C. D. Dermer, M. Böttcher, and J. Chiang,
Astrophysical Journal Letters, 515, L49 (1999)
In the external shock model, gamma-ray burst (GRB)
emissions are produced by the energization and
deceleration of a thin relativistic blast wave that
interacts with the circumburst medium (CBM).
We study the physical properties of an analytic function
which describes temporally evolving GRB spectra in the
limit of a smooth CBM with density
n(x) ~ x-µ,
where x is the radial coordinate. The hard-to-soft
spectral evolution and the intensity-hardness correlation
of GRB peaks are reproduced. We predict that (1) GRB
peaks are aligned at high photon energies and lag at low
energies according to a simple rule; that (2) temporal
indices at the leading edge of a GRB peak display a
well-defined shift with photon energy; and that (3)
the change in the spectral index values between the
leading and trailing edges of a GRB peak decreases
at higher photon energies. The reason that GRBs are
usually detected with 
peaks in the 50 keV to several MeV range for detectors
triggering on peak flux over a fixed time interval
is shown to be a consequence of the inverse correlation
of the peak flux and the duration of the radiation emitted
by decelerating blast waves.