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

Threshold effects in electron-positron pair creation from the vacuum: Stabilization and longitudinal vs transverse momentum sharing