Shell closures, loosely bound structures, and halos in exotic nuclei

Abstract

Inspired by the recent experiments [1, 2] indicating doubly magic nuclei that lie near the drip-line and encouraged by the success of our relativistic mean-field (RMF) plus state-dependent BCS approach to the description of the ground-state properties of drip-line nuclei, we develop this approach further, across the entire periodic table, to explore magic nuclei, loosely bound structures, and halo formation in exotic nuclei. In our RMF+BCS approach, the single-particle continuum corresponding to the RMF is replaced by a set of discrete positive-energy states for the calculations of pairing energy. Detailed analysis of the single-particle spectrum, pairing energies, and densities of the nuclei predict the unusual proton shell closures at proton numbers Z = 6, 14, 16, 34, and unusual neutron shell closures at neutron numbers N = 6, 14, 16, 34, 40, 70, 112. Further, in several nuclei like the neutron-rich isotopes of Ca, Zr, Mo, etc., the gradual filling of lowlying single-particle resonant state together with weakly bound single-particle states lying close to the continuum threshold helps accommodate more neutrons but with an extremely small increase in the binding energy. This gives rise to the occurrence of loosely bound systems of neutron-rich nuclei with a large neutron-to-proton ratio. In general, the halo-like formation, irrespective of the existence of any resonant state, is seen to be due to the large spatial extension of the wave functions for the weakly bound single-particle states with low orbital angular momentum having very small or no centrifugal barriers.