Simple analysis of scattering data with Ornstein-Zernike equation

TL;DR

This paper introduces a pragmatic method for analyzing scattering data of liquids by numerically solving the Ornstein-Zernike equation with a variational potential, avoiding artificial small parameters.

Contribution

It presents a novel approach that directly uses experimental data to iteratively solve the Ornstein-Zernike equation without relying on perturbation theory or small parameters.

Findings

Successfully applied to model systems and real experimental data.

Accurately reproduces correlation functions from scattering data.

Provides a flexible framework for analyzing liquid-like systems.

Abstract

In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquid-like systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results e.g., for hard spheres or sticky-hard spheres (all the more that in the agreement with the notorious Landau statement, there is no any physical small parameter for liquids). Instead of it guided by the experimental data we are solving the the Ornstein-Zernike equation with a trial (variational) form of the inter-particle interaction potential. To find all needed correlation functions this variational input is iterated numerically to satisfy the Ornstein-Zernike equation supplemented by a closure relation. We illustrate by a number of model and real experimental examples of the X-ray and neutron scattering data how the approach works.