  We study the extension of our translationally invariant treatment of few-body
nuclear systems to heavier nuclei. At the same time we also introduce
state-dependent correlation operators. Our techniques are tailored to those
nuclei that can be dealt with in $LS$ coupling, which includes all nuclei up to
the shell closure at $A=40$. We study mainly $p$-shell nuclei in this paper. A
detailed comparison with other microscopic many-body approaches is made, using
a variety of schematic nuclear interactions. It is shown that our methodology
produces very good energies, and presumably also wave functions, for medium
mass nuclei.
