We study the electric Helmholtz equation \(\Delta u + Vu + \lambda u =f\) and show that, for certain potentials, the solution u given by the limited absorption principle obeys a Sommerfeld radiation condition. We use a non-spherical approach based on the solution K of the eikonal equation \(|\nabla K|^2=1 + \frac{p}{\lambda }\) to improve previous results in that area and extend them to long-range potentials which decay like \(|x|^{-2-\alpha }\) at infinity, with \(\alpha > 0\) .
