Eizo Uzu

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 6He-n-n and 8He-n-n systems for 8He and 10He 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 8He and 10He. The 1- state of 10He, which has not been detected yet in experiments, is located in the energy level between the 0+ and 2+ states.

Separability of a Low-Momentum Effective Nucleon-Nucleon Potential

A realistic nucleon-nucleon potential is transformed into a low-momentum effective one (LMNN) using the Okubo theory. The separable potentials are converted from the LMNN with a universal separable expansion method and a simple Legendre expansion. Through the calculation of the triton binding energies, the separability for the convergence of these ranks is evaluated. It is found that there is a tendency for the lower momentum cutoff parameter Λ of LMNN to gain good separability.

Study of Four-Nucleon Systems by Four-Body Faddeev-Yakubovsky Equations

Complex energy method is introduced to handle singularity of Green’s function in fourbody Faddeev-Yakubovsky equations. We find that it is applicable to finding resonance states. Finite range expansion method is introduced to reduce the size of matrices of the Faddeev-Yakubovsky equations. We think this is applicable even in the energy region above the four-body break-up threshold when we employ low-momentum NN interactions.

Four-Body Faddeev-Yakubovsky Calculation Using the Finite Range Expansion Method

The finite range expansion method [Y. Koike, Prog. Theor. Phys. 87 (1992), 775], which gives well converged solutions of the three-body Faddeev equations, is extended to the three-body and two-two subsystems in order to solve the four-body Faddeev-Yakubovsky equations. A feasibility study is carried out to check the convergence in a four-nucleon system at 3.45 MeV below the four-body break-up threshold, which is in between the 2N-2N and 2N - N - N break-up thresholds. We obtain a converged phase shift and inelasticity parameter to 6 digits for 3N + N elastic scattering.

Four-body calculation above four-body break-up threshold

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.

FOUR-BODY FADDEEV-YAKUBOVSKY CALCULATION USING COMPLEX ENERGY METHOD

Three-nucleons force (3NF) is studied actively on three-nucleon systems in these several years. We can expect its larger influence in four-nucleon systems due to a naive idea that there is only one combination to choose three particles in a three-body system, while there are four in a four-body system. This is an advantage to study 3NF on four-nucleon systems. On the other hand, recent investigations show that influence of 3NF appears larger in higher energy region. Therefore, it is beneficial to study reaction problems of four-nucleon systems at higher incident energies. However, nobody have succeeded to solve the four-body Faddeev-Yakubovsky (FY) equations above the four-body breakup threshold due to complexity of boundary con-