  Model-space effective interactions $V_{eff}$ derived from free-space
nucleon-nucleon interactions $V_{NN}$ are reviewed. We employ a double
decimation approach: first we extract a low-momentum interaction $V_{low-k}$
from $V_{NN}$ using a $T$-matrix equivalence decimation method. Then $V_{eff}$
is obtained from $V_{low-k}$ by way of a folded-diagram effective interaction
method. For decimation momentum $\Lambda \simeq 2 fm^{-1}$, the $V_{low-k}$
interactions derived from different realistic $V_{NN}$ models are nearly model
independent, and so are the resulting shell-model effective interactions. For
nucleons in a low-density nuclear medium like valence nucleons near the nuclear
surface, such effective interactions derived from free-space $V_{NN}$ are
satisfactory in reproducing experimental nuclear properties. But it is not so
for nucleons in a nuclear medium with density near or beyond nuclear matter
saturation density. In this case it may be necessary to include the effects
from Brown-Rho (BR) scaling of hadrons and/or three-nucleon forces $V_{3N}$,
effectively changing the free-space $V_{NN}$ into a density-dependent one. The
density-dependent effects from BR scaling and $V_{3N}$ are compared with those
from empirical Skyrme effective interactions.
