  We propose a method for calculating Coulomb matrix elements between exciton
and biexciton states in semiconductor nanocrystals based on the envelope
function formalism. We show that such a calculation requires proper treatment
of the Bloch parts of the carrier wave functions which, in the leading order,
leads to spin selection rules identical to those holding for optical interband
transitions. Compared to the usual (intraband) Coulomb couplings, the resulting
matrix elements are additionally scaled by the ratio of the lattice constant to
the nanocrystal radius. As a result, the Coulomb coupling between exciton and
biexciton states scale as 1/R^2. We present also some statistical estimates of
the distribution of the coupling magnitudes and energies of the coupled states
The number of biexciton states coupled to exciton states form a certain energy
range shows a power-law scaling with the ratio of the coupling magnitude to the
energy separation. We estimate also the degree of mixing between exciton and
biexciton states. The amount of biexciton admixture to exciton states at least
1 eV above the multiple exciton generation threshold can reach 80% but varies
strongly with the nanocrystal size.
