  We report on a multiband microscopic theory of many-exciton complexes in
self-assembled quantum dots. The single particle states are obtained by three
methods: single-band effective-mass approximation, the multiband $k\cdot p$
method, and the tight-binding method. The electronic structure calculations are
coupled with strain calculations via Bir-Pikus Hamiltonian. The many-body wave
functions of $N$ electrons and $N$ valence holes are expanded in the basis of
Slater determinants. The Coulomb matrix elements are evaluated using statically
screened interaction for the three different sets of single particle states and
the correlated $N$-exciton states are obtained by the configuration interaction
method. The theory is applied to the excitonic recombination spectrum in
InAs/GaAs self-assembled quantum dots. The results of the single-band
effective-mass approximation are successfully compared with those obtained by
using the of $k\cdot p$ and tight-binding methods.
