  Treating the production of electron and positron pairs by a strong electric
field from the vacuum as a quantum tunneling process we derive, in
semiclassical approximation, a general expression for the pair production rate
in a $z$-dependent electric field $E(z)$ pointing in the $z$-direction. We also
allow for a smoothly varying magnetic field parallel to $E(z)$. The result is
applied to a confined field $E(z)\not=0$ for $|z|\lesssim \ell $, a
semi-confined field $E(z)\not=0$ for $ z\gtrsim 0 $, and a linearly increasing
field $E(z)\sim z$. The boundary effects of the confined fields on
pair-production rates are exhibited. A simple variable change in all formulas
leads to results for electric fields depending on time rather than space.
  In addition, we discuss tunneling processes in which empty atomic bound
states are spontaneously filled by negative-energy electrons from the vacuum
under positron emission. In particular, we calculate the rate at which the
atomic levels of a bare nucleus of finite size $r_{\rm n}$ and large $Z\gg 1$
are filled by spontaneous pair creation.
