  We present a theory of highly excited interacting carriers confined in a
semiconductor nanostructure, incorporating Auger coupling between excited
states with different number of excitations. The Coulomb matrix elements
connecting exciton, bi-exciton and tri-exciton complexes are derived and an
intuitive picture of breaking neutral multi-exction complexes into positively
and negatively charged multi-exciton complexes is given. The general approach
is illustrated by analyzing the coupling of biexciton and exciton in CdSe
spherical nanocrystals. The electron and hole states are computed using
atomistic $sp^3d^5s^*$ tight binding Hamiltonian including an effective crystal
field splitting and surface passivation. For each number of electron-hole pairs
the many-body spectrum is computed in the configuration-interaction approach.
The low-energy correlated biexciton levels are broken into charged complexes: a
hole and a negatively charged trion and an electron and a positively charged
trion. Out of a highly excited exciton spectrum a subspace coupled to
bi-exciton levels via Auger processes is identified. The interaction between
correlated bi-exciton and exciton states is treated using exact diagonalization
techniques. This allows to extract the spectral function of the biexciton and
relate its characteristic width and amplitude to the characteristic amplitude
and timescale of the coherent time evolution of the coupled system. It is shown
that this process can be described by the Fermi's Golden Rule only if a fast
relaxation of the excitonic subsystem is accounted for.
