Scattering intensity limit value at very small angles

TL;DR

This paper investigates the theoretical limit of scattering intensity at very small angles, establishing a relationship with density fluctuations and analyzing implications for samples with two phases.

Contribution

It provides a rigorous derivation of the scattering intensity limit based on density fluctuation behavior and extends the analysis to two-phase samples.

Findings

The scattering intensity limit equals the square of the fluctuation constant.

Mean density fluctuations scale as $ u V^{-1/2}$ for large volume $V$.

Implications for two-phase samples are discussed.

Abstract

The existence of the limit of a sample scattering intensity, as the scattering vector approaches zero, requires and is ensured by the property that the mean value of the scattering density fluctuation over volume $V$ asymptotically behaves, at large $V$s, as $\nu V^{-1/2}$, $\nu$ being an appropriate constant. Then, the limit of the normalized scattering intensity is equal to $\nu^2$. The implications of this result are also analyzed in the case of samples made up of two homogeneous phases.16 pages, 3 figures