  Given a self-adjoint operator H, a self-adjoint trace class operator V and a
fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using
limiting absorption principle an explicit set of full Lebesgue measure is
defined such that for all points of this set the wave and the scattering
matrices can be defined and constructed unambiguously. Many well-known
properties of the wave and scattering matrices and operators are proved,
including the stationary formula for the scattering matrix. This new abstract
scattering theory allows to prove that for any trace class perturbations of
arbitrary self-adjoint operators the singular part of the spectral shift
function is an almost everywhere integer-valued function.
