Peculiarities of Pair Creation by a Peak Electric Field

Abstract

Exact, numerical, and asymptotic calculations concerning the vacuum instability by the so-called peak electric field are explored in detail. Peculiarities discussed in this article are complementary to those published recently by us in Eur. Phys. J. C, 76, p. 447 (2016), in which the effect was studied in the framework of QED with t -electric potential steps. To discuss features beyond the asymptotic regime, we present numerical details of exact and asymptotic expressions inherent to the peak field and discuss differential and total quantities. The results show wider distributions, with respect to the longitudinal momentum, as the phases k₁ and k₂ of the electric field decrease and larger distributions as the amplitude E increases. Moreover, the total density of pairs created decreases as k₁ and k₂ increase, its dependence being proportional to \( {k}_1^{-1} \) and \( {k}_2^{-1} \). The latter result is more accurate as k₁ and k₂ decrease and confirms, in particular, our asymptotic estimates obtained previously.