  In this article we continue our analysis of Schroedinger operators with a
random potential using scattering theory. In particular the theory of Krein's
spectral shift function leads to an alternative construction of the density of
states in arbitrary dimensions. For arbitrary dimension we show existence of
the spectral shift density, which is defined as the bulk limit of the spectral
shift function per unit interaction volume. This density equals the difference
of the density of states for the free and the interaction theory. This extends
the results previously obtained by the authors in one dimension. Also we
consider the case where the interaction is concentrated near a hyperplane.
