On the Faraday effect in O 2

Abstract

From Hamiltonians containing the interaction of the magnetic moment of the molecule with the magnetic field of the radiation, the imaginary parts of the magnetic susceptibilities for right and left circular polarization are calculated. The dispersion relations appropriate to tensor media is then applied yielding the difference between the real parts of the magnetic susceptibilities for the two states of circular polarization. Subject to the assumptions that the spin multiplet and adjacent rotational levels spacings are small compared to kT and that the frequency of the radiation is much greater than the frequencies of the absorption bands, an expression for the contribution of the magnetic susceptibility to the Verdet constant is obtained which is frequency independent. This contribution to the Verdet constant is calculated numerically for O 2, under experimental conditions, to be 1.96 μmin per gauss per cm. When the frequency-independent term is combined with a term of the earlier work of Serber, an expression for the total Verdet constant of O 2 in the near infrared, visible, and ultraviolet is obtained which can be fit to the experimental data to 1%. The results obtained here are in complete agreement with those derived earlier by Hougen using a different method.