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

Abstract

Abstract We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase $$\delta _{\varkappa }$$ δ ϰ and its dependence on the energy $$\varepsilon $$ ε of the diving electronic level, for which we give both exact and approximate formulas. The Coulomb potential $$Z\alpha /r$$ Z α / r is rounded to the constant $$Z\alpha /R$$ Z α / R for $$r < R$$ r < R . We confirm the resonant behavior of $$\delta _{\varkappa }$$ δ ϰ that we investigate in detail. 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.