H. Nemura

Three-Cluster Equation Using the Two-Cluster RGM Kernel

We propose a new type of three-cluster equation which uses two-cluster resonating-groupmethod (RGM) kernels. In this equation, the orthogonality of the total wave function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy dependence inherent in the exchange RGM kernel is self-consistently determined. For bound-state problems, this equation is straightforwardly transformed into the Faddeev equation, which uses a modified singularity-free T -matrix constructed from the two-cluster RGM kernel. The approximation of the present three-cluster formalism can be examined with a more complete calculation using the threecluster RGM. As a simple example, we discuss three di-neutron (3d � ) and 3α systems in the harmonic-oscillator variational calculation. The result of the Faddeev calculation is also

Redundant components in the 3α Faddeev equation using the 2α RGM kernel

The 3α Faddeev equation using the 2α RGM kernel involves redundant components whose contribution to the total wave function cancels out completely. We propose a practical method to solve this Faddeev equation, by eliminating the admixture of such redundant components. The equivalence of the present Faddeev approach and a variational approach using the translationally invariant harmonic-oscillator basis was numerically demonstrated with respect to the 3α bound state corresponding to the ground state of 12 C. A preliminary problem to be solved for the purpose of applying realistic quark model baryon-baryon interactions to few-baryon systems, such as the hypertriton, is to find a basic three-cluster equation that is formulated by using a microscopic twocluster quark-exchange kernel of the resonating-group method (RGM). This problem is non-trivial, not only because the quark-exchange kernel is non-local and energy dependent, but also because RGM equations sometimes involve redundant components, due to the effect of the antisymmetrization, i.e., the Pauli-forbidden states. A desirable feature of such a three-cluster equation is that it can be solved using either or both the variational approach and the Faddeev formalism, with identical results. In a previous paper 1) (which is referred to as I hereafter), we proposed a simple three-cluster equation, which is similar to the orthogonality condition model (OCM), 2) but employs the two-cluster RGM kernel as the interaction potential. The three-cluster Pauli-allowed space is constructed using the orthogonality of the total wave functions to the pairwise Pauli forbidden states. Although this definition of the three-cluster Pauli-allowed space is not exactly equivalent to the standard definition given by the three-cluster normalization kernel, this condition of the orthogonality is essential to achieve the equivalence of the proposed three-cluster equation and the Faddeev equation, which employs a singularity-free T -matrix derived from the RGM

Triton binding energy calculated from the SU6 quark-model nucleon-nucleon interaction

Properties of the three-nucleon bound state are examined in the Faddeev formalism, in which the quark-model nucleon-nucleon interaction is explicitly incorporated to calculate the off-shell T-matrix. The most recent version, fss2, of the Kyoto-Niigata quark-model potential yields the ground-state energy ^3H=-8.514 MeV in the 34 channel calculation, when the np interaction is used for the nucleon-nucleon interaction. The charge root mean square radii of the ^3H and ^3He are 1.72 fm and 1.90 fm, respectively, including the finite size correction of the nucleons. These values are the closest to the experiments among many results obtained by detailed Faddeev calculations employing modern realistic nucleon-nucleon interaction models.

Stochastic Variational Search for

A four-body calculation of the

^{4}_{\Lambda\Lambda}

pn\Lambda\Lambda

H

bound state,

Full-coupled channel approach to S=−2 s-shell hypernuclear systems

^{\ 4}_{\Lambda\Lambda}

Study of Pentaquark and Λ(1405)

H, is performed using the stochastic variational method and phenomenological potentials. The

Λ(1405) in a hybrid quark model

NN

Few-Body Problems with Strangeness

,