Small‐Angle Scattering by Spherical Inhomogeneities of Different Radii and Refractive Indexes

The cross‐section σ of small‐angle scattering of neutrons by inhomogeneities of a wide variety of sizes R min < R < R max is considered when the scattering crossover from diffraction R < R c to refraction R > R c takes place within the available range of size distribution. When qR c ≫ 1 the cross‐section averaged by the distribution function P(R) ∝ R −3−Δ (0 < Δ < 1) results in the dependence σ (q) ∝ q −4 + 4 in the Born approximation, where q is the transfer momentum, and in case qR c ≪ 1 the averaging leads to the dependence σ (q) ∝ q −2+Δ . In the case of scattering in condensed matter containing large scale and loose pores, to which a distribution of the scattering potential can be attributed, the averaging in refractive index fluctuations is carried out. The result of such an averaging is demonstrated by means of a homogeneous distribution.