Resonance states of5Hand5Bein a microscopic three-cluster model

Abstract

Resonance states of ${}^{5}\mathrm{H}$ and ${}^{5}\mathrm{Be}$ have been studied using microscopic $t+n+n$ and $h+p+p$ three-cluster models, respectively. The resonance positions are localized by the three-body complex scaling method. An effective nucleon-nucleon interaction, which reproduces the $\ensuremath{\alpha}+N$ low energy phase shifts and the energies of the ${0}^{+}$ ground and ${2}^{+}$ first excited states of ${}^{6}\mathrm{He}$ with the three-cluster model, is used to calculate resonance states of ${}^{5}\mathrm{H}$ and ${}^{5}\mathrm{Be}.$ This model can reasonably reproduce the experimental $t+n$ and $h+p$ phase shifts at low energies. It gives a ${1/2}^{+}$ broad resonance as the ground state in ${}^{5}\mathrm{H}$ and ${}^{5}\mathrm{Be}$ and in addition it gives two excited resonance states of ${3/2}^{+}$ and ${5/2}^{+}.$ The resonance parameters of the ${1/2}^{+}$ state of ${}^{5}\mathrm{H}$ in the present model are close to those deduced from their recent experimental data by Korsheninnikov et al. The same effective nucleon-nucleon interaction is used for a tentative investigation in order to explore the possibility of a tetra-neutron ${(}^{4}n)$ resonance by means of the $n+n+n+n$ four-body complex scaling method on a restricted set of model configurations. Our model does not give any evidence for a tetraneutron resonance.