Effect of fermionic components on trion–electron scattering

To test the validity of replacing a composite fermion by an elementary fermion,we calculate the transition rate from a statemade of one free electron and one trion to a similar electron–trion pair, through the time evolution of such a pair induced by Coulomb interaction between elementary fermions. It is convenient to describe trion as one electron interacting with one exciton. This allows us to use the tools we have developed in the new composite-exciton many-body theory. The trion–electron scattering contains a direct channel in which ‘‘in’’ and ‘‘out’’ trions aremadewith the same fermions, and an exchange channel in which the ‘‘in’’ free electron becomes one of the ‘‘out’’ trion components. As expected, momenta are conserved in these two channels. The direct scattering is found to read as the bare Coulomb potential between elementary particles multiplied by a form factor which depends on the ‘‘in’’ and ‘‘out’’ trion relative motion indices η and η, this factor reducing to δηη′ in the zero momentum transfer limit. In this direct channel, the trion at large distance reacts as an elementary particle, its composite nature showing up at large momentum transfer. In contrast, the fact that the trion is not elementary does affect the exchange channel for all momentum transfers. We thus conclude that a 3-component fermion behaves as an elementary fermion for direct processes in the small momentum transfer limit only. © 2008 Elsevier Ltd. All rights reserved.