#### Abstract

A two-frequency shell model is proposed for investigating the structure of hypernuclei starting with a hyperon-nucleon potential in free space. In a calculation using the folded-diagram method for ${}_{\Lambda}^{16}\mathrm{O},$ the $\Lambda $ single particle energy is found to have a saturation minimum at an oscillator frequency $\u0127{\omega}_{\Lambda}\approx 10\mathrm{MeV},$ for the $\Lambda $ orbit, which is considerably smaller than $\u0127{\omega}_{N}=14\mathrm{}\mathrm{MeV}$ for the nucleon orbit. The spin-dependence parameters derived from the Nijmegen NSC89 and NSC97f potentials are similar, but both are rather different from those obtained with the Jülich-$B$ potential. The $\Lambda \mathrm{NN}$ three-body interactions induced by $\Lambda N-\Sigma N$ transitions are important for the spin parameters, but relatively unimportant for the low-lying states of ${}_{\Lambda}^{16}\mathrm{O}.$

DOI: http://dx.doi.org/10.1103/PhysRevC.61.031305

- Received 29 January 1999
- Revised 28 July 1999
- Published 18 February 2000

© 2000 The American Physical Society