  We present a detailed discussion of the elastic scattering of a
supersymmetric neutralino off a nucleon or nucleus, with emphasis on the
spin--independent interaction. We carefully treat QCD effects on the squark
exchange contribution. In particular, we identify a class of terms that survive
even in the absence of mixing in both the neutralino and squark sectors; the
corresponding quark and gluon operators also appear in analyses of
deep--inelastic lepton--nucleon scattering (``twist--2 operators''), so their
hadronic matrix elements are well known. We also re--emphasize the importance
of mixing between the superpartners of left-- and right--handed quarks, and of
the contribution from the heavier scalar Higgs boson. We use our refined
calculation of the scattering amplitude to update predictions of signal rates
for cosmic relic neutralino searches with Germanium detectors. In general the
counting rate varies strongly with the values (even the signs) of model
parameters; typical results lie between a few times $10^{-4}$ and a few times
$10^{-1}$ events/(kg$\cdot$day).
