Small-angle scattering of neutrons on large scale inhomogeneities in refraction range

TL;DR

This paper investigates neutron small-angle scattering on large inhomogeneities, revealing two main scattering contributions with distinct asymptotic behaviors related to diffraction and Fraunhofer effects.

Contribution

It introduces a model considering Gaussian phase shifts and derives the asymptotic behavior of the scattering cross section for large transfer momentum.

Findings

Scattering cross section has two contributions: diffraction and Fraunhofer-like.

Asymptotic behavior shows a power-law decay with transfer momentum q.

Diffraction contribution scales as q^{- to }, Fraunhofer as q^{-3}.

Abstract

The small-angle scattering of neutrons on large scale inhomogeneities of two-component systems in refraction range is considered. We supposed, that neutrons acquire phase shifts describing by the Gaussian distribution function. It is shown that the average cross section of scattering contains two contributions. The first contribution describes the diffraction and in the asymptotic limit of large transfer momentum this contribution is proportional to q^{- \Delta}, where 2 \leq \Delta \leq 4. The second contribution is similar to the Fraunhofer diffraction, which in the asymptotic limit of large transfer momentum is proportional to q^{-3}.