  Momentum distributions of electron-positron pairs created from the vacuum by
an oscillating in time electric field are calculated in the framework of
quantum field theory. A pronounced enhancement of those distributions is
observed as the frequency of the electric field passes across the one-photon
threshold. Below that threshold the pairs preferentially carry a longitudinal
momentum, while above the threshold they tend to carry a transverse momentum.
Such momentum sharing has an impact on the number of produced pairs: It grows
fast with increasing the field frequency below the threshold but it saturates
at a roughly constant value above it. On the other hand, at the fixed frequency
above the one-photon threshold, the number of pairs scales quadratically with
the field strength. This typically perturbative scaling holds even for large
electric fields. Thus, the validity of the perturbation theory is extended here
to processes which result in creation of particles with substantial transverse
momenta.
