Structure of6Hewith an extended three-cluster model

The core breakup or distortion effects in the neutron-halo nucleus ${}^6\mathrm{He}$ are studied with an extended microscopic $\alpha +n+n$ three-cluster model, in which the core particle, i.e., the $\alpha$ cluster is described as a $3N+N$ two-cluster system. The two-cluster description improves the tail behavior of the $\alpha$ particle with respect to the standard $0s$ harmonic-oscillator shell-model description, and makes the first excited state of the $\alpha$ particle realistic. The allowance for the core breakup in ${}^6\mathrm{He}$ enhances not only the binding energy but also the probability of the $t+t$ component. This model gives a binding energy and $t+t$ probability that are similar to the $\{\alpha +n+n;t+t\}$ model, and both can reproduce the very small binding energy of ${}^6\mathrm{He}.$ The inclusion of the $t+t$ channel deepens the binding substantially only when added to the conventional $\alpha +n+n$ model; when the extended three-cluster model is augmented by $t+t,$ its contribution is insignificant. Our results show that, for a weakly bound system such as a halo nucleus, the core internal motion must be treated realistically since the tail behavior of the core affects the binding mechanism of the halo nucleons.