Abstract
We study the character of the first excited $1/{2}^{+}$ state of $^{9}\mathrm{Be}$, which is observed as a low-lying sharp peak in the cross section of $^{9}\mathrm{Be}(\ensuremath{\gamma},n)2^{4}\mathrm{He}$ just above the $^{8}\mathrm{Be}+n$ threshold. Using the $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ three-body model, we describe the ground and excited unbound states of $^{9}\mathrm{Be}$ above the $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ threshold. Applying the complex scaling method to the three-body model, we find no $1/{2}^{+}$ resonant solutions with the scaling angle of $\ensuremath{\theta}\ensuremath{\le}{15}^{\ensuremath{\circ}}$, while the low-lying peak in the photodisintegration cross section is reproduced in the present calculation. It is found that the $^{8}\mathrm{Be}+n$ continuum states dominate the low-lying peak in the cross section. Furthermore, using the analytical continuation of the coupling constant of the three-body interaction for the $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ system, we discuss the virtual-state character of the $1/{2}^{+}$ state.
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