Effect of a realistic three-body force on the spectra of medium-mass hypernuclei

We adopt the Hartree-Fock (HF) method in the proton-neutron-$\Lambda$ (p-n-$\Lambda$) formalism and the nucleon-$\Lambda$ Tamm-Dancoff Approximation (N$\Lambda$ TDA) to study the energy spectra of medium-mass hypernuclei. The formalism is developed for a potential derived from effective field theories which includes explicitly the 3-body $NNN$ forces plus the $YN$ LO potential. The energy spectra of selected medium-mass hypernuclei are presented and their properties discussed. The present calculation is the first step of a project devoted to {\it ab initio} studies of hypernuclei in medium and heavy mass regions. This may provide a guide for a better understanding of the $YN$ interactions at momentum scales not accessible in few-body hypernuclei.