  We investigate the finite-time behavior of pair production from the vacuum by
a time-dependent Sauter pulsed electric field using the spinor quantum
electrodynamics (QED). In the adiabatic basis, the one-particle distribution
function in momentum space is determined by utilizing the exact analytical
solution of the Dirac equation. By examining the temporal behavior of the
one-particle distribution function and the momentum spectrum of created pairs
in the sub-critical field limit $(E_0 = 0.2E_c)$, we observe oscillatory
patterns in the longitudinal momentum spectrum(LMS) of particles at finite
times. These oscillations arise due to quantum interference effects resulting
from the dynamical tunneling. Furthermore, we derive an approximate and
simplified analytical expression for the distribution function at finite times,
which allows us to explain the origin and behavior of these oscillations.
Additionally, we discuss the role of the vacuum polarization function and its
counter term to the oscillations in LMS vacuum excitation. We also analyse the
transverse momentum spectrum (TMS).
