  The nonproportional response and related energy resolution of
LaBr$_3$:Ce$^3+$ scintillation crystals doped with different concentrations of
cerium were studied between 80K and 450K. For Ce$^3+$ concentration of 5% and
30%, LaBr$_3$ showed best proportionality and energy resolution at 80K. For
LaBr$_3$:0.2%Ce$^3+$ the best energy resolution and the lowest degree of
nonproportional response were instead observed around room temperature. The
experimental results were analyzed in terms of charge carrier mobility and
using theory of carrier transport in wide band gap semiconductors. We found
that scattering of carriers by both lattice and impurity are the key processes
determining the particular temperature dependence of carrier mobility and
ultimately the scintillation nonproportionality. The calculated maximum of the
LaBr$_3$:0.2%Ce$^3+$ carrier mobility corresponds well with the experimentally
observed minima of its degree of nonproportionality, when assuming about 100ppm
ionized impurity concentration.
