Core-excitation three-cluster model description of 8He and 10He

We introduce a new model applying to the core-nucleus and two-neutron system. The Faddeev equations of He-6-n-n and He-8-n-n systems for He-8 and He-10 are solved, respectively. The potential of the subsystem in the model has been determined to make a coupling both of the ground state and the excited one inside the core nucleus. By a similar mechanism the three-nucleon system is solved with the three-body force originating from an isobar excitation of the nucleon. Inputting only the information of subsystem energy levels and widths we get the coupling constants of rank 1 Yamaguchi potential between the core nucleus and neutron. We calculate the Faddeev three-cluster equations to obtain the low-lying energy levels of He-8 and He-10. The 1(-) state of He-10, which has not been detected yet in experiments, is located in the energy level between the 0(+) and 2(+) states.