Theory of hyperfine and superfine levels in symmetric polyatomic molecules. II. Elementary cases in octahedral hexafluoride molecules

Abstract

A simple approximate theory is developed for high-$J$ spin-rotational levels and very-high-resolution spectra of octahedral $X{Y}_{6}$ ($X$ spin-zero, $Y$ spin-1/2) molecules. The structure and theory of S${\mathrm{F}}_{6}$ spectra is reintroduced and the properties of rotational energy level and spectral clusters are explained in terms of angular-momentum uncertainty relations and axis tunneling. An analogy between axis tunneling and nuclear-spin tunneling is used to provide a simple quasiparticle picture of hyperfine effects in strong (case-2) rotational clusters. Analogous types of clusters within clusters are discussed using this theoretical model. The possibility emerges for new and very sensitive type of spectra which we label superhyperfine structure. This structure has some remarkable similarities with nuclear magnetic resonance (NMR) spectra, and it might be an even more revealing indicator of internal molecular dynamics than NMR. Model Hamiltonians are represented in all the elementary types of cluster bases and some examples are solved using tableau techniques. Level correlations between case-1 and case-2 clusters are sketched. Nomograms for visualizing laser-saturation-absorption spectra are introduced, and examples of case-1 to case-1 and case-2 to case-1 transitions are given.