Neutron Magic Numbers in $sd$ Shell from Nuclear Charge Radii within Neutron-Proton Correction around the Fermi Surface

Abstract

Charge radii are sensitive indicators to identify the nuclear structure phenomena throughout the whole nuclide chart. In particular, the shrunken trend of changes of charge radii along a long isotopic chain is intimately associated with the shell quenching effect. In this work, the systematic evolution of charge radii along the proton numbers $Z=8$, $10$, $12$, $14$, $18$ isotopes is investigated by a relativistic Hartree Bogoliubov model. A ansatz about neutron-proton correlation around Fermi surface is considered for describing the abnormal behavior of nuclear charge radii. Our results show that the neutron-proton pairing corrections around the Fermi surface lead to a sudden strengthening of the charge radii of these isotopic chains at $N=8$, 20 and 28, reflecting the fact that this correction enhances the shell closure across $N=8$, 20 and 28. The reproduction of the $N=14$ charge radius in the Mg isotopes is affected by the way in which pairing correlations are handled, with BCS theory overestimating the shell effect of $N=14$, and the Bogoliubov quasiparticle transformation suggests a stronger pairing correlation near the proton Fermi surface, which is more consistent with experimental results. An analysis of the deviations from the theoretical and available experimental data for the charge radii of the 24 selected even-even nuclei shows that the neutron-proton pairing correction around the Fermi surface has an improved effect on the calculation of the charge {radii} using the meson-exchange effective interactions, but it does not help to significantly improve the results calculated by the density-dependent effective interactions.