Evolution of nuclear charge radii in copper and indium isotopes

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