Low-Pressure Senftleben Effects for Molecular Oxygen

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Abstract
The effect of a magnetic field on the thermal conductivity and viscosity coefficients of paramagnetic Hund's case (b) multiplet Σ molecules, and in particular Σ3 oxygen, is investigated theoretically for the low-pressure region, where the effects are functions of H / p. In this region the fields involved are correspondingly low, so that the total angular momentum J is well defined, and the distribution-function density matrix may be assumed to commute with J2. This fact is exploited in the solution of the kinetic equation. The present treatment makes only very weak assumptions about the nature of the collisions, basically only that the collision (super)operator R is spin independent, which makes it possible to choose a basis in which the R matrix is diagonally dominant. Through detailed analysis of the dependence of all quantities involved on the mean rotational quantum number, N = 〈[N(N + 1)]1/2〉, information about the transport coefficients is obtained in a manner independent of the precise structure of the collision matrix. It is shown that the transport coefficients can be represented as series in powers of N−2, and since N−2 is small, even at liquid-nitrogen temperature, this suggests that the leading terms are the only significant ones. For Σ3 molecules such as oxygen, the even effects show a structure which is a simple superposition of two features of the type found in diamagnetic molecules, one at low field associated primarily with J = N ± 1, and the other at high field, associated primarily with J = N. This formal result depends on very few assumptions about R, whereas the exact positions and intensities depend on the detailed values of the R-matrix elements. The observed 2:1 intensity ratio is consistent with the assumption that R is equivalent within an N shell to a unit superoperator, but this assumption, while sufficient, is not necessary. The odd effects also show a two-feature structure. The high-field feature is again of simple diamagnetic type, while the low-field feature is of reduced intensity, and in general of more complex form.