We investigate here the effect of non-magnetic impurities on the SDW s
tate of the two-dimensional electron gas at half filling. The dependen
ce on the impurity concentration (n(i)) of the relevant SDW quantities
is obtained within an Abrikosov-Gorkov-type approach. To account appr
opriately for the actual Fermi surface topology we introduce a classif
ication of the electron-impurity scattering processes. Analytic result
s are obtained for a general type scattering in the limit of low- and
high n(i)-values. In addition, the presently introduced classification
allows us to find a (rather general) class of scattering processes fo
r which analytic results can be derived for arbitrary n(i) values. The
logarithmic singularity in the density of electronic states turns out
to have a notable (qualitative and quantitative) influence on the SDW
properties in the presence of impurities. The limitations of the pres
ently employed approximations are also discussed.