A microscopic calculation of reaction cross sections for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all particle-hole excitations in the target and one-nucleon pickup channels. The particle-hole states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm were described in a random-phase framework using a Skyrme functional. Reaction cross sections obtained agree very well with experimental data and predictions of a state-of-the-art fitted optical potential. Couplings between inelastic states were found to be negligible, while the pickup channels contribute significantly. The effect of resonances from higher-order channels was assessed. Elastic angular distributions were also calculated within the same method, achieving good agreement with experimental data. For the first time observed absorptions are completely accounted for by explicit channel coupling, for incident energies between 10 and 70 MeV, with consistent angular distribution results.