Halo Nuclei from Ab Initio Nuclear Theory

Abstract

A realistic description of halo nuclei, characterized by low-lying breakup thresholds, requires a proper treatment of continuum effects. We have developed an ab initio approach, the no-core shell model with continuum (NCSMC), capable of describing both bound and unbound states in light nuclei in a unified way. With chiral two- and three-nucleon interactions as the only input, we can predict structure and dynamics of halo and other light nuclei and, by comparing to available experimental data, test the quality of chiral nuclear forces. We review NCSMC calculations of weakly bound states and resonances of exotic halo nuclei $^6$He, $^8$B, $^{11}$Be, and $^{15}$C. For the latter, we discuss its production in the capture reaction $^{14}$C(n,$γ$)$^{15}$C. We highlight challenges of a description of $^6$He as a Borromean n-n-$^4$He system. Finally, we present calculations of excited states in $^{10}$Be exhibiting a one-neutron halo structure and a large scale no-core shell model investigation of $^{11}$Li as a precursor of a full n-n-$^9$Li NCSMC study.

Figures (16)

• Figure S1: Schematic depiction of the NCSMC basis expansion for $^6$He showing the NCSM $^6$He part and the three-body cluster part consisting of the $^4$He ground state and two neutrons.
• Figure S2: NCSMC spectrum of $^{11}$Be with respect to the $n+^{10}$Be threshold for different chiral interactions compared to experiment. Dashed black lines indicate the energies of the $^{10}$Be states. Light boxes indicate resonance widths.
• Figure S3: (a) NCSMC calculated and experimental levels of $^{11}$Be. Only states corresponding to experimentally bound states with respect to the $^{10}$Be$+n$ threshold (horizontal red dashed line) are shown. (b) NCSMC-calculated $^{10}$Be$+p$ eigenphase shifts. The vertical dashed line indicates the experimentally predicted location of the ($1/2^+$, 1/2) resonance at 197 keV. The NN-N$^4$LO+3N$_{\rm lnl}$ interaction was used. Adapted from Ref. Atkinson2022.
• Figure S4: Cluster form factors of $^{11}$Be $1/2^+$ (a) and $1/2^-$ (b) states obtained with the N$^2$LOsat interaction. The solid lines show the NCSMC-pheno results, the black dashed (dotted) lines are the NCSMC (NCSM) $S$-wave (a) and $P$-wave (b) results. The legend columns show the $^{10}$Be eigenstate, the channel spin $s$ and the relative orbital momentum $l$ of $^{10}$Be+n. See the text for further details.
• Figure S5: (a) Calculated energies of low-lying states of $^{15}$C compared to experiment. The crosses correspond to NCSM calculations in basis spaces up to $N_{\rm max}{=}8$. The NCSMC calculations has been performed in $N_{\rm max}{=}7$. All energies are with respect to the $^{14}$C+n threshold, the calculated one obtained in the consistent $N_{\rm max}$ space. (b) Diagonal $^{14}$C+n phase shift dependence on the energy in the center of mass obtained within the NCSMC-pheno approach in $N_{\rm max}{=}7$ space. The NN N$^3$LO + 3N$_{\rm lnl}$ interaction and the HO frequency of $\hbar\Omega{=}20$ MeV has been used in all calculations. See the text for further details.