$^{10}$Be+$\alpha$ correlation in $^{14}$C

We will report structure of excited states in $^{14}$C while paying attention to $^{10}$Be$+\alpha$ correlation. In the stable carbon nucleus, $^{12}$C, it is already known that various 3 $\alpha$ cluster structures appear in the excited states. It is natural to expect that rich phenomena may appear also in $^{14}$C which is an unstable neutron-rich nucleus. Many experiments indicate that there are various clustering structures in excited states of $^{14}$C. In these structures, a $^{10}$Be+$\alpha$ structure attracts much interest in association with a linear-chain structure of 3 $\alpha$ that has been studied for many years. For the systematic study of $^{14}$C, we adopted AMD(Antisymmetrized Molecular Dynamics) which has proved to be a powerful approach to describe various structures. The configurations were superposed in the GCM framework using ($\beta$, $\gamma$) as the generator coordinates. As the results, we obtained various states which have characteristic structures such as a triaxial structure, an equilateral-triangular structure and a linear-chain structure. We examined the possibility of the existence of $^{10}$Be+$\alpha$ correlation in these states. In linear-chain states, it was suggested that strong $^{10}$Be+$\alpha$ correlation exists, and this correlation plays an important role to stabilize the linear-chain structure.