[en] Exact expressions for the amplitudes for scattering of a particle by a complex nucleus are written down. It is then shown that, with a particular weight function, the scattering amplitude can be averaged over energy by going to a complex energy, i. e., [S (E)]_AV = S(E + iI), where I is the interval averaged over. The average amplitude is then expressed in terms of a perturbation expansion. In perturbation theory of the first kind, expansion in powers of the nucleus is carried out. In the second kind of perturbation theory, all particles are treated symmetrically and all but the average effects of the interactions are treated as perturbations. This allows one to relate the parameters of the optical potential back to nucleon-nucleon forces. It is shown that these expansions are, in general, convergent, due to the fact that the excitation into which a given excitation decays has a longer life-time than the original one. Reprint of a paper published in 'Annals of physics', vol 6, N. 3, mar 1959, p. 209-229