A general procedure for the theoretical study of the Λ-doubling

Abstract

A perturbation matrix procedure for the theoretical study of Λ-doubling is suggested based on van Vlecks formalism. It is independent of Hund's coupling cases and yields directly the energy levels and wavefunctions in terms of perturber states. The procedure is applied to the X ²Π states of OH and SH whereby the perturbation matrix was constructed in the basis of large-scale multi-reference configuration interaction wavefunctions, which are computed for the X ²Π, A ²Σ⁺, B ²Σ⁺, 1²Σ^-, ²Δ and ⁴Σ^- and ⁴Π states as a function of internuclear separation. In OH a splitting of 0·1591 cm^-1 for the ²Π_1/2(j = ½) state and 0·0521 cm^-1 for the ²Π_3/2(j = 3/2) state is calculated compared to the corresponding measured splittings of 0·1577 cm^-1 and 0·0551 cm^-1. For SH the corresponding splittings are 0·3062 cm^-1 compared to the experimental value of 0·2814 cm^-1 for the ²Π_1/2 component and 0·0041 cm^-1 compared to the measured value of 0·0035 cm^-1 for the ²Π_3/2 component. It is found that for large internuclear separations in SH the ⁴Σ^- and ²Σ^- states are the dominant perturbers, and that the ⁴Π state is not negligible, while as expected the A ²Σ⁺ state is the dominant contributor near equilibrium. This shows that the standard restriction to include only doublet states must be abandoned if the Λ-splitting of high vibrational levels is of interest. The results are quite encouraging and it is expected that the suggested procedure can be applied with comparable success to the Λ-splitting in ²Π states of arbitrary diatomics.