Potential signature of new magicity from universal aspects of nuclear charge radii

Abstract

Shell quenching phenomena in nuclear charge radii are typically observed at the well-established neutron magic numbers. However, the recent discovery of potential new magic numbers at the neutron numbers $N = 32$ and $N = 34$ has sparked renewed interest in this mass region. This work further inspects into the charge radii of nuclei around the $N = 28$ shell closure using the relativistic Hartree-Bogoliubov model. We incorporate meson exchange and point-coupling effective nucleon-nucleon interactions alongside the Bogoliubov transformation for pairing corrections. To accurately capture the odd-even staggering and shell closure effects observed in charge radii, neutron-proton correlations around Fermi surface are explicitly considered. The charge radii of Ca and Ni isotopes are used to test the theoretical model and show an improvement with neutron-proton pairing corrections, in particular for neutron-rich isotopes. Our calculations reveal a inverted parabolic-like trend in the charge radii along the $N = 28$ isotones for proton numbers $Z$ between 20 and 28. Additionally, the shell closure effect of $Z = 28$ persists across the $N = 28$, 30, 32, and 34 isotonic chains, albeit with a gradual weakening trend. Notably, the significantly abrupt changes in charge radii are observed across $Z = 22$ along both the $N = 32$ and $N = 34$ isotonic chains. This kink at $Z = 22$ comes from the sudden decrease of the neuron-proton correlation around Fermi surfaces across $Z = 22$ for $N = 30$, 32, and 34 isotones, and might provide a signature for identifying the emergence of neutron magic numbers $N = 32$ and 34. Furthermore, the calculated charge radii for these isotonic chains ($N = 28$, 30, 32, and 34) can serve as reliable guidelines for future experimental measurements.