Evolution of nuclear charge radii in copper and indium isotopes

Abstract

The systematic trend in charge radii along isotopic chain is of great interest due to its distinctive aspect at the nucleon-shell closure and the odd-even staggering (OES) behavior. In this work, the modified root mean square (rms) charge radius formula to phenomenally account for the formation of neutron-proton short-range correlations (np-SRCs) is firstly extended to study the heavier odd-Z copper and indium isotopic chains. The parabolic-like shape of rms charge radii can be remarkably reproduced between two strong closure shells. In addition, the OES and abrupt changes in the slope of the rms charge radii across N = 50 and 82 shell closure are also identified evidently, but the odd-even oscillation is slightly overestimated for cooper isotopes. This means the np-SRCs play an indispensable role to determine the fine structures of nuclear charge radii along isotopic chain quantitatively.

Local variations of charge radii for nuclei with even $Z$ from 84 to 120

“…As a complex many-body quantum system, the remarkably abrupt changes in charge radii are observed naturally across neutron shell closures. RMF(BCS) * model can reproduce the shell effect in nuclear size fairly well for Ca, K, Cu and In isotopes [44,65,66], etc, especially the inverted parabolic-like behaviors between two closed-shells. This is an indication of the shell effect along isotopic chain.…”

“…The modified term whose presence in this expression is firstly mandatory for describing the odd-even oscillations of nuclear charge radii along calcium and potassium isotopic chains [44,65]. Besides, the abrupt changes of nuclear charge radii across shell closures can also be reproduced well [66]. This introduced term is obtained self-consistently by resolving the state-dependent BCS equations with a δ-force interaction [30].…”

“…NL3 force is especially favorable to the calculation of charge radii along a long isotopic chain [67]. Actually, parametrization set PK1 and NL3 * cannot change the conclusions in quantitative level [66].…”