The ${}^{10}$He nucleus, being a “maximal neutron-rich nucleus” in the ratio of neutrons to protons $\mathrm{}(p:n=1:4\mathrm{})\mathrm{}$ among nuclei observed so far, is investigated within the ${}^8\mathrm{He}+n+n$ model. The energy and decay width of the three-body system are solved by applying the complex scaling method to the ${}^8\mathrm{He}+n+n$ Hamiltonian, where the folding-type ${}^8\mathrm{He}-n$ potential is carefully chosen through the analysis of the experimental resonance energy 1.16 MeV of ${}^9$He and in comparison with the ${}^9\mathrm{Li}-n$ folding potential employed successfully in the description of the loosely bound ${}^{11}$Li system. The calculated result ${(E}_r=1.8\mathrm{}$ MeV, $\Gamma =1.4\mathrm{}$ MeV) of the ${}^{10}$He ground state corresponds well to the observed values.

• Received 16 December 1996

DOI:https://doi.org/10.1103/PhysRevC.55.2379