The determination of fragment particle number distributions in
microscopic systems is a fundamental problem. It requires a proper quantum
mechanical treatment accounting for indistinguishability of identical particles.
The results also depend on the predictive power of the many-body dynamical
theory used to describe the evolution of the system. The widely used timedependent
Hartree-Fock (TDHF) mean-field approximation can describe quasielastic
transfer probabilities, but it underpredicts the variance of the fragment
particle number distributions in more violent reactions such as deep-inelastic collisions.
The latter require beyond mean-field fluctuations which are described,
e.g., within the time-dependent random-phase approximation (TDRPA). Applications
of the TDHF formalism and its extension including pairing correlations
at the BCS level, as well as TDRPA calculations are presented in the nuclear
physics context. Examples include transfer reactions and fission. Numerical
aspects are emphasised.
Keywords: transfer reactions, mass and charge distributions, particle number projection
technique, Time-Dependent Hartree-Fock theory, Time-Dependent Random Phase Approximation
