\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.