  Excitons, being made of two fermions, may appear from far as bosons. Their
close-to-boson character is however quite tricky to handle properly. Using our
commutation technique especially designed to deal with interacting
close-to-boson particles, we here calculate the exact expansion in Coulomb
interaction of theexciton-exciton correlations, and show that a naive effective
bosonic hamiltonian for excitons cannot produce these X-X correlations
correctly.
