Doublet 1/2+ resonances of B9 in the complex scaling method

Abstract

We try to resolve the longstanding controversy over the low-lying $1/{2}^{+}$ state in $^{9}\mathrm{B}$. Experimentally, the energies for this state show a gap between various measurements done by different groups and some of them reported that the existence of the state is unclear. The situation is similar in the theoretical calculations. We study the existence and structure of the $^{9}\mathrm{B}(1/{2}^{+}$) state based on our previous method for the $\ensuremath{\alpha}+\ensuremath{\alpha}+N$ cluster model with the complex scaling method that well explains the measured photodisintegration cross section for the $^{9}\mathrm{Be}(1/{2}^{+})$. We find two resonances at the energies of ${E}_{1}^{\mathrm{res}}=1.81$ MeV with a decay width $\mathrm{\ensuremath{\Gamma}}=1.98$ MeV and ${E}_{2}^{\mathrm{res}}=2.38$ MeV, $\mathrm{\ensuremath{\Gamma}}=1.81$ MeV in $^{9}\mathrm{B}$. The charge radii and the three-body channel configurations are calculated to see the properties of two resonances. We also calculate the level density of two resonances, which indicates the difficulty to distinguish them in the energy distribution.