${}^4\mathrm{He}+n+n$ Continuum within an Ab initio Framework

The low-lying continuum spectrum of the ${}^6\mathrm{He}$ nucleus is investigated for the first time within an ab initio framework that encompasses the ${}^4\mathrm{He}+n+n$ three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core shell model combined with the resonating-group method, in which energy-independent nonlocal interactions among three nuclear fragments can be calculated microscopically, starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with three-body scattering boundary conditions by means of the hyperspherical-harmonics method on a Lagrange mesh. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we find the known $J^{\pi }=2^{+}$ resonance as well as a result consistent with a new low-lying second $2^{+}$ resonance recently observed at GANIL at 2.6 MeV above the ${}^6\mathrm{He}$ ground state. We also find resonances in the $2^{-}$, $1^{+}$, and $0^{-}$ channels, while no low-lying resonances are present in the $0^{+}$ and $1^{-}$ channels.

Figure 1

Calculated ${}^4\mathrm{He}+n+n$ (a) positive- and (b) negative-parity attractive eigenphase shifts as a function of the kinetic energy $E_{\text{kin}}$ with respect to the two-neutron emission threshold. See the text for further details.

Figure 2

Comparison of the spectrum obtained within this work using the NCSM/RGM to the experimental spectrum measured at the SPIRAL facility (GANIL) [4].

Figure 3

Convergence behavior of calculated ${}^4\mathrm{He}+n+n$ (a) $J^{\pi }=1^{-}$ and (b) $0^{+}$ eigenphase shifts at $K_{\max }=19$ and 28, respectively, and (c) $2^{+}$ and (d) $1^{+}$ diagonal phase shifts at $K_{\max }=20$ with respect to the size $N_{\max }$ of the NCSM/RGM model space for the SRG ${\mathrm{N}}^3\mathrm{LO}$ $NN$ potential with $\mathrm{\Lambda }=1.5{\mathrm{fm}}^{-1}$. For these calculations, we used an extended HO model space of $N_{\text{ext}}=70$ and a matching radius of $a=30\mathrm{fm}$. In (a), $1^{-}$ phase shifts obtained with the $\mathrm{\Lambda }=1.8{\mathrm{fm}}^{-1}$ SRG $NN$ potential at $N_{\max }=11$ are also shown for comparison. When presenting eigenphase shifts on (a) and (b), the quantum numbers of the dominant components are shown in parentheses. These have been identified by comparing the eigenphase shifts with the diagonal phase shifts.

Figure 4

Dependence on the size of the extended HO model space $N_{\text{ext}}$ of calculated ${}^4\mathrm{He}+n+n$ (a) $J^{\pi }=2^{+}$ diagonal phase shifts corresponding to the $2_1^{+}$ and $2_2^{+}$ resonances at $N_{\max }=7$ and (b) the first three eigenphase shifts for the $J^{\pi }=0^{+}$ channel at $N_{\max }=13$. The curves overlap for the $2_2^{+}$ resonance in (a).