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 ${}_{\Lambda }^{40}\mathrm{Ca}$ 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 $ħ{\omega }_N{=45A}^{-1/3}-{25A}^{-2/3},$ 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 $\mathrm{Q̂}$-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 $\Lambda N-\Sigma N$ coupling diagram. Although this diagram contributes significantly to $V_{\mathrm{eff}}$ in most cases, it does not alter much to the final spectrum.

• Received 12 December 2001

DOI:https://doi.org/10.1103/PhysRevC.65.047303