  The prompt emission from GRBs is the brightest electromagnetic emission known
yet it's origin is not understood. The flux density of individual prompt pulses
of a GRB can be represented by an analytical expression derived assuming the
emission is from a thin, ultra-relativistically expanding, uniform, spherical
shell over a finite range of radii. We present the results of fitting this
analytical expression to the lightcurves from the four standard Swift BAT
energy bands and two standard Swift XRT energy bands of 12 bursts. The
expression includes the High Latitude Emission (HLE) component and the fits
provide a rigourous demonstration that the HLE can explain the Rapid Decay
Phase (RDP) of the prompt emission. The model also accommodates some aspects of
energy-dependent lag and energy-dependent pulse width, but there are features
in the data which are not well represented. Some pulses have a hard, narrow
peak which is not well fitted or a rise and decay which is faster than expected
using the standard indices derived assuming synchrotron emission from internal
shocks, although it might be possible to accommodate these features using a
different emission mechanism within the same overall framework. The luminosity
of pulses is correlated with the peak energy of the pulse spectrum, Lf ~
(Epeak(1+z))^1.8, and anti-correlated with the time since ejection of the
pulse, Lf ~ (Tf/(1 + z))^-2.0.
