  An analysis of the interaction between a spherical relativistic blast-wave
shell and a stationary cloud with a spherical cap geometry is performed
assuming that the cloud width << x, where x is the distance of the cloud from
the GRB explosion center. The interaction is divided into three phases: (1) a
collision phase with both forward and reverse shocks; (2) a penetration phase
when either the reverse shock has crossed the shell while the forward shock
continues to cross the cloud, or vice versa; and (3) an expansion phase when,
both shocks having crossed the cloud and shell, the shocked fluid expands.
Temporally evolving spectral energy distributions (SEDs) are calculated for the
problem of the interaction of a blast-wave shell with clouds that subtend large
and small angles compared with the Doppler(-cone) angle 1/Gamma_0, where
Gamma_0 is the coasting Lorentz factor. The Lorentz factor evolution of the
shell/cloud collision is treated in the adiabatic limit. Behavior of the light
curves and SEDs on, e.g., Gamma_0, shell-width parameter eta, and properties
and locations of the cloud is examined. Short timescale variability (STV) in
GRB light curves, including ~100 keV gamma-ray pulses observed with BATSE and
delayed ~1 keV X-ray flares found with Swift, can be explained by emissions
from an external shock formed by the GRB blast wave colliding with small
density inhomogeneities in the "frozen pulse" approximation (eta -> 0, where
Delta_0 + eta x/Gamma_0^2 is the blast-wave shell width), and perhaps in the
thin-shell approximation (eta ~ 1/Gamma_0), but not when eta ~ 1. If this
approximation is valid, then external shock processes could make the dominant
prompt and afterglow emissions in GRB light curves, consistent with short delay
two-step collapse models for GRBs.
