P-wave Lambda N - Sigma N coupling and the spin-orbit splitting of 9 Lambda Be

TL;DR

This paper investigates the spin-orbit splitting in Lambda Be-9 using a quark-model baryon-baryon interaction, emphasizing the importance of P-wave Lambda N - Sigma N coupling and achieving agreement with experimental data.

Contribution

It introduces a new calculation of the Lambda alpha LS Born kernel incorporating P-wave Lambda N - Sigma N coupling, improving the prediction of spin-orbit splitting.

Findings

Reproduces experimental spin-orbit splitting with FSS model at k_F=1.0 fm^{-1}.

Highlights the significance of P-wave Lambda N - Sigma N coupling in hypernuclear interactions.

Demonstrates the effectiveness of the quark-model G-matrix LS interaction in hypernuclear physics.

Abstract

We reexamine the spin-orbit splitting of 9 Lambda Be excited states in terms of the SU_6 quark-model baryon-baryon interaction. The previous folding procedure to generate the Lambda alpha spin-orbit potential from the quark-model Lambda N LS interaction kernel predicted three to five times larger values for Delta E_{ell s}=E_x(3/2^+)-E_x(5/2^+) in the model FSS and fss2. This time, we calculate Lambda alpha LS Born kernel, starting from the LS components of the nuclear-matter G-matrix for the Lambda hyperon. This framework makes it possible to take full account of an important P-wave Lambda N - Sigma N coupling through the antisymmetric LS^{(-)} force involved in the Fermi-Breit interaction. We find that the experimental value, Delta E^{exp}_{ell s}=43 pm 5 keV, is reproduced by the quark-model G-matrix LS interaction with a Fermi-momentum around k_F=1.0 fm^{-1}, when the model FSS is used in the energy-independent renormalized RGM formalism.