The effect of inversion of $p$ and $f$ orbits on halo formation in heavy sodium isotopes

Abstract

The role of the inversion of the $p$ and $f$ shell-model orbits in the emergence of halo structures in the ground states of neutron-rich $^{34,37,39}$Na is investigated. Families of two- and three-body models are constructed with effective core-neutron interactions, with parameter choices based on a combination of the available experimental data and systematic trends, as well as the GPT $n$-$n$ interaction and a phenomenological three-body force. Our results indicate a possible one-neutron halo in $^{34}$Na, while $^{37,39}$Na exhibit features of Borromean halos. The halo formation is driven by the weakening of the shell gap and inversion of the $2p_{3/2}$ and $1f_{7/2}$ orbits expected to occur somewhere near these masses. We further show that the electric dipole response provides a clear and sensitive probe of halo structure in these isotopes.