Resonances in positron scattering on a supercritical nucleus and spontaneous production of $e^{+}{e}^{-}$ pairs

Abstract

We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase ${\delta }_{\varkappa }$ and its dependence on the energy $\epsilon$ of the diving electronic level, for which we give both exact and approximate formulas. The Coulomb potential $Z\alpha /r$ is rounded to the constant $Z\alpha /R$ for $r<R$. We confirm the resonant behavior of ${\delta }_{\varkappa }$ that we investigate in details. In addition to solving the Dirac equation for an electron, we solve it for a positron, in the field of the same nucleus. This clarifies the interpretation of the resonances. Our results are compared with claims made in previous works.

18 pages, 3 figures, 1 table

References in corpus (3)

• Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
• Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene
• Electron-positron pair creation in low-energy collisions of heavy bare nuclei

Cited by in corpus (10)

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• How to access QED at supercritical Coulomb field
• Electron-positron pair production in slow collisions of heavy nuclei beyond the monopole approximation
• Electron-positron vacuum instability in strong electric fields. Relativistic semiclassical approach
• Ground state of superheavy elements with $120\le Z\le 170$: systematic study of the electron-correlation, Breit, and QED effects
• Spontaneous vacuum decay in low-energy collisions of heavy nuclei beyond the monopole approximation
• Angular and energy distributions of positrons created in subcritical and supercritical slow collisions of heavy nuclei
• Three-dimensional calculations of positron creation in supercritical collisions of heavy nuclei
• On the resonances near the continua boundaries of the Dirac equation with a short-range interaction
• Positron supercritical resonances and spontaneous positron creation in slow collisions of heavy nuclei