The Intermediate Spin-Orbit Coupling for Large Rotational Quantum Number

If a nucleus of spin one-half is cosine-coupled to the molecular rotation, its molecular beam spectrum can be predicted for all values of the magnetic field from the Zeeman to the Paschen-Back region with one, closed expression. This expression is valid for large values of rotational quantum number and small rotational g-factor and is averaged over a Boltzmann distribution of rotational states. The special case of spin one-half is simple because the symmetry permits cosine coupling only, and the energy levels are well known for this hamiltonian. A kind of correspondence principle can be developed for this example which does two things. It shows that the other nucleus in a diatomic molecule has little effect on the spectrum of the first because the coupling of the second nucleus due to the rotation. Second, it permits the extension of the calculation to nuclei of spins greater than one-half when the coupling is predominantly cosinelike.