P-WAVE ΛN-ΣN COUPLING AND THE SPIN-ORBIT SPLITTING OF $_\Lambda^9 {\rm{Be}}$

Abstract

We reexamine the spin-orbit splitting of [Formula: see text] excited states in terms of the SU6 quark-model baryon-baryon interaction. The previous folding procedure to generate the Λα spin-orbit potential from the quark-model ΛN LS resonating-group kernel predicted three to five times larger values for ΔEℓs = Ex(3/2+) - Ex(5/2+) in the model FSS and fss2. This time, we calculate Λα LS Born kernel, starting from the LS components of the nuclear-matter G-matrix for the Λ hyperon. This framework makes it possible to take full account of an important P-wave ΛN-ΣN coupling through the antisymmetric LS(-) force involved in the Fermi-Breit interaction. We find that the experimental value, [Formula: see text], is reproduced by the quark-model G-matrix LS interaction with a Fermi-momentum around kF = 1.0 fm -1, when the model FSS is used in the energy-independent renormalized RGM formalism. On the other hand, the model fss2 gives too large splitting of almost 200 keV, owing to the uncanceled contribution of the scalar-meson exchange LS components.