Critical Charge in Quantum Electrodynamics

The critical nuclear charge Zcr and the critical distance Rcr 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 > Zcr or R < Rcr) spontaneous positron production from a vacuum becomes possible—are important parameters in the quantum electrodynamics of ultrastrong Coulomb fields. Various methods for calculating Zcr and Rcr 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 Rcr in the relativistic problem of two Coulomb centers are described. © 2001 MAIK “Nauka/Interperiodica”. Dedicated to the blessed memory of Arkadiœ Benediktovich Migdal and Mikhail Samuilovich Marinov Es war ... eine Zeit die Riesen brauchte und Riesen zeugte, Riesen an Denkkraft, Leidenschaft und Character, an Vielseitigkeit und Gelehrsamkeit. Friedrich Engels “Dialektik der Natur”1) Mighty, Immense, and Great is the Distant Astral Law ... 1)