Point-proton density distributions of stable nuclei

TL;DR

This study deduces point-proton density distributions for 130 stable nuclei using elastic electron scattering data, providing model-dependent and independent forms, and analyzes their properties and inconsistencies in experimental data.

Contribution

It offers a comprehensive set of point-proton density distributions for stable nuclei, including model-dependent and model-independent forms, and investigates their properties and data inconsistencies.

Findings

Point-proton rms radii are consistent across different density models.

Surface diffuseness parameters can be empirically derived from charge densities.

Identifies inconsistencies in experimental charge density data.

Abstract

Point-proton density distributions are deduced for 130 stable nuclei from $^{7}\mathrm{Li}$ to $^{232}\mathrm{Th}$ from nuclear charge densities determined in elastic electron scattering. There are 171 cases are presented in model-dependent forms, including the modified Harmonic-oscillator function, two-parameter Femi function (2pF), three-parameter Femi function, three-parameter Gaussian function, and 97 in Fourier-Bessel series model-independent forms. Independent of density functions, the point-proton root-mean-square (rms) radii of the derived point-proton density show excellent agreement with each other. We identify cases where the tabulated data of charge densities and charge radii are inconsistent, and the deduced point-proton density distributions are inaccurate due to insufficient experimental momentum transfer coverage or inconsistent scattering experiments. For the widely used 2pF distribution, it is found that the surface diffuseness parameters can be empirically calculated from those of charge density, while the half-density radius parameters follow the $A^{1/3}$ rule. The derived point-proton density distributions can be used as input in nuclear reaction studies and compared with nuclear model predictions.