These lecture notes are addressed to PhD student and/or researchers who want
a general overview of microscopic approaches based on mean-field and applied to
nuclear dynamics. Our goal is to provide a good description of low energy
heavy-ion collisions. We present both formal aspects and practical applications
of the time-dependent Hartree-Fock (TDHF) theory. The TDHF approach gives a
mean field dynamics of the system under the assumption that particles evolve
independently in their self-consistent average field. As an example, we study
the fusion of both spherical and deformed nuclei with TDHF. We also focus on
nucleon transfer which may occur between nuclei below the barrier. These
studies allow us to specify the range of applications of TDHF in one hand, and,
on the other hand, its intrinsic limitations: absence of tunneling below the
Coulomb barrier, missing dissipative effects and/or quantum fluctuations.
Time-dependent mean-field theories should be improved to properly account for
these effects. Several approaches, generically named "beyond TDHF" are
presented which account for instance for pairing and/or direct nucleon-nucleon
collisions. Finally we discuss recent progresses in exact ab-initio methods
based on the stochastic mean-field concept.Comment: 55 pages. Lecture given at the "Joliot Curie" school, Maubuisson,
september 17-22, 2007. A french version is available at
http://www.cenbg.in2p3.fr/heberge/EcoleJoliotCurie/coursannee/cours/CoursSimenel.pd
