Universal trend of charge radii of even-even Ca-Zn nuclei

TL;DR

This study reveals a universal pattern in the differential charge radii of even-even Ca-Zn nuclei, modeled by two parameters, highlighting the influence of both bulk properties and shell effects.

Contribution

It demonstrates that the universal trend in charge radii can be described by just two parameters across multiple isotopic chains using advanced nuclear theories.

Findings

Both theories reproduce the smooth rise of differential charge radii.

The trend is captured by slope and curvature parameters.

Model dependence and lack of correlation with single properties are shown.

Abstract

Radii of nuclear charge distributions carry information about the strong and electromagnetic forces acting inside the atomic nucleus. While the global behavior of nuclear charge radii is governed by the bulk properties of nuclear matter, their local trends are affected by quantum motion of proton and neutron nuclear constituents. The measured differential charge radii $\delta\langle r^2_c\rangle$ between neutron numbers $N=28$ and $N=40$ exhibit a universal pattern as a function of $n=N-28$ that is independent of the atomic number. Here we analyze this remarkable behavior in even-even nuclei from calcium to zinc using two state-of-the-art theories based on quantified nuclear interactions: the ab-initio coupled cluster theory and nuclear density functional theory. Both theories reproduce the smooth rise of differential charge radii and their weak dependence on the atomic number. By considering a large set of isotopic chains, we show that this trend can be captured by just two parameters: the slope and curvature of ${\delta\langle r^2_c\rangle(n)}$. We demonstrate that these parameters show appreciable model dependence, and the statistical analysis indicates that they are not correlated with any single model property, i.e., they are impacted by both bulk nuclear properties as well as shell structure.