Orientational averaging of light-scattering observables in the T-matrix approach

The formalism of the quantum theory of angular momentum is used for orientational averaging of the a matrix, the Hermitian tensorJ(+)J, and the direct product T(*)(vv')T(Tmicromicro'). These results are independent of the nature of waves and scatterers. Equations for ?J? and ?J(+)I? are interpreted as specific forms of the generalized Wigner-Eckart theorem for the matrix elements of operators J and J(+)J which are calculated in terms of symmetrical top eigenfunctions. The averaged values of the above three types of tensor are used for the analytical calculation of a complete set of incoherent light-scattering observables, i.e., the total scattering and extinction cross sections and the Mueller matrix elements.