The Complex Energy Method [Prog. Theor. Phys. 109, 869L (2003)] is applied to the four body Faddeev-Yakubovsky equations in the four nucleon system. We obtain a well converged solution in all energy regions below and above the four nucleon break-up threshold.PACS numbers: 25.10.+s, 11.80.Jy, 02.40.Xx Calculations for scattering systems in configuration space require boundary conditions which increase in complexity with growing particle numbers. These boundary conditions appear in the form of Green's functions in momentum space which carry singularities of increasing complexity. The Green's functions are expressed as G 0 = 1/(E + iε − H 0 ) where E and H 0 are the total and kinetic energy, respectively, and the limit ε → 0 has to be taken. In the two-body system there is one (relative) momentum variable p and G 0 has a pole in the complex p-plane. It is easy to handle it using the principal value prescription and (half) the residue theorem (PVR). In the three body case there arises already a difficulty in the form of so called moving singularities [1,2], however, PVR is still applicable [3], or one can use the contour deformation [4,5,6,7] (CD) technique. Summarizing these techniques, first one takes the limiting value ε → 0 and next the equation is solved avoiding the integration path on the complex plane. This is illustrated in Fig. 1.The situation is more complicated in the four body system. Employing a separable potential and a separable expansion technique for the three body, and [2+2] subamplitudes, the four body Faddeev-Yakubovsky (FY) equations [8] for four identical particles can be expressed as * Electronic address: j-uzu@ed.noda.tus.ac.jp

We introduce a new model applying to the core-nucleus and two-neutron system. The Faddeev equations of 6 He-n-n and 8 He-n-n systems for 8 He and 10 He 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 8 He and 10 He. The 1 − state of 10 He, which has not been detected yet in experiments, is located in the energy level between the 0 + and 2 + states.

No abstract

No abstract

No abstract