Relativistic version of the imaginary time method

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.