  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.
