Evolution of nuclear charge radii in copper and indium isotopes * *Supported by the Reform and Development Project of Beijing Academy of Science and Technology (13001-2110); Supported in part by the National Natural Science Foundation of China (12135004, 11635003, 11961141004, 12047513). X. J. is grateful for the support of the National Natural Science Foundation of China (11705118). L.-G. C. is

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 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 to 50 for copper isotopes and 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.