  The effect of carrier multiplication (CM) in semiconductor nanocrystals is
systematically treated by employing an exciton scattering approach. Using
projection operators, we reduce the Coulomb coupled multi-exciton dynamics to
scattering dynamics in the space spanning both single- and bi-exciton states.
We derive a closed set of equations determining the scattering matrix elements.
This allows us to interpret CM dynamics as a series of odd-order interband
scattering events. Using the time-dependent density matrix formalism, we
provide a rigorous description of the CM dynamics induced by a finite-time pump
pulse. Within this approach, both processes of single- and bi-exciton
photogeneration and the consequent population relaxation are treated on the
same footing. This approach provides a framework for numerical calculations and
for comparisons of the quantum efficiencies associated with each process. For
applications, the limit of weak interband Coulomb coupling is considered.
Finally, we demonstrate that three previously used theoretical models can be
recovered as limiting cases of our exciton scattering model.
