Isotropic orientation fourth moment
= Isotropic orientation fourth moment
For a uniformly distributed <unit vector> in three dimensions, $\langle u_iu_ju_ku_l\rangle=(\delta_{ij}\delta_{kl}+\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk})/15$. Contracting indices fixes the coefficient. This identity is useful for incoherent scattering averages and random-axis material models.