A molecular theory of natural and magneto-optical rotation in gases

Natural and magneto-optical rotations in an ideal diamagnetic gas have been related by means of statistical mechanics to various electric and magnetic polarizability parameters of an individual molecule By admitting electric and magnetic dipoles of second and third order in H , the external magnetic field, and by taking into account the orientation of molecules by the external field, higher-order field effects have been calculated The composite natural and induced rotation θ T per unit path length may be expanded as a power series in H θ T = (ω/2 c )(2π N / v )( A + BH + CH 2 + DH 3 + ...) where A, B , etc., are functions of molecular polarizabilities Calculation of A and B yields the familiar expressions for natural rotation and the Verdet constant. C , like A , exists only for optically active molecules, so that the term in D is required to describe departure from the Verdet constant of other molecules at high fields C and D each contain a temperature-dependent term which describes orientation effects due to the field, as well as a temperature-independent term which arises from the modification of molecular parameters by the external field. For spherically symmetric molecules all temperature-dependent terms are zero. The temperature-independent terms cannot be evaluated with the data at present available, and tentative order-of-magnitude calculations indicate that for non-spherical molecules the modification of the Verdet constant due to orientation effects is of the order of 1 part in 10 6 at fields of 10 5 gauss