The imaginary-time method for relativistic problems

A relativistic version of the imaginary-time method is presented. The method is used to calculate the probability w of ionization of a bound state by electric and magnetic fields of various configurations (including the case when the binding energy E _b is comparable to mc ₂). The formulas cover as limiting cases both the ionization of nonrelativistic bound systems (atoms and ions) and the case E _b =2mc ₂, when w equals the probability of electron-positron pair production from the vacuum in the presence of a strong field. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 213–218 (25 August 1997)