Λα, Σα and Ξα potentials derived from the [formula omitted] quark-model baryon–baryon interaction

Abstract

We calculate Λα, Σα and Ξα potentials from the nuclear-matter G-matrices of the SU 6 quark-model baryon–baryon interaction. The α-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 α. We find that the SU 6 quark-model baryon–baryon interactions, FSS and fss2, yield a reasonable bound-state energy for 5 Λ He, from −3.18 to − 3.62 MeV , in spite of the fact that they give relatively large depths for the Λ single-particle potentials, 46–48 MeV, in symmetric nuclear matter. An equivalent local potential derived from the Wigner transform of the nonlocal Λα kernel shows a strong energy dependence for the incident Λ-particle, indicating the importance of the strangeness-exchange process in the original hyperon–nucleon interaction. For the Σα and Ξα 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 ΣN and ΞN interactions are added up. These components show a strong isospin dependence: they are attractive in the isospin I = 1 / 2 ( Σα) and I = 0 ( Ξα) components and repulsive in I = 3 / 2 ( Σα) and I = 1 ( Ξα) components, which indicate that Σ and Ξ potentials could be attractive in some particular systems such as the well-known 4 Σ He system.