  The effect of the temporal pulse shape of intense pulses on the momentum
distribution of $e^+e^-$ pairs is studied using the quantum kinetic equation.
Two closely resembling temporal envelopes namely, Gaussian and Sauter, keeping
all the other pulse parameters the same, are considered to this end. Contrary
to the common perception which can be gauged from the interchangeable use of
these temporal profiles, the longitudinal momentum spectrum of the pairs
created by the two pulses is found to differ significantly in all the temporal
regimes. For the pulses having a few cycles of oscillations, the temporal
profile of the pulse is revealed in the oscillatory interference pattern riding
over the otherwise smooth longitudinal momentum spectrum at asymptotic times.
The onset of the oscillation due to the quantum interference of reflection
amplitudes from the scattering potential due to the pulses having a temporal
structure of multiple barriers takes place for few-cycle oscillations for the
Gaussian pulse than that for the Sauter pulse. Furthermore, the oscillation
amplitude for the same number of oscillations within the pulse duration is
larger for the Gaussian pulse. The presence of the carrier-envelope phase and
the frequency chirping is found to magnify these differences. In the absence of
any appreciable interference effect for the pulses having less than five
oscillations, the longitudinal momentum spectrum has a higher peak value for
the Sauter pulse at asymptotic times. On the hand, before the transient stage
of evolution, the peak of the spectrum shows the opposite trend.
