Analytical evaluation of atomic form factors: application to Rayleigh scattering

TL;DR

This paper derives an analytical expression for atomic form factors using nonrelativistic hydrogenic wavefunctions, compares it with Hartree-Fock results, and applies it to Rayleigh scattering calculations.

Contribution

It introduces a new analytical formula for atomic form factors within the independent particle model, validated against Hartree-Fock calculations.

Findings

Analytical form factors closely match Hartree-Fock results.

The formula effectively predicts Rayleigh scattering cross sections.

Applicable to various atomic targets in scattering analyses.

Abstract

Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wavefunctions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.