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

TL;DR

This study uses ab initio no-core shell model calculations to analyze two-nucleon spatial correlations in helium isotopes, revealing the halo structure of $^6$He and the dominant spin-singlet configuration of its valence neutrons.

Contribution

It provides a detailed ab initio analysis of two-nucleon correlations and halo structure in $^6$He, highlighting the role of off-centering effects and specific two-body correlations.

Findings

Valence neutrons in $^6$He form a spin-singlet state.

Pair separations between core and halo neutrons are about 80% larger than within the core.

Off-centering of the halo neutrons explains increased point-proton radius in $^6$He.

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 (NCSM) 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 is about 80% larger than pair separations within the swollen and off-centered "$\alpha$ 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.