The structure of the excited states of ${}^{10}\mathrm{Be}$ is theoretically explored by means of the microscopic $\alpha +\alpha +n+n$ four-cluster model. The two-body scattering problem of $\left\{{}^9\mathrm{Be}\left(3∕2^{-},1∕2^{+},5∕2^{-}\right)+n\right\}+\left\{{}^6\mathrm{He}\left(0^{+},2^{+}\right)+\alpha \right\}$ is solved by the microscopic $R$-matrix method in order to localize the resonance excited states in ${}^{10}\mathrm{Be}$. The wave functions of ${}^9\mathrm{Be}$ and ${}^6\mathrm{He}$ are given by the microscopic $\alpha +\alpha +n$ and $\alpha +n+n$ three-cluster models, respectively. Our model can reproduce not only the ground $0^{+}$ state but also the second $0^{+}$ state simultaneously. The second $0^{+}$ state has a highly developed $\alpha +\alpha \left({}^6\mathrm{He}+\alpha \right)$ clustering and is dominated by the $2\hslash \omega$ excitation in the shell-model configuration wherein two neutrons occupy the $1s_{1∕2}$ orbit. The ground state has a more compact structure due to the large binding energy but some weak $\alpha +\alpha$ clustering still persists. Our microscopic multicluster model is applied to the resonance excited states lying above the ${}^9\mathrm{Be}+n$ threshold, and the present model gives various resonance excited states. Among these states, the $0_2^{+}$, $2_4^{+}$, and $4_2^{+}$ states could constitute a $K^{\pi }=0_2^{+}$ rotational band which has a large deformation owing to the $\alpha +\alpha$ clustering. In the wave function for the second $0^{+}$ state in ${}^{10}\mathrm{Be}$, as well as for the $1∕2^{+}$ first excited state of ${}^9\mathrm{Be}$, the motion of the valence neutrons around the two $\alpha$ particles appears to be consistent with the $\sigma$ orbit in the molecular orbital model. We find that two or three competing configurations are necessary to reproduce these two anomalous states (the $1∕2^{+}$ and $0_2^{+}$ states), where one configuration produces a spatially extended neutron distribution outside the ${}^8\mathrm{Be}$ core and another has a strong core $(\alpha +\alpha )$ distortion induced by the valence neutron, with the latter being responsible for lowering the energies of these two states.

• Received 12 August 2003

DOI:https://doi.org/10.1103/PhysRevC.69.014309