  We develop the variational/parquet diagram approach to the structure of
nuclear systems with strongly state-dependent interactions. For that purpose,
we combine ideas of the general Jastrow-Feenberg variational method and the
local parquet-diagram theory for bosons with state-dependent interactions (R.
A. Smith and A. D. Jackson, Nucl. Phys. {\bf 476}, 448 (1988)). The most
tedious aspect of variational approaches, namely the symmetrization of an
operator dependent variational wave function, is thereby avoided. We carry out
calculations for neutron matter interacting via the Reid and Argonne $v_6$
models of the nucleon-nucleon interaction. While the equation of state is a
rather robust quantity that comes out reasonably well even in very simplistic
approaches, we show that effective interactions, which are the essential input
for calculating dynamic properties, depend sensitively on the quality of the
treatment of the many-body problem.
