Critical charge in quantum electrodynamics

The critical nuclear charge Z cr and the critical distance R cr in the system of two colliding heavy nuclei—they are defined as those at which the ground-state level of the electron spectrum descends to the boundary of the lower continuum, with the result that beyond them (that is, for Z>Z cr or R<R cr) spontaneous positron production from a vacuum becomes possible—are important parameters in the quantum electrodynamics of ultrastrong Coulomb fields. Various methods for calculating Z cr and R cr are considered, along with the dependence of these quantities on the screening of the Coulomb field of a nucleus by the electron shell of the atom, on an external magnetic field, on the particle mass and spin, and on some other parameters of relevance. The effective-potential method for the Dirac equation and the application of the Wentzel-Kramers-Brillouin method to the Coulomb field for Z>137 and to the two-body Salpeter equation for the quark-antiquark system are discussed. Some technical details in the procedure for calculating the critical distance R cr in the relativistic problem of two Coulomb centers are described.

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