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Finite pulse effects on $e^{+}e^{-}$ pair creation from strong electric fields

We investigate electron-positron pair creation from the vacuum in a pulsed electric background field. Employing the Sauter-type pulsed field $E(t)=E_0 {\rm sech}^2 (t/τ)$ with height $E_0$ and width $τ$, we demonstrate explicitly the interplay between the nonperturbative and perturbative aspects of pair creation in the background field. We analytically compute the number of produced pairs from the vacuum in the Sauter-type field, and the result reproduces Schwinger's nonperturbative formula in the long pulse limit (the constant field limit), while in the short pulse limit it coincides with the leading-order perturbative result. We show that two dimensionless parameters $ν= |eE_0| τ^2$ and $γ= |eE_0| τ/m_e$ characterize the importance of multiple interactions with the fields and the transition from the perturbative to the nonperturbative regime. We also find that pair creation is enhanced compared to Schwinger's formula when the field strength is relativity weak $|eE_0|/m_e^2 \lesssim 1$ and the pulse duration is relatively short $m_e τ\lesssim 1$, and reveal that the enhancement is predominantly described by the lowest order perturbation with a single photon.