Lifshitz tails for random Schrodinger operators with negative singular Poisson potential

We develop a method of asymptotic study of the integrated density of states (IDS) N(E) of a random Schrodinger operator with a non-positive (attractiv e) Poisson potential. The method is based on the periodic approximations of the potential instead of the Dirichlet-Neumann bracketing used before. Thi s allows us to derive more precise bounds for the rate of approximations of the IDS by the IDS of respective periodic operators and to obtain rigorous ly for the first time the leading term of log N(E) as E --> - infinity for the Poisson random potential with a singular single-sire (impurity) potenti al, in particular, for the screened Coulomb impurities, dislocations, etc.