaction potential at medium and long range, and can be deduced using approximate theoretical surfaces or empirical models. An analogy is drawn with the experimental rates of rotational energy transfer in the closely related system H + NH$_{2}(\tilde{A},^{2}$A$_{1})$, which are $ca$. $10^{-9}$ cm$^{3}$ s$^{-1}$, and which have been successfully interpreted using the distorted wave Born approximation. These results are used to give qualitative predictions of population inversion in the $\Lambda $-doublets of OH, OD and CH in interstellar clouds. We show that the ground $J=1\frac{1}{2}$ doublet, and excited doublets of the F$_{1}$ manifold, of OH and OD will be inverted following collisions with H, H$_{2}$ and He. The $J=\frac{1}{2}$ doublet of the F$_{2}$ manifold of OH and OD will be inverted by collisions with the ions H$^{+}$ and H$_{3}^{+}$. In CH low temperature collisions with H atoms will result in inversion of the ground $J=\frac{1}{2}$ doublet. Collisions with H$_{2}$ and He at low temperature result in cooling of the doublet. Implications for maser action are briefly discussed.