Multiple-scattering treatment for small-angle scattering problems

Abstract

Analytical explicit expressions have been derived for multiple‐scattering effects under assumptions which are usually fulfilled in small‐angle scattering. The expressions are used to evaluate quantitatively distortions of scattering patterns caused by multiple scattering. The distortions are discussed in terms of changes of the forward‐scattering cross section, the radius of the gyration, the integrated intensity, the Porod region and Porod constant. In addition, the analytical expressions have been used to calculate the scattering cross section of the sample from scattering patterns which are strongly affected by multiple scattering.

Evaluation of multiple small-angle neutron scattering including magnetic interactions

“…We may see that, without the nuclear-magnetic interference term, there is no substantial difference in the treatment of multiple scattering with respect to the result obtained by Schelten & Schmatz (1980). Obviously, it is the nuclear-magnetic interference term which is responsible for partial polarization of the scattered neutron beam and may lead, in combination with multiple scattering, to an anomalous shape of scattered beam profiles.…”

“…The formulae for MSAS of neutrons by nonmagnetic materials obtained by Schelten & Schmatz (1980) for isotropic systems can be expressed more generally in a vector form, which permits the inclusion of anisotropic scattering as well as an easy transition to the case of infinite-slit geometry. Let us start with the single-scattering differential cross section, dAE/d (q), which is related to the autocorrelation function of the medium by the pair of Fourier transformations…”

“…The theory is valid for any form of differential singlescattering cross section, provided that the scattering is limited to small angles and the mean free path of the particles is large compared to the size of the scatterers or, more generally, to the correlation length of the scattering medium. Schelten & Schmatz (1980) arrived at Moliè re's expressions using a multiconvolution approach, which turns out to be equivalent to Bethe's solution of the transport equation. They assumed the diffractive regime of neutron and X-ray scattering, in which scattering by a single particle is kinematical (described by the Born approximation).…”

Evaluation procedure for anisotropic SANS

“…its intersection with Ewald-sphere surface), corrections of the modeled 2D scattering pattern are performed. They include correction for multiple scattering (Schelten & Schmatz, 1980) and smearing by the 2D resolution function.…”

Intensity of secondary scattering of X-rays by non-crystalline materials. Transmission gemoetry with an incident-beam monochromator

“…A general analytical method for calculating multiple X-ray scattering is usually impossible to obtain, and a general numerical treatment can require numerical integration over many variables or use of Monte Carlo methods that consume a very large amount of computer time (Schelten & Schmatz, 1980). When the intensity of small-angle scattering is very high and itself produces much multiple scattering in the smallangle region, a good method for making the corrections for multiple scattering has been developed by Schelten & Schmatz (1980).…”