Resonances in positron scattering on a supercritical nucleus and spontaneous production of

We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase $$\delta _{\varkappa }$$ and its dependence on the energy $$\varepsilon $$ 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 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