The conventional theory of shell-model effective interactions encounte
rs a divergence in its perturbation expansion owing to intruder states
. By enlarging the model space to eliminate the core, and, hence, all
core-polarization processes, we circumvent this problem. The perturbat
ion expansion for the effective interaction can then be reasonably exp
ressed in terms of only the Brueckner reaction matrix G in the no-core
space plus all folded diagrams. The effective interaction for A = 2 i
s simply the Brueckner G-matrix. For A > 2 exact results for the eigen
energies are obtained, if the generalized, A-nucleon G matrix can be c
onstructed. For A = 4 to 7, we approximate the A-nucleon G-matrix with
the Brueckner G-matrix. Reasonable results can be obtained by treatin
g the starting energy for the G matrix as a variable parameter to fix
the binding energy.