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

TL;DR

This work tackles how halo structure in $^6$He can be understood from first-principles, by analyzing two-body spatial correlations computed with ab initio no-core shell model (NCSM) wave functions using the Daejeon16 NN interaction plus Coulomb.The authors introduce and employ rotationally invariant two-body operators, the pair-number operator $r^0[S,t_{za},t_{zb}]$ and the square-separation operator $r^2[S,t_{za},t_{zb}]$, within a coupled-$J$ framework to extract detailed pair distributions from the many-body density matrices.Analysis of $^4$He and $^6$He shows that the two valence neutrons in $^6$He predominantly form a spin-singlet and occupy low-lying ($s$-state) configurations, while core–halo separations grow substantially, accounting for much of the observed increase in the point-proton radius $r_p$; a minimal binary core-halo model (with parameters $x\approx0.93$, $y\approx1.78$) reproduces the main trends in inter-nucleon separations.These findings demonstrate that two-body correlation observables provide a quantitative, geometrical picture of halo formation and establish a framework for extending ab initio studies of clustering in light nuclei.

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 "$α$ 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.

Figures (4)

• Figure 1: $r_p$, $r_n$ and $r_m$ of $^4$He ($^6$He) with the Daejeon16 interaction plus Coulomb potential, calculated using ab initio NCSM. Results for $^4$He ($^6$He) are represented by filled (open) circles, which are connected by straight lines for the same $N_\text{max}$, with darker lines for higher $N_\text{max}$ ($N_\text{max}$ values are labeled on the right of the $^6$He results). The horizontal red dashed lines indicate $r^*_{p/n/m}$ of $^4$He ($^6$He) for $N_{\text{max}}=18$ with $\hbar\Omega$ determined by the minimum gap between $N_{\text{max}}=18$ and $N_{\text{max}}=16$ results. The experimental ranges are indicated by blue (for $^4$He) and yellow (for $^6$He) bands.
• Figure 2: The difference in $r_{p/n/m}$ between consecutive $N_\text{max}$ values: $N_\text{max}=18$ values minus $N_\text{max}=16$ values (color) and $N_\text{max}=16$ values minus $N_\text{max}=14$ values (gray). The absolute value of the difference $|\Delta r|$ serves as an indicator of the basis truncation uncertainty of $r_{p/n/m}$ at $N_\text{max}=16$.
• Figure 3: Occupancy of protons and neutrons in HO single-particle states for the ground state of $^4$He (a) and $^6$He (b), with $N_\text{max}=16$ and $\hbar\Omega=10$ MeV. The HO single-particle state occupancies that are major contributors are shown and aggregate to more than $90\%$ of the proton number or neutron number of each nucleus.
• Figure 4: Major $\langle r^0\rangle$ two-body contributions of the ground state of $^4$He and $^6$He with $N_\text{max}=16$ and $\hbar\Omega=10$ MeV, for $pp$ (a), $pn$ (b) and $nn$ (c) pairs according to the HO state of relative motion. The bins are arranged by decreasing magnitude for $^6$He, with the corresponding $^4$He bins shown alongside for comparison. The states shown above account for more than $90\%$ of $\langle r^0\rangle$ in each isospin-projected pair configuration.