  It is shown that statistical mechanics is applicable to quantum systems with
finite numbers of particles, such as complex atoms, atomic clusters, etc.,
where the residual two-body interaction is sufficiently strong. This
interaction mixes the unperturbed shell-model basis states and produces
``chaotic'' many-body eigenstates. As a result, an interaction-induced
equilibrium emerges in the system, and temperature can be introduced. However,
the interaction between the particles and their finite number can lead to
prominent deviations of the equilibrium occupation numbers distribution from
the Fermi-Dirac shape. For example, this takes place in the cerium atom with
four valence electrons, which was used to compare the theory with realistic
numerical calculations.
