Λα, Σα and Ξα potentials derived from the SU6 quark-model baryon-baryon interaction

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 Bom 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 He-5(Lambda), from -3.18 to -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. For the Sigma alpha and Xi alpha potentials, we only discuss the zero-momentum Wigner transform of the interaction kernels, since these interactions turn out to be repulsive when the two isospin contributions for the EN and EN interactions are added up. These components show a strong isospin dependence: they are attractive in the isospin I = 1/2 (Sigma alpha) and I = 0 (Xi alpha) components and repulsive in I = 3/2 (Sigma alpha) and I = 1 (Xi alpha) components, which indicate that Sigma and Xi potentials could be attractive in some particular systems such as the well-known He-4(Sigma) system. (c) 2006 Elsevier B.V. All rights reserved.