  We report collisional broadening of the E3 excitonic resonances in optical
absorption spectra of PbS nanocrystallites of widely varying sizes.
Significance of the underlying extended band structure of bulk solids to
understand the physics of exciton scattering in semiconductor nanocrystallites
of this size range is discussed. We propose an empirical notion of 'effective
Bohr exciton radius' as a direct consequence of significant departure from
usual static screening limits of coulomb interactions of 'hot' excitons in the
region of strong dispersion at energies much above the fundamental band gap.
Temperature variation of excitonic resonance reveals how non-phonon energy
relaxation processes affects the collisional broadening of E3 resonance over
this size range. We argue that ballistic transport of hot excitons can suppress
exciton-exciton scattering necessary for photo-induced impact ionization in
very small quantum dots. This evidently indicates that impact ionization of hot
excitons may be efficient only inside an intermediate nanoscale 'size window'.
