Implication of odd-even staggering in the charge radii of calcium isotopes

TL;DR

This study investigates the odd-even staggering in calcium isotopes' charge radii using covariant energy density functionals, revealing the sensitivity of charge radii to nuclear interactions and the complex behavior of proton Fermi energies.

Contribution

It introduces a radius constraint method within covariant density functional theory to analyze charge radii and odd-even effects in calcium isotopes, highlighting the importance of isospin dependence.

Findings

Charge radii increase by 1-2% under the radius constraint.

Charge radii exhibit odd-even staggering linked to isospin effects.

Proton Fermi energies show opposite trends to binding energies and radii.

Abstract

Inspired by the profoundly observed odd-even staggering and the inverted parabolic-like shape in charge radii along calcium isotopic chain, the ground state properties of calcium isotopes are investigated by constraining the root-mean-square (rms) charge radii under the covariant energy density functionals with effective forces NL3 and PK1. In this work, the pairing correlations are tackled by solving the state-dependent Bardeen-Cooper-Schrieffer equations. The calculated results suggest that the binding energies obtained by the radius constraint method have been slightly changed by about $0.2\%$. But for charge radii, the corresponding results deriving from NL3 and PK1 forces have been increased by about $1.0\%$ and $2.0\%$, respectively. This means that charge radius is a more sensitive quantity in the calibrated protocol. Meanwhile, it is found that the reproduced charge radii of calcium isotopes are attributed to the rather strong isospin dependence of effective potential. The odd-even oscillation behavior can also be presented in the proton Fermi energies along calcium isotopic family, but keep opposite trends with respect to the corresponding binding energies and charge radii. As encountered in charge radii, the weakened odd-even oscillation behavior is still emerged from the proton Fermi energies at the neutron numbers $N=20$ and $28$ as well, but not in binding energies.