  We prove the existence of solutions for the singularly perturbed
Schr\"odinger--Newton system
  {ll}
  \hbar^2 \Delta \psi - V(x) \psi + U \psi =0
  \hbar^2 \Delta U + 4\pi \gamma |\psi|^2 =0 . \hbox{in $\mathbb{R}^3$} with an
electric potential (V) that decays polynomially fast at infinity. The solution
$\psi$ concentrates, as $\hbar \to 0$, around (structurally stable) critical
points of the electric potential. As a particular case, isolated strict extrema
of (V) are allowed.
