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Two $^9$Li clusters connected with two valence neutrons in $^{20}$C

Many preceding works have shown in $^{11}$Li the presence of the halo structure comprised of the weakly bound two neutrons around $^9$Li, and it is intriguing to see how this halo structure changes when another $^9$Li approaches. In this study, we introduce a four-body model for $^{20}$C with two $^9$Li clusters and two valence neutrons. The recent development of the antisymmetrized quasi cluster model (AQCM) makes it possible to generate $jj$-coupling shell-model wave functions from $α$ cluster models. Here, $jj$-coupling shell model wave function of $^9$Li is regarded as a cluster, which corresponds to the subclosure configuration of $p_{3/2}$ for the neutrons, and we discuss how the two neutrons connect two $^9$Li clusters. Until now, most of the clusters in the conventional models have been limited to the closures of the three-dimensional harmonic oscillators, such as $^4$He, $^{16}$O, and $^{40}$Ca; however, owing to AQCM, it is feasible to utilize the $jj$-coupling shell model wave functions as plural subsystems quite easily. The appearance of a rotational band structure with a cluster structure around the four-body threshold energy is discussed.