Halo Structures in p-Shell Hypernuclei with Natural Orbitals

TL;DR

This work extends natural orbitals to hypernuclei within an ab initio no-core shell-model framework, demonstrating reduced dependence on the harmonic-oscillator basis and accelerated convergence when including Λ and Σ hyperons with chiral EFT interactions. By diagonalizing the correlated one-body density matrix in a HF-MBPT up to second order and applying NO2B, the authors construct a hypernuclear NAT basis that enables efficient and physically informative many-body calculations. The NAT basis not only improves numerical convergence but also provides detailed, species-resolved radial information that reveals hyperon halos in ΛHe and multi-layer halos in A=6–7 hypernuclei, underscoring the interplay between hyperon-nucleon interactions and halo formation. The results offer a robust diagnostic framework for halo phenomena in light hypernuclei and point to future work on multi-reference NAT approaches to address open-shell systems and further refine ab initio hypernuclear theory.

Abstract

We extend the concept of natural orbitals as an optimized single-particle basis for ab initio nuclear many-body calculations to hypernuclei and show that their superior properties, in particular accelerated convergence and independence of the underlying harmonic-oscillator frequency, can be directly transferred to the hypernuclear regime as demonstrated in no-core shell model calculations for selected p-shell hypernuclei. Moreover, the radial single-particle wavefunctions associated with the natural-orbital basis yield important structural information with respect to the different particle species allowing us to identify a hyperon halo in ΛHe5. We further explore nucleonic and hyperonic halo structures in A=6 and A=7 singly-strange hypernuclei based on one-body densities and point-particle radii obtained from no-core shell model calculations with realistic interactions from chiral effective field theory.

Figures (8)

• Figure 1: Squared single-particle radial wavefunctions in units of $\mathrm{fm}^{-1}$ in HO basis (colored) and NAT basis for $\isotope[5\,][\Lambda]{\mathrm{He}}$ (black) for $\hbar\Omega=16~(\textcolor{MPLblue}{---}),20~(\textcolor{MPLorange}{---}),24~(\textcolor{MPLgreen}{---}),28~(\textcolor{MPLred}{---}),$ and $32~(\textcolor{MPLpurple}{---})$ MeV. Shown here are the five lowest-lying orbitals (rows) for all considered particle species (columns). Colored background indicates occupied orbitals.
• Figure 2: NCSM calculations of ground-state energies of $\isotope[5\,][\Lambda]{\mathrm{He}}$ (upper panels) and $\isotope[7\,][\Lambda]{\mathrm{He}}$ (lower panels) for HO basis with full two-body and three-body forces (left), HO basis with NO2B approximation (center), and NAT basis (right) as a function of $\hbar\Omega$. Different colors correspond to $N_\mathrm{max}\xspace=2$ (---), 4 (---), 6 (---), 8 (---), 10 (---), and 12 (---). The black dashed lines indicate the lowest energy from the full HO calculation for comparison.
• Figure 3: Excitation energies of the lowest-lying natural-parity states of $\isotope[7\,][\Lambda]{\mathrm{He}}$ in HO basis (left) and NAT basis (right) for $N_\mathrm{max}\xspace=8,10,$ and $12$ at $\hbar\Omega\xspace=16$ MeV.
• Figure 4: (Left-hand panels) Particle-specific one-body densities in $\isotope[5\,][\Lambda]{\mathrm{He}}$ and $\isotope[7\,][\Lambda]{\mathrm{He}}$ for neutrons (---), protons (---), and $\Lambda$ particles (---) up to $N_\mathrm{max}\xspace=14,12$ for $\hbar\Omega\xspace=16$ MeV. Line thickness increases with model-space size. (Right-hand panels) Rms mass radii for $\isotope[5\,][\Lambda]{\mathrm{He}}$ and $\isotope[7\,][\Lambda]{\mathrm{He}}$ as a function of $\hbar\Omega$ for $N_\mathrm{max}\xspace=2$ (---), 4 (---), 6 (---), 8 (---), 10 (---), and 12 (---).
• Figure 5: (Left-hand panel) Particle-specific one-body densities in $\isotope[7\,][\Lambda]{\mathrm{He}}$ for neutrons (---), protons (---), and $\Lambda$ particles (---) for $N_\mathrm{max}\xspace=8$ and $\hbar\Omega\xspace=16$ MeV. (Right-hand panels) Ground-state energies (upper) and rms mass radii (lower) for $\isotope[7\,][\Lambda]{\mathrm{He}}$ as a function of $\hbar\Omega$ for $N_\mathrm{max}\xspace=8$ (red). Gray markers indicate data for $N_\mathrm{max}\xspace=2$ to $12$ from \ref{['fig:NCSM_compare_bases', 'fig:OBD_radii']} for comparison. All results are shown for $e_\mathrm{max}=8$ (dotted), 10 (dashed), and 12 (solid).