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.
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