Halo structure of $^6$He from $\textit{ab initio}$ two-nucleon spatial correlations

Abstract

We evaluate pairwise correlations using ground state wave functions for $^4$He and $^6$He obtained by $\textit{ab initio}$ no-core shell model calculations with the Daejeon16 nucleon-nucleon interaction plus Coulomb interaction, to characterize the structures of these two systems. We demonstrate that two-nucleon spatial correlations, specifically the pair-number operator $r^0$ and the square-separation operator $r^2$ projected on two-body spin $S$ and isospin $z$ components encode important details of the halo structure of $^6$He. We also analyze the single-particle state occupancies and the two-body state occupancies for the ground state of $^4$He and $^6$He. Our results indicate that the two valence neutrons in the ground state of $^6$He dominantly form a spin-singlet configuration. The rms pair separations between core nucleons and halo neutrons of $^6$He are, on average, about 80% larger than pair separations within the swollen and off-centered "$α$ core". We show that this off-centering effect is primarily responsible for the observed increase in point-proton radius $r_p$ in $^6$He relative to $^4$He.