Kinetic Equations for Orientational Relaxation in Depolarized Scattering

12 2 KINETIC EQUATIONS FOR ORIENTATIONAL RELAXATION IN DEPOLARIZED SCATTERING 

First we consider the symmetry properties of 8aaf(q, t). As we have shown in Appendix 7.B, the polarizability of a symmetric top is given by Eq. (7.B.1). Combining this with Eq. (3.3.4) gives 

It should be noted that a reflection through the xz plane followed by a reflection through the yz plane (or vice versa) reverses the sign of Sayz(q, t) but leaves 8axy(q, t) unchanged. As a consequence of this, the correlation functions f axj,(q, 0) 8ayz(q, t) and f)a yZ(q, 0)Saxy(q, t) ) are zero. Substitution of Eq. (12.2.1) into Eq. (3.3.13) then gives, aside from the multiplicative constant 

It follows from Eq. (12.2.2) that -8aaj(q, t) transforms to eig/lz Saaf(q, t) under the arbitrary translation Az along the z direction, that Saaf(q, t) has even time reversal symmetry, and that 5aaf(q, t) transforms to 5aaf(—q, t) under inversion symmetry. 

Having discussed the symmetry properties of the primary variables 5aap(q, t), let us now pass to the derivation of the relaxation equations that describe evolution of 5a 

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