Electron-positron pair production in heavy atomic nucleus collisions - I. Consistent quantum-mechanical approach

The electron-positron pair production in collisions between two heavy nuclei with near-threshold energy is considered. A consistent quantum-mechanical approach to the electron-nuclear system as a whole is developed, account being taken of the relativistic nature of the electron subsystem. The motion of the electron and nuclear subsystems is regarded as being independent in the zero-order approximation. The high-order corrections coupling of the two subsystems are accounted for effectively. The model potential of the whole system accounts for the finite size of nuclei and possible resonances of the superheavy compound nucleus formed from the original nuclei. The zero-order potential of the electron subsystem satisfies the following conditions: (1) its spectrum qualitatively coincides with the spectrum of the potential of the electric field of the compound nucleus including the diving of the bound atomic state into the negative continuum at super-critical total nuclear subsystem charge Z, (2) the "no-particle" state of the system is stationary relative to the spontaneous pair production in the zero-order approximation, (3) the perturbation is small at any internuclear separation and vanishes at asymptotically large separations. Resonance phenomena in the nuclear subsystem lead to the structurization of the positron spectrum produced. The fine structurization reflecting details of the compound nucleus spectrum is the characteristic feature of the system with a rather shallow potential pocket (< 1 MeV). The article deals with this effect.