  Particle scattering and vacuum instability in a constant inhomogeneous
electric field of particular peak configuration that consists of two
(exponentially increasing and exponentially decreasing) independent parts are
studied. It presents a new kind of external field where exact solutions of the
Dirac and Klein-Gordon equations can be found. We obtain and analyze in- and
out-solutions of the Dirac and Klein-Gordon equations in this configuration. By
their help we calculate probabilities of particle scattering and
characteristics of the vacuum instability. In particular, we consider in
details three configurations: a smooth peak, a sharp peak, and a strongly
asymmetric peak configuration. We find asymptotic expressions for total mean
numbers of created particles and for vacuum-to-vacuum transition probability.
We discuss a new regularization of the Klein step by the sharp peak and compare
this regularization with another one given by the Sauter potential.
