  For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function
$k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. We denote by
$dw(\mathbf{x})=\Pi_{\alpha \in R}|\langle \mathbf{x},\alpha
\rangle|^{k(\alpha)}\,d\mathbf{x}$ the associated measure in $\mathbb{R}^N$.
Let $L=-\Delta +V$, $V\geq 0$, be the Dunkl--Schr\"odinger operator on $\mathbb
R^N$. Assume that there exists $q >\max(1,\frac{\mathbf{N}}{2})$ such that $V$
belongs to the reverse H\"older class ${\rm{RH}}^{q}(dw)$. For $\lambda>0$ we
provide upper and lower estimates for the number of eigenvalues of $L$ which
are less or equal to $\lambda$. Our main tool in the Fefferman--Phong type
inequality in the rational Dunkl setting.
