  Using the quantum field theory approach developed in Phys. Rev. D. 93, 045002
(2016), we consider particle scattering and vacuum instability in the so-called
L-constant electric field, which is a constant electric field confined between
two capacitor plates separated by a finite distance L. We obtain and analyze
special sets of stationary solutions of the Dirac and Klein-Gordon equations
with the L-constant electric field. Then, we represent probabilities of
particle scattering and characteristics of the vacuum instability (related to
pair creation) in terms of the introduced solutions. From exact formulas, we
derive asymptotic expressions for the differential mean numbers, for the total
mean number of created particles, and for the vacuum-to-vacuum transition
probability. Using the equivalence principle, we demonstrate that the
distributions of particles created by the L-constant electric field and the
gravitational field of a black hole have a similar thermal structure.
