Structure of the exotic ${}^9\mathrm{He}$ nucleus from the no-core shell model with continuum

Background: The exotic ${}^9\mathrm{He}$ nucleus, which presents one of the most extreme neutron-to-proton ratios, belongs to the $N=7$ isotonic chain famous for the phenomenon of ground-state parity inversion with decreasing number of protons. Consequently, it would be expected to have an unnatural (positive) parity ground state similar to ${}^{11}\mathrm{Be}$ and ${}^{10}\mathrm{Li}$. Despite many experimental and theoretical investigations, its structure remains uncertain. Apart from the fact that it is unbound, other properties including the spin and parity of its ground state, and the very existence of additional low-lying resonances are still a matter of debate.

Purpose: In this work, we study the properties of ${}^9\mathrm{He}$ by analyzing the $n+{}^8\mathrm{He}$ continuum in the context of the ab initio no-core shell model with continuum (NCSMC) formalism with chiral nucleon-nucleon interactions as the only input.

Methods: The NCSMC is a state-of-the-art approach for the ab initio description of light nuclei. With its capability to predict properties of bound states, resonances, and scattering states in a unified framework, the method is particularly well suited for the study of unbound nuclei such as ${}^9\mathrm{He}$.

Results: Our analysis produces an unbound ${}^9\mathrm{He}$ nucleus. Two resonant states are found at the energies of $\sim 1$ and $\sim 3.5$ MeV, respectively, above the $n+{}^8\mathrm{He}$ breakup threshold. The first state has a spin-parity assignment of $J^{\pi }={1/2}^{-}$ and can be associated with the ground state of ${}^9\mathrm{He}$, while the second, broader state has a spin parity of ${3/2}^{-}$. No resonance is found in the ${1/2}^{+}$ channel, only a very weak attraction.

Conclusions: We find that the ${}^9\mathrm{He}$ ground-state resonance has a negative parity and thus breaks the parity-inversion mechanism found in the ${}^{11}\mathrm{Be}$ and ${}^{10}\mathrm{Li}$ nuclei of the same $N=7$ isotonic chain.

Figure 1

Ground-state energy of ${}^6\mathrm{He}$ as function of $\hslash \mathrm{\Omega }$ calculated for different values of $N_{\max }$ within the NCSM and using the SRG-evolved $\mathrm{N}{}^4\mathrm{LO}NN$ potential [90, 91] with ${\lambda }_{\mathrm{SRG}}=2.4{\mathrm{fm}}^{-1}$. The shaded band represents the result of the exponential extrapolation performed at $\hslash \mathrm{\Omega }=20$ MeV with the estimated theoretical error.

Figure 2

The ground-state energy for ${}^8\mathrm{He}$ as a function of $\hslash \mathrm{\Omega }$ and $N_{\max }$. The details are the same as in Fig. 1.

Figure 3

Ground-state energy of ${}^6\mathrm{He}$ as function of $N_{\max }$ calculated with $\hslash \mathrm{\Omega }=20$ MeV within the NCSM and using the SRG-evolved $\mathrm{N}{}^4\mathrm{LO}NN$ potential [90, 91] with ${\lambda }_{\mathrm{SRG}}=2.4{\mathrm{fm}}^{-1}$. The circles represent the calculated results while the squares are the energies obtained from the exponential extrapolation.

Figure 4

The ground-state energy for ${}^8\mathrm{He}$ and the $1/2^{-}$ and $1/2^{+}$ eigenenergies of ${}^9\mathrm{He}$ as a function of $N_{\max }$. The details are the same as in Fig. 3.

Figure 5

Dependence of the NCSMC results from the $N_{\max }$ basis size of the ${}^{2}S_{1/2}$ phase shift as a function of the kinetic energy in the center of mass. The SRG-evolved $\mathrm{N}{}^4\mathrm{LO}NN$ potential [90, 91] with ${\lambda }_{\mathrm{SRG}}=2.4{\mathrm{fm}}^{-1}$ and the HO frequency of $\hslash \mathrm{\Omega }=20$ MeV were used.

Figure 6

The ${}^{2}P_{1/2}$ phase shift in analogy to Fig. 5.

Figure 7

The ${}^{6}P_{3/2}$ phase shift in analogy to Fig. 5.

Figure 8

NCSMC $n+{}^8\mathrm{He}$ diagonal phase shifts as a function of the kinetic energy in the center of mass computed at $N_{\max }=11$. The SRG-evolved $\mathrm{N}{}^4\mathrm{LO}NN$ potential [90, 91] with ${\lambda }_{\mathrm{SRG}}=2.4{\mathrm{fm}}^{-1}$ and the HO frequency of $\hslash \mathrm{\Omega }=20$ MeV were used.

Figure 9

(a) NCSMC $n+{}^8\mathrm{He}$ eigenphase shifts as a function of the kinetic energy in the center of mass. (b) NCSMC-pheno $n+{}^8\mathrm{He}$ eigenphase shifts as a function of the kinetic energy in the center of mass and setting the energy of the first excited state of ${}^8\mathrm{He}$ at the experimental energy of 3.1 MeV. In both cases, the results were obtained at $N_{\max }=11$ using the SRG-evolved $\mathrm{N}{}^4\mathrm{LO}NN$ potential [90, 91] with ${\lambda }_{\mathrm{SRG}}=2.4{\mathrm{fm}}^{-1}$ and the HO frequency of $\hslash \mathrm{\Omega }=20$ MeV were used.