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 $\mathcal{T}$ matrix, the Hermitian tensor ${\mathcal{T}}^{+}\mathcal{T}$, and the direct product T*_νν′ T_μμ′. These results are independent of the nature of waves and scatterers. Equations for 〈 $\mathcal{T}$〉 and 〈 ${\mathcal{T}}^{+}\mathcal{T}$〉 are interpreted as specific forms of the generalized Wigner–Eckart theorem for the matrix elements of operators $\mathcal{T}$ and ${\mathcal{T}}^{+}\mathcal{T}$, 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.