Nuclear shell evolution near N = 6, 14, 20 and 28: insights from nuclear charge radii of short-lived nuclei derived from binding energies

Abstract

A deep understanding of the evolution of nuclear shell structure correlating with the nucleon number is crucial for unraveling the fundamental properties of the nuclear structure and for exploring new nuclear physics phenomena far from the $β$-stability line. Although significant progress has been made in probing nuclear shell evolution via the measurements of nuclear root-mean-square charge radii, $R_{\text{ch}}$, the scarcity of new data for short-lived and exotic nuclei due to the increasing difficulty of measurements presents a formidable challenge in obtaining deeper and more universal insights into the nature of shell evolution. To mitigate this issue, we develop an improved method, accounting for the exchange term, charge-symmetry breaking effect, and odd-even staggering effect in the Coulomb energy formulation compared with that proposed by Liu et al. [Phys. Lett. B 872, 140046 (2026)], to determine unmeasured $R_{\text{ch}}$ values. Using the improved method, the $R_{\text{ch}}$ values of 59 nuclei are determined from their measured binding energies ($B$) and the respective $B$ and $R_{\text{ch}}$ of their mirror partners. We then systematically study the shell evolution near $N=6$, 14, 20 and 28 (sub)shells by placing the newly obtained $R_{\text{ch}}$ values into the corresponding isotopic chains. More comprehensive insights into the properties of nuclear shell evolution, particularly for the neutron-deficient sectors of the studied shell regions, e.g., $p$, $sd$ and $pf$ shells, are acquired, advancing our understanding of nuclear shell evolution in the light and intermediate mass region.