The hyperfine structure of diatomic molecules: Hund's case ( cα)

Abstract

The hyperfine splitting in diatomic molecules is treated according to an unperturbed model that is denoted Hund's coupling case ( c α ). The advantages of this model are: (i) Rapid convergence of the perturbation expansion (spin-orbit interaction is included in the unperturbed Hamiltonian), (ii) hyperfine interactions of the type Δ J ≠ 0 are automatically included, (iii) simple rotational-independent matrix elements result for the hyperfine Hamiltonian, and (iv) it is rather easy to judge whether the various hyperfine parameters are correlated or not. Numberical diagonalization of a secular matrix of dimension (2 S + 1)(2 I + 1) (or less for singular levels) yields the hyperfine splittings. The interaction with remote electronic states is included through a Van Vleck transformation. The coupling case ( c) matrix elements are readily specialized to coupling case ( a), and the present method is applied to the a 3Π 1 substate of InH (optical), the X 3Σ − state of 33SO and 17O 16O (microwave) and to the X 2Π state of 7LiO (radio frequency).