  Despite the great variation in the light curves of Gamma Ray Burst (GRB)
prompt emission, their spectral energy distribution is generally curved and
broadly peaked. In particular, their spectral evolution is well described by
the hardness-intensity correlation during a single pulse decay phase, when the
SED peak height S_p decreases as its peak energy E_p decreases. We propose an
acceleration scenario, based on electrostatic acceleration, to interpret the
E_p distribution peak at ~ 0.25 MeV. We show that during the decay phase of
individual pulses in the long GRB light curve, the adiabatic expansion losses
likely dominate the synchrotron cooling effects. The energy loss as due to
adiabatic expansion can also be used to describe the spectral evolution
observed during their decay phase. The spectral evolution predicted by our
scenario is consistent with that observed in single pulses of long BATSE GRBs.
