  We present a new exactly solvable case in strong-field QED with
one-dimensional step potential (x-step). The corresponding x-step is given by
an analytic asymmetric with respect to the axis x reflection function. The step
can be considered as a certain analytic "deformation" of the symmetric Sauter
field. Moreover, it can be treated as a new regularization of the Klein step
field. We study the vacuum instability caused by this x-step in the framework
of a nonperturbative approach to strong-field QED. Exact solutions of the Dirac
equation used in the corresponding nonperturbative calculations, are
represented in the form of stationary plane waves with special left and right
asymptotics and identified as components of initial and final wave packets of
particles. We show that in spite of the fact that the symmetry with respect to
positive and negative bands of energies is broken, distribution of created
pairs and other physical quantities can be expressed via elementary functions.
We consider the processes of transmission and reflection in the ranges of the
stable vacuum and study physical quantities specifying the vacuum instability.
We find the differential mean numbers of electron-positron pairs created from
the vacuum, the components of current density and energy-momentum tensor of the
created electrons and positrons leaving the area of the strong field under
consideration. Besides, we study the particular case of the particle creation
due to a weakly inhomogeneous electric field and obtain explicitly the total
number, the current density and energy-momentum tensor of created particles.
Unlike the symmetric case of the Sauter field the asymmetric form of the field
under consideration causes the energy density and longitudinal pressure of
created electrons to be not equal to the energy density and longitudinal
pressure of created positrons.
