Coexistence of $\alpha +\alpha +n+n$ and $\alpha +t+t$ cluster structures in ${}^{10}\mathrm{Be}$

The coexistence of the $\alpha +\alpha +n+n$ and $\alpha +t+t$ cluster structures in the excited states of ${}^{10}\mathrm{Be}$ has been discussed. In the previous analysis, all the low-lying states of ${}^{10}\mathrm{Be}$ were found to be well described by the motion of the two valence neutrons around two α clusters. However, the $\alpha +t+t$ cluster structure was found to coexist with the $\alpha +\alpha +n+n$ structure around $E_x=15$ MeV, close to the corresponding threshold. We have introduced a microscopic model to solve the coupling effect between these two configurations. The $K=0$ and $K=1$ states are generated from the $\alpha +t+t$ configurations due to the spin coupling of two triton clusters. The present case of ${}^{10}\mathrm{Be}$ is one of the few examples in which completely different configurations of triton-type ($\alpha +t+t$ three-center) and α-type ($\alpha +\alpha +n+n$ two-center) clusters coexist in a single nucleus in the same energy region.

Figure 1

Energy levels of ${}^{10}\mathrm{Be}$ (positive parity) calculated assuming the equilateral triangular shape of the $\alpha +t+t$ configurations. The left-hand side shows the $K=0$ case; right-hand side, $K=1$. The horizontal lines at $-55.1$ and $-41.3$ MeV show the thresholds of $\alpha +\alpha +n+n$ and $\alpha +t+t$, respectively.

Figure 2

Energy convergence of the seven lowest $0^{+}$ states of ${}^{10}\mathrm{Be}$ as a function of the number of Slater determinants introduced.

Figure 3

Energy convergence of the $1^{+}$ ($K=1$) states of ${}^{10}\mathrm{Be}$ as a function of the number of Slater determinants introduced. The solid and dash-dotted lines are the cases of $\alpha +t+t$ and $\alpha +\alpha +n+n$ configurations, respectively.