We evaluate pairwise correlations using ground-state wave functions for ${}^4\mathrm{He}$ and ${}^6\mathrm{He}$ obtained by 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 ${}^6\mathrm{He}$. We also analyze the single-particle state occupancies and the two-body state occupancies for the ground state of ${}^4\mathrm{He}$ and ${}^6\mathrm{He}$. Our results indicate that the two valence neutrons in the ground state of ${}^6\mathrm{He}$ dominantly form a spin-singlet configuration. The rms pair separations between core nucleons and halo neutrons of ${}^6\mathrm{He}$ are, on average, 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 ${}^6\mathrm{He}$ relative to ${}^4\mathrm{He}$.

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• Nuclear radii
• Nuclear structure & decays
• Nucleon distribution
• 6 ≤ A ≤ 19
• A ≤ 5
• Ab initio calculations
• Nuclear many-body theory