  We use a many-body, atomistic empirical pseudopotential approach to predict
the multi-exciton emission spectrum of a lens shaped InAs/GaAs self-assembled
quantum dot. We discuss the effects of (i) The direct Coulomb energies,
including the differences of electron and hole wavefunctions, (ii) the exchange
Coulomb energies and (iii) correlation energies given by a configuration
interaction calculation. Emission from the groundstate of the $N$ exciton
system to the $N-1$ exciton system involving $e_0\to h_0$ and $e_1\to h_1$
recombinations are discussed. A comparison with a simpler single-band,
effective mass approach is presented.
