  It is believed that in presence of some strong electromagnetic fields, called
overcritical, the (Dirac) vacuum becomes unstable and decays leading to a
spontaneous production of an electron-positron pair. Yet, the arguments are
based mainly on the analysis of static fields and are insufficient to explain
this phenomenon completely. Therefore, we consider time-dependent overcritical
fields and show, within the external field formulation, how spontaneous
particle creation can be defined and measured in physical processes. We prove
that the effect exists always when a strongly overcritical field is switched
on, but it becomes unstable and hence generically only approximate and
non-unique when the field is switched on and off. In the latter case, it
becomes unique and stable only in the adiabatic limit.
