GRB spectral parameters within the fireball model
  Fireball model of the GRBs predicts generation of numerous internal shocks,
which then efficiently accelerate charged particles and generate magnetic and
electric fields. These fields are produced in the form of relatively
small-scale stochastic ensembles of waves, thus, the accelerated particles
diffuse in space due to interaction with the random waves and so emit so called
Diffusive Synchrotron Radiation (DSR) in contrast to standard synchrotron
radiation they would produce in a large-scale regular magnetic fields. In this
paper we present first results of comprehensive modeling of the GRB spectral
parameters within the fireball/internal shock concept. We have found that the
non-perturbative DSR emission mechanism in a strong random magnetic field is
consistent with observed distributions of the Band parameters and also with
cross-correlations between them; this analysis allowed to restrict GRB physical
parameters from the requirement of consistency between the model and observed
distributions.
