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The prompt emission from gamma‐ray burst is the brightest electromagnetic emission known, yet its 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, ultrarelativistically expanding, uniform, spherical shell over a finite range of radii. We present the results of fitting this analytical expression to the light curves from the four standard  Swift  Burst Alert Telescope energy bands and two standard  Swift  X‐ray Telescope energy bands of 12 bursts. The expression includes the high latitude emission (HLE) component and the fits provide a rigorous demonstration that the HLE can explain the rapid decay phase 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 are 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,   L f  ∝[ E  peak (1 + z )] 1.8  , and anticorrelated with the time since ejection of the pulse,   L f  ∝[ T f  /(1 + z )] −2.0  .

The spectral–temporal properties of the prompt pulses and rapid decay phase of gamma‐ray bursts