HypernucleusΛ40Caand recent hyperon-nucleon potentials

Abstract

The Nijmegen NSC89 and the most recent NSC97 hyperon-nucleon potentials are adopted to study the structures of hypernuclei. Investigations are concentrated on the hypernucleus ${}_{\ensuremath{\Lambda}}^{40}\mathrm{Ca}$ by using our two-frequency shell-model folded-diagram approach. We first calculate the $\mathrm{YN}$ G matrix with an exact Pauli exclusion operator. The nucleon frequency for the harmonic oscillator basis wave function is chosen from the empirical formula $\ensuremath{\Elzxh}{\ensuremath{\omega}}_{N}{=45A}^{\ensuremath{-}1/3}\ensuremath{-}{25A}^{\ensuremath{-}2/3},$ while the hyperon one is obtained as the frequency when the lowest hyperon single-particle energy in the hypernucleus reaches a saturation minimum. The energy-independent effective interaction ${V}_{\mathrm{eff}}$ is then obtained from the $\mathrm{YN}$ G matrix elements, using a $\mathrm{Q\ifmmode \hat{}\else \^{}\fi{}}$-box folded-diagram framework. We will examine how our calculated spectra vary via these different versions of the realistic hyperon-nucleon potentials. Special attention is drawn on the contribution of the $\ensuremath{\Lambda}N\ensuremath{-}\ensuremath{\Sigma}N$ coupling diagram. Although this diagram contributes significantly to ${V}_{\mathrm{eff}}$ in most cases, it does not alter much to the final spectrum.