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

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 $\delta ⟨r_c^2⟩$ 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 $\delta ⟨r_c^2⟩(n)$. 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.

7 pages, 6 figures

References in corpus (12)

• Chiral effective field theory and nuclear forces
• Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new version of the program
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
• Coupled-cluster theory for three-body Hamiltonians
• Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of $N=32$
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Delta-excitations and the three-nucleon force
• Nuclear charge densities in spherical and deformed nuclei: towards precise calculations of charge radii
• Nuclear Charge Radii of the Nickel Isotopes ${}^{58-68,70}$Ni
• Extraction of the neutron charge radius from a precision calculation of the deuteron structure radius
• Central depression in nucleonic densities: Trend analysis in nuclear density-functional-theory approach
• Systematics of collective correlation energies from self-consistent mean-field calculations