Pre-equilibrium nuclear reactions occur on a time scale intermediate between the fast direct reactions and the slow evaporation from the compound nucleus. With increasing projectile energy, the pre-equilibrium reaction component becomes more and more visible in the reaction spectra and angular distributions, being of special importance in applications using energetic beams of nucleons such as in proton radiotherapy or accelerator-driven-systems (ADS). Although these reactions have been studied for over 50 years, due to their complexity, it has not yet been possible to obtain a fundamental description of them. The only quantum models of these reactions were proposed 30 years ago and are limited to processes in which at most one particle is emitted. They also make use of statistical hypotheses and approximations that are, at best, difficult to justify. Our objectives concentrate on an analysis of the first two steps of a pre-equilibrium reaction and on the extension of the quantum formalism to include up to two particles in the continuum afte the first interaction and up to three after the second interaction, the maximum number of continuum particles physically permitted. We also intend to study in detail the coherence / incoherence between pairs of excitations that lead to the same state after the second collision.
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