Dynamics of neutral vacuum decay

A time-independent Hamiltonian formulation of relativistic atomic structure and scattering problems is developed in which virtual-pair creation and annihilation effects are explicitly included. The method is discussed in the context of a specific problem---the scattering of a positron by a system consisting of two electrons bound to a nucleus of charge Z. This provides the basis for a consistent treatment of spontaneous positron production that can occur when Z exceeds a critical value Zcr∼173. For Z not too much greater than Zcr the two-electron atom is stable and represents the (doubly charged) vacuum state. In the approach adopted here the one-electron state, which is unstable against spontaneous pair creation, is viewed as a resonance in the scattering of the positron by the two-electron target atom. The lifetime of the unstable state is determined, in the usual way, from a knowledge of the width of the resonance. The formal resonance theory required to carry out this analysis is developed here with the aid of an effective-potential description of the scattering problem of the type familiar from standard treatments of resonant processes in nonrelativistic atomic and nuclear reaction theories