Coherent Multiple Backscattering of Waves in Random Medium beyond the   Diffusion Approximation
  In this paper the validity of the diffusion approximation for multiple scattering of classical waves in random medium in different regimes is investigated, with emphasize to weak localization effects. Many principle topics are discussed once again. We obtain new expressions for the incoherent and coherent multiple scattering intensities for the more general case of large scattering angles and various observation points inside the medium with moving scatterers and absorption. (The results, we reached, assuming white-noise disorder for the impurities correlator, contain one-dimensional integration in its final analytical form). Also new self-consistent formulas for incoherent and coherent intensities for fixed multiplicity orders of scattering are given and their lineshapes are graphically represented. Through these formulas we clearly demonstrate that the impurities motion reduces the contribution to the intensity of the scatterings with large multiplicity orders. The total scattering intensities in $4\pi$ solid angle are calculated for the general case and compared with their diffusion approximation. For coherent intensities it is shown that a drastic deviation from the exact results occurs. It turns out that the region of angles, for which the observed lineshape of the weak localization effect tends to the incoherent background, give the main contribution to the total coherent scattered intensity. The last quantity happens to depend linearly instead of predicted quadratic dependence on the perturbation parameter, 1/kl. 
Peter Slavov