  We estimate locations of the regions of the percolation and of the
non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse
temperature, for interacted particle systems in finite dimension Euclidean
spaces. Our results about the percolation and about the non-percolation are
obtained under different assumptions. The intersection of two groups of the
assumptions reduces the results to two dimension Euclidean space, $\R^2$, and
to a potential function of the interactions having a hard core.
  The technics for the percolation proof is based on a contour method which is
applied to a discretization of the Euclidean space. The technics for the
non-percolation proof is based on the coupling of the Gibbs field with a
branching process.
