  We determine the principal term of the asymptotics of the integrated density
of states (IDS) $N(\lambda)$ for the Schr\"odinger operator with point
interactions on $\mathbf{R}^3$ as $\lambda \to -\infty$, provided that the set
of positions of the point obstacles is the Poisson configuration, and the
interaction parameters are bounded i.i.d.\ random variables. In particular, we
prove $N(\lambda) =O(|\lambda|^{-3/2})$ as $\lambda\to -\infty$. In the case
that all interaction parameters are equal to a constant, we give a more
detailed asymptotics of $N(\lambda)$, and verify the result by a numerical
method using R.
