Microscopic description of low-energy nuclear collisions: Review and perspective

The primary goal of this lecture is a review of the microscopic approaches to nuclear reactions. Semi-phenomenological theories will not be discussed. First the Time-Dependent Hartree-Fock formalism is recalled. The effective nucleon-nucleon interactions used in TDHF calculations are discussed. Appl ications to collisions are presented in different approximation scheme, one -dimensional dynamics, approximate three-dimensional ones.... Finally two m icroscopic extensions beyond mean-field are reviewed: the variational princ ipal of Balian and Vereroni and the implementation of residual two-body int eractions in the Time-Dependent Density Matrix (TDDM) and the Extended Time -Dependent Hartree-Fock schemes (ETDHF).