  We have developed a model describing the non-proportional response in
scintillators based on non-thermalised carrier and phonon transport. We show
that the thermalization of e-h distributions produced in scintillators
immediately after photon absorption may take longer than the period over which
the non-proportional signal forms. The carrier and LO-phonon distributions
during this period remain non-degenerate at quasi-equilibrium temperatures far
exceeding room temperature. We solve balance equations describing the energy
exchange in a hot bipolar plasma of electrons/holes and phonons. Taking into
account dynamic screening we calculate the ambipolar diffusion coefficient at
all temperatures. The non-proportional light yields calculated for NaI are
shown to be consistent with experimental data. We discuss the implications of a
non-equilibrium model, comparing its predictions with a model based on the
transport of thermalised carriers. Finally, evidence for non-equilibrium
effects is suggested by the shape of non-proportionality curve and wide
dispersion in data observed in K-dip spectroscopy near the threshold. A
comparison of the predicted curves shows good agreement for deformation
potential value in the range 7-8 eV.
