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

Abstract

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 the use of the least-squares method for $^{40}$Ca, $^{48}$Ca and $^{208}$Pb. From the intersection of the obtained straight line and the line of the experimental value for $R^2_c $ or $Q^4_c$ 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.