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Register a new userLambda alpha, Sigma alpha and Xi alpha potentials derived from the SU6 quark-model baryon-baryon interaction
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Y. Fujiwara Kyoto
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We calculate Lambda alpha, Sigma alpha and Xi alpha potentials from the nuclear-matter G-matrices of the SU6 quark-model baryon-baryon interaction. The alpha-cluster wave function is assumed to be a simple harmonic-oscillator shell-model wave function. A new method is proposed to derive the direct and knock-on terms of the interaction Born kernel from the hyperon-nucleon G-matrices, with explicit treatments of the nonlocality and the center-of-mass motion between the hyperon and alpha. We find that the SU6 quark-model baryon-baryon interactions, FSS and fss2, yield a reasonable bound-state energy for 5 He Lambda, -3.18 -- -3.62 MeV, in spite of the fact that they give relatively large depths for the Lambda single-particle potentials, 46 -- 48 MeV, in symmetric nuclear matter. An equivalent local potential derived from the Wigner transform of the nonlocal Lambda alpha kernel shows a strong energy dependence for the incident Lambda-particle, indicating the importance of the strangeness-exchange process in the original hyperon-nucleon interaction. The Sigma alpha and Xi alpha potentials are repulsive with the attractive isospin I=1/2 (Sigma alpha) and I=0 (Xi alpha) components and the repulsive I=3/2 (Sigma alpha) and I=1 (Xi alpha) components.
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Interactions between the octet-baryons (B8) in the spin-flavor SU6 quark model are investigated in a unified coupled-channels framework of the resonating-group method (RGM). The interaction Hamiltonian for quarks consists of the phenomenological confinement potential, the color Fermi-Breit interaction with explicit flavor-symmetry breaking (FSB), and effective-meson exchange potentials of scalar-, pseudoscalar- and vector-meson types. The model parameters are determined to reproduce the properties of the nucleon-nucleon (NN) system and the low-energy cross section data for the hyperon-nucleon (YN) interactions. The NN phase shifts and many observables for the NN and YN interactions are nicely reproduced. Properties of these B8 B8 interactions are analyzed through the G-matrix calculations. The B8 B8 interactions are then applied to some of few-baryon systems and light Lambda-hypernuclei in a three-cluster Faddeev formalism using two-cluster RGM kernels. An application to the three-nucleon system shows that the quark-model NN interaction can give a sufficient triton binding energy with little room for the three-nucleon force. The hypertriton Faddeev calculation indicates that the attraction of the Lambda N interaction in the 1S0 state is only slightly more attractive than that in the 3S1 state. In the application to the alpha alpha Lambda system, the energy spectrum of 9 Lambda Be is well reproduced using the alpha alpha RGM kernel. The very small spin-orbit splitting of the 9 Lambda Be excited states is also discussed. In the Lambda Lambda alpha Faddeev calculation, the NAGARA event for 6 Lambda Lambda He is found to be consistent with the quark-model Lambda Lambda interaction.
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.
Quark-model hyperon-nucleon and hyperon-hyperon interactions by the Kyoto-Niigata group are applied to the two-Lambda plus alpha system in a new three-cluster Faddeev formalism using two-cluster resonating-group method kernels. The model fss2 gives a reasonable two-Lambda separation energy Delta B_{Lambda Lambda}=1.41 MeV, which is consistent with the recent empirical value, Delta B^{exp}_{Lambda Lambda}=1.01 +/- 0.20 MeV, deduced from the Nagara event. Some important effects that are not taken into account in the present calculation are discussed.
We carry out Faddeev calculations of three-alpha (3 alpha) and two-alpha plus Lambda (alpha alpha Lambda) systems, using two-cluster resonating-group method kernels. The input includes an effective two-nucleon force for the alpha alpha resonating-group method and a new effective Lambda N force for the Lambda alpha interaction. The latter force is a simple two-range Gaussian potential for each spin-singlet and triplet state, generated from the phase-shift behavior of the quark-model hyperon-nucleon interaction, fss2, by using an inversion method based on supersymmetric quantum mechanics. Owing to the exact treatment of the Pauli-forbidden states between the clusters, the present three-cluster Faddeev formalism can describe the mutually related, alpha alpha, 3 alpha and alpha alpha Lambda systems, in terms of a unique set of the baryon-baryon interactions. For the three-range Minnesota force which describes the alpha alpha phase shifts quite accurately, the ground-state and excitation energies of 9Be Lambda are reproduced within 100 - 200 keV accuracy.
We study the structure of $^9_Lambda$Be in the framework of three body $alpha+alpha+Lambda$ cluster model using YNG-NF interaction with the Gaussian expansion method. Employing the complex scaling method, we obtain the energies of bound states as well as energies and decay widths of the resonant states. By analyzing our wave functions of bound states and resonant states, we confirm three analogue states of $^9_Lambda$Be pointed out by Band${rm bar{o}}$ and Motoba {it et al.} cite{motoba1983,motoba1985,bando1983}, $^8$Be analogue states, $^9_{Lambda}$Be genuine states and $^9$Be analogue states. The new states of $^9_Lambda$Be are also obtained at a high energy region with broader decay widths.
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