Yasuro Koike

Complex Energy Method for Scattering Processes

A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering t-matrix with real positive energy. Numerical examples document that the method works well for two-nucleon scattering and three-nucleon scattering, if the set of complex energies is properly chosen.

New Screened Coulomb Potentials and Renormalization

We introduce a new screening function which is useful for the few-body Coulomb scattering problem in the screening and renormalization scheme. We modify the Yukawa-type screened Coulomb potential more useful. In the proton-proton scattering, we demonstrate high precision calculations of the new renormalization.

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-