  An elementary kinematic model for emission produced by relativistic spherical
colliding shells is studied. The case of a uniform blast-wave shell with jet
opening angle $\theta_j \gg 1/\Gamma$ is considered, where $\Gamma$ is the
Lorentz factor of the emitting shell. The shell, with comoving width $\Delta
r^\prime$, is assumed to be illuminated for a comoving time $\Delta t^\prime$
and to radiate a broken power-law $\nu L_\nu$ spectrum peaking at comoving
photon energy $\e_{pk,0}^{\prime}$. Synthetic GRB pulses are calculated, and
the relation between energy flux and internal comoving energy density is
quantified. Curvature effects dictate that the measured $\nu F_\nu$ flux at the
measured peak photon energy $\e_{pk}$ is proportional to $\e^3_{pk}$ in the
declining phase of a GRB pulse. Possible reasons for discrepancy with
observations are discussed, including adiabatic and radiative cooling processes
that extend the decay timescale, a nonuniform jet, or the formation of pulses
by external shock processes. A prediction of a correlation between prompt
emission properties and times of the optical afterglow beaming breaks is made
for a cooling model, which can be tested with Swift.

Astrophysics