  Given an infinite countable discrete amenable group $\Gamma$, we construct
explicitly sharply weak mixing nonsingular Poisson $\Gamma$-actions of each
Krieger's type: $III_\lambda$, for $\lambda\in[0,1]$, and $II_\infty$. The
result is new even for $\Gamma=\Bbb Z$. As these Poisson suspension actions are
over very special dissipative base, we obtain also new examples of sharply weak
mixing nonsingular Bernoulli $\Gamma$-actions and IDPFT systems of each
possible Krieger's type.
