Description of the smooth rms charge radius surface R(N, Z) and prediction of neutron skin by a two-liquid drop model

Abstract

The smooth N and Z dependence of nuclear rms charge radii is interpereted by a two-liquid drop model with ϱp+ϱn=ϱ0=const. Proton and neutron radii R p and R n are given in closed form. In addition to rms charge radii, the model yields the nucleon number dependence of the skin thickness, s, e.g. ds=0.00124×dA for Sn isotopes, in agreement with experimental results and theoretical calculations. A strong correlation between the two global parameters of the model — including s stthe skin thickness of the stable isotope — is established. If s stis taken from experiment, the other parameter is also fixed; this parameter (m) characterizes the restoring force responsible for the skin thickness. Its value m=2.2 suggests that — in addition to the number of nucleons in the skin — the skin thickness also influences the distribution of “surplus” nucleons between volume and skin.