Evolution of nuclear charge radii in copper and indium isotopes

TL;DR

This study applies a modified charge radius formula to odd-Z copper and indium isotopes, successfully reproducing experimental trends and shell effects, highlighting the importance of neutron-proton correlations in nuclear structure.

Contribution

First application of the modified rms charge radius formula to odd-Z isotopes, demonstrating its effectiveness in capturing shell effects and fine structures in nuclear charge radii.

Findings

Both odd-even staggering and shell closure effects are reproduced.

Inverted parabolic behaviors between neutron magic numbers are well described.

Results are robust across different relativistic mean field models.

Abstract

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton ($np$) correlations, is here applied for the first time to the study of odd-$Z$ copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3$^{*}$ parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across $N=50$ and $82$ shell closures are clearly reproduced in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers, namely $N=28$ to $50$ for copper isotopes and $N=50$ to $82$ for indium isotopes. This implies that the $np$-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-$Z$ isotopic chains. Also, our conclusions have almost no dependence on the effective forces.