The imaginary-time method for relativistic problems

Abstract

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.