\Lambda^{\ast}-hypernuclei in phenomenological nuclear forces

Abstract

The ${\Lambda }^{\ast }$-hypernuclei, which are bound states of $\Lambda (1405)$ and nuclei, are discussed as a possible interpretation of the $\bar{K}$-nuclei. The Bonn and Nijmegen potentials are extended and used as a phenomenological potential between ${\Lambda }^{\ast }$ and $N$. The $K$-exchange potential is also considered in the ${\Lambda }^{\ast }$ and $N$ interaction. The two-body (${\Lambda }^{\ast }N$) and three-body (${\Lambda }^{\ast }NN$) systems are solved by a variational method. It is shown that the spin and isospin of the ground states are assigned as ${\Lambda }^{\ast }N(S=1,I=1/2)$ and ${\Lambda }^{\ast }NN(S=3/2,I=0)$, respectively. The binding energies of the ${\Lambda }^{\ast }$-hypernuclei are discussed in comparison with experiment.