Critical charge in quantum electrodynamics

The essential parameters in quantum electrodynamics of strong Coulomb fields are critical charge of the nucleus Zcr and the critical distance Rcr between two colliding heavy nuclei. At Z = Zcr or at R = Rcr the electron ground state reaches the boundary of the lower continuum and the spontaneous production of positrons from vacuum becomes possible. Different methods for calculation of Zcr and Rcr, the dependence of these quantities on the screening of the nuclear charge Z by an atomic shell, on the external magnetic field, on the mass and spin of the particle, etc. are discussed. The effective potential method for the Dirac equation and application of the WKB method to the Coulomb field at Z > 137 and to the two-particle Salpeter equation for the quark-antiquark system are discussed. Some technical details of the calculation of the critical distance Rcr in the relativistic two-Coulomb-centre problem are described