Rotationally inelastic collisions between a diatomic molecule in a 2S+1Σ electronic state and a 2S atom: The optimal choice for the total-𝒥 representation

The close-coupled formalism for rotationally inelastic collisions is extended to 2S+1 Σ state molecule-2S atom systems by using a Hund’s case (b) coupling scheme for the open-shell molecule. A novel total-𝒥 representation is introduced that is independent of 𝒥 and block diagonal in both the rotational-orbital and the electronic spin subspaces whenever the spin splitting of the molecular rotational levels is negligible. This total-𝒥 representation is based on an angular momentum vector recoupling algorithm that reduces the computing time required for the solution of the scattering problem by 94% for a doublet molecule and by 97% for a triplet molecule. The result of a lack of fine-structure resolution in a molecular beam scattering experiment is discussed, and it is demonstrated that rotationally inelastic cross sections for unresolved fine-structure transitions are equivalent to a degeneracy-weighted average of cross sections for scattering off the allowed adiabatic Born–Oppenheimer atom–molecule potential energy surfaces.