Critical charge in quantum electrodynamics

The critical nuclear charge Z(cr) and the critical distance R-cr in the sys tem of two colliding heavy nuclei-they art: defined as those at which the g round-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) o r R < R-cr) spontaneous positron production from a vacuum becomes possible- are important parameters in the quantum electrodynamics of ultrastrong Coul omb fields. Various methods for calculating Z(cr) and R-cr are considered, along with the dependence of these quantities on the screening of the Coulo mb field of a nucleus by the electron shell of the atom, on an external mag netic field, on the particle mass and spin. and on some other parameters of relevance. The effective-potential method for the Dirac equation and the a pplication of the Wentzel-Kramers-Brillouin method to the Coulomb field for Z > 137 and to the two-body Salpeter equation for the quark-antiquark syst em are discussed. Some technical details in the procedure for calculating t ile critical distance R-cr in the relativistic problem of two Coulomb cente rs are described. (C) 2001 MAIK "Nauka/Interperiodica".