Effects of hyperonic many-body force on $B_\Lambda$ values of hypernuclei

The stiff equation of state (EoS) giving the neutron-star mass of $2M_{\odot}$ suggests the existence of strongly repulsive many-body effect (MBE) not only in nucleon channels but also in hyperonic ones. As a specific model for MBE, the repulsive multi-pomeron exchange potential (MPP) is added to the two-body interaction together with the phenomenological three-body attraction. For various versions of the Nijmegen interaction models, the MBE parts are determined so as to reproduce the observed data of $B_\Lambda$. The mass dependence of $B_\Lambda$ values is shown to be reproduced well by adding MBE with the strong MPP repulsion assuring the stiff EoS of hyperon-mixed neutron-star matter, when $P$-state components of the adopted interaction model lead to almost vanishing contributions. The nuclear matter $\Lambda\!N$ $G$-matrix interactions are derived and used in $\Lambda$ hypernuclei on the basis of the averaged-density approximation (ADA). The $B_\Lambda$ values of hypernuclei with $9 \le A \le 59$ are analyzed in the framework of Antisymmetrized Molecular Dynamics with use of the two types of $\Lambda\!N$ $G$-matrix interactions including strong and weak MPP repulsions. The calculated values of $B_\Lambda$ reproduce the experimental data finely within a few hundred keV. The values of $B_\Lambda$ in $p$-states also can be reproduced well, when ADA is modified to be suitable also to weakly-bound $\Lambda$ states.