Addendum: Triton and hypertriton binding energies calculated from SU_6 quark-model baryon-baryon interactions

Previously we calculated the binding energies of the triton and hypertriton, using an SU_6 quark-model interaction derived from a resonating-group method of two baryon clusters. In contrast to the previous calculations employing the energy-dependent interaction kernel, we present new results using a renormalized interaction, which is now energy independent and reserves all the two-baryon data. The new binding energies are slightly smaller than the previous values. In particular the triton binding energy turns out to be 8.14 MeV with a charge-dependence correction of the two-nucleon force, 190 keV, being included. This indicates that about 350 keV is left for the energy which is to be accounted for by three-body forces.Comment: 4 pages, 1 figur

Quark-Model Baryon-Baryon Interaction and its Applications to Hypernuclei

The quark-model baryon-baryon interaction fss2, proposed by the Kyoto-Niigata group, is a unified model for the complete baryon octet (B_8=N, Lambda, Sigma and Xi), which is formulated in a framework of the (3q)-(3q) resonating-group method (RGM) using the spin-flavor SU_6 quark-model wave functions and effective meson-exchange potentials at the quark level. Model parameters are determined to reproduce properties of the nucleon-nucleon system and the low-energy cross section data for the hyperon-nucleon scattering. Due to the several improvements including the introduction of vector-meson exchange potentials, fss2 has achieved very accurate description of the NN and YN interactions, comparable to various one-boson exchange potentials. We review the essential features of fss2 and our previous model FSS, and their predictions to few-body systems in confrontation with the available experimental data. Some characteristic features of the B_8 B_8 interactions with the higher strangeness, S=-2, -3, -4, predicted by fss2 are discussed. These quark-model interactions are now applied to realistic calculations of few-body systems in a new three-cluster Faddeev formalism which uses two-cluster RGM kernels. As for the few-body systems, we discuss the three-nucleon bound states, the Lambda NN-Sigma NN system for the hypertriton, the alpha alpha Lambda system for 9Be Lambda, and the Lambda Lambda alpha system for 6He Lambda Lambda.Comment: 20 pages, 12 figures, 18th Nishinomiya Yukawa Memorial Symposium on Strangeness in Nuclear Matter, 4 - 5 December 2003, Nishinomiya, Japan. (to be published in Prog. Theor. Phys. Suppl.

Three-Cluster Equation Using Two-Cluster RGM Kernel

We propose a new type of three-cluster equation which uses two-cluster resonating-group-method (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 to 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 more complete calculation using the three-cluster RGM. As a simple example, we discuss three di-neutron (3d') and 3 alpha systems in the harmonic-oscillator variational calculation. The result of the Faddeev calculation is also presented for the 3' system.Comment: 12 pages, no figur

P-wave Lambda N - Sigma N coupling and the spin-orbit splitting of 9 Lambda Be

We reexamine the spin-orbit splitting of 9 Lambda Be excited states in terms of the SU_6 quark-model baryon-baryon interaction. The previous folding procedure to generate the Lambda alpha spin-orbit potential from the quark-model Lambda N LS interaction kernel predicted three to five times larger values for Delta E_{ell s}=E_x(3/2^+)-E_x(5/2^+) in the model FSS and fss2. This time, we calculate Lambda alpha LS Born kernel, starting from the LS components of the nuclear-matter G-matrix for the Lambda hyperon. This framework makes it possible to take full account of an important P-wave Lambda N - Sigma N coupling through the antisymmetric LS^{(-)} force involved in the Fermi-Breit interaction. We find that the experimental value, Delta E^{exp}_{ell s}=43 pm 5 keV, is reproduced by the quark-model G-matrix LS interaction with a Fermi-momentum around k_F=1.0 fm^{-1}, when the model FSS is used in the energy-independent renormalized RGM formalism.Comment: 5 pages, no figure