The mean square radius of the neutron distribution and the skin thickness derived from electron scattering

TL;DR

This paper estimates neutron and proton distribution radii and skin thickness in nuclei using electron scattering data and nuclear models, highlighting differences between relativistic and non-relativistic approaches.

Contribution

It introduces a method to derive neutron distribution radius and skin thickness from electron scattering data using linear relationships in nuclear models.

Findings

Neutron and proton radii are estimated for specific nuclei.

Relativistic and non-relativistic models yield different skin thicknesses.

The method links experimental moments to nuclear structure parameters.

Abstract

The second-order moment of the nuclear charge density($R^2_c$) is dominated by the mean square radius(msr) of the point proton distribution($R_p^2$), while the fourth-order moment($Q^4_c$) depends on the msr of the point neutron one($R_n^2$) also. Moreover, $R^2_n$ is strongly correlated to $R^2_c$ in nuclear models. According to these facts, the linear relationship between various moments in the nuclear mean field models are investigated with use of the least squares method for $^{40}$Ca, $^{48}$Ca and $^{208}$Pb. From the intersection points of the obtained straight lines with those of the experimental values for $R^2_c$ and $Q^4_c$ determined through electron scattering, the values of $R_p$ and $R_n$ are estimated. Since relativistic and non-relativistic models provide different lines, the obtained values of $R_n$ and the skin thickness($R_n-R_p$) differ from each other in the two frameworks.