  We establish precise asymptotics near zero of the integrated density of
states for the random Schr\"{o}dinger operators $(-\Delta)^{\alpha/2} +
V^{\omega}$ in $L^2(\mathbb R^d)$ for the full range of $\alpha\in(0,2]$ and a
fairly large class of random nonnegative alloy-type potentials $V^{\omega}$.
The IDS exhibits the Lifschitz tail singularity. We prove the existence of the
limit $$\lim_{s\to 0} s^{d/\alpha}\ln\ell([0,s]) = -C
\left(\lambda_d^{(\alpha)}\right)^{d/\alpha},$$ with $C \in (0,\infty]$. The
constant $C$ is is finite if and only if the common distribution of the lattice
random variables charges $\left\{0\right\}$. In this case, the constant $C$ is
expressed explicitly in terms of such a probability. In the limit formula,
$\lambda_d^{(\alpha)}$ denotes the Dirichlet ground-state eigenvalue of the
operator $(-\Delta)^{\alpha/2}$ in the unit ball in $\mathbb R^d.$
