Exact limiting relation between the structure factors in neutron and x-ray scattering

TL;DR

This paper derives an exact quantum statistical mechanics relation showing that, in the long-wavelength limit, the ratio of X-ray to neutron static structure factors equals the nucleus charge, applicable to pure Coulomb systems.

Contribution

It establishes a precise theoretical link between neutron and X-ray scattering structure factors in Coulomb systems, verified in the long-wavelength limit.

Findings

The ratio of structure factors equals the nucleus charge in the long-wavelength limit.

The relation holds for any thermodynamic parameters of a pure Coulomb system.

Experimental verification is possible with long-wavelength X-ray and neutron scattering.

Abstract

The ratio of the static matter structure factor measured in experiments on coherent X-ray scattering to the static structure factor measured in experiments on neutron scattering is considered. It is shown theoretically that this ratio in the long-wavelength limit is equal to the nucleus charge at arbitrary thermodynamic parameters of a pure substance (the system of nuclei and electrons, where interaction between particles is pure Coulomb) in a disordered equilibrium state. This result is the exact relation of the quantum statistical mechanics. The experimental verification of this relation can be done in the long wavelength X-ray and neutron experiments.