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We consider the Dirac equation for massless particles in an external Coulomb field of vanishingly small but finite size. We show that the onset of spontaneous pair creation is signaled by the occurrence of a pole in the complex energy plane; the pole argument is directly related to the point-Coulomb pair-creation probability. We also consider spontaneous pair creation in the framework of an approximate uncoupled Dirac equation, and we discuss its connection with the description of pair creation by means of the full Dirac equation.
M. Bawin (1981) studied this question.