Electron Scattering Intensities and Patterson Functions of Skyrmions

TL;DR

This paper investigates electron scattering off spin-zero nuclei modeled as Skyrmions, comparing two computational methods and matching results with experimental data to understand nuclear structure.

Contribution

It introduces two methods for calculating electron scattering intensities of Skyrmions and simplifies the process using the Born approximation, providing analytical formulas for key form factor features.

Findings

Form factors and Patterson functions yield consistent scattering intensities.

Analytical formulas for the first zero and stationary point of the form factor.

Results agree with experimental scattering data.

Abstract

The scattering of electrons off nuclei is one of the best methods of probing nuclear structure. In this paper we focus on electron scattering off nuclei with spin and isospin zero within the Skyrme model. We consider two distinct methods and simplify our calculations by use of the Born approximation. The first method is to calculate the form factor of the spherically averaged Skyrmion charge density; the second uses the Patterson function to calculate the scattering intensity off randomly oriented Skyrmions, and spherically averages at the end. We compare our findings with experimental scattering data. We also find approximate analytical formulae for the first zero and first stationary point of a form factor.