This article considers the scattering of particles off complex, central-field potentials. Starting from the Schrödinger radial-equation, we find that the partial-wave -element can be decomposed as a sum of two contributions, , due to the real and imaginary parts of the potential. We obtain element as the asymptotical limit of a single, ordinary, first-order, nonlinear, differential equation. This equation is only associated to the imaginary part of the potential. We apply the procedure, combined with the semiclassical uniform WKB method, to the scattering of and systems.