  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.

Nuclear Theory