  We examine the influence of the Pauli exclusion principle on the scattering
properties of composite bosons (cobosons) made of two fermions, such as the
exciton quasiparticle. The scattering process incorporates boson-phonon
interactions that arise due to lattice vibrations. Composite boson scattering
rates increase with the entanglement between the two fermionic constituents,
which comes with a larger number of available single-fermion states. An
important role is played by probabilities associated with accommodating an
incoming boson among the remaining unoccupied Schmidt modes in the initial
composite system. While due attention is given to bi-fermion bosons, the
methodology is applicable to any composite boson made up of smaller boson
fragments. Due to super-bunching in a system of multiple boson condensates such
as bi-bosons, there is enhanced scattering associated with bosons occupying
macroscopically occupied Schmidt modes, in contrast to the system of bi-fermion
pairs.
