We present the relativistic version of the imaginary time method (ITM). The
ionization probability w of the bound state under the action of electric a
nd magnetic fields (for the case when the binding energy E-b is comparable
with mc(2)) has been calculated using the ITM. The formulae obtained cover
both the ionization of nonrelativistic bound systems (atoms, ions) and the
case of E-b = 2mc(2), when w is compared with the probability of electron-p
ositron pair production from vacuum in a strong held. (C) 1998 Published by
Elsevier Science B.V.