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

We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase delta(kappa) 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(kappa) that we investigate in detail. In addition to solving the Dirac equation for an electron, wesolve 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.