  In this paper, we are concerned with the hydrodynamic limit to rarefaction
waves of the compressible Euler system for the Landau equation with Coulomb
potentials as the Knudsen number $\epsilon>0$ is vanishing. Precisely, whenever
$\epsilon>0$ is small, for the Cauchy problem on the Landau equation with
suitable initial data involving a scaling parameter $a\in [\frac{2}{3},1]$, we
construct the unique global-in-time uniform-in-$\epsilon$ solution around a
local Maxwellian whose fluid quantities are the rarefaction wave of the
corresponding Euler system. In the meantime, we establish the convergence of
solutions to the Riemann rarefaction wave uniformly away from $t=0$ at a rate
$\epsilon^{\frac{3}{5}-\frac{2}{5}a}|\ln \epsilon|$ as $\epsilon\to 0$. The
proof is based on the refined energy approach combining [19] and [32] under the
scaling transformation $(t,x)\to (\epsilon^{-a}t,\epsilon^{-a}x)$.
