Superradiation in scattering of a Dirac particle off a point-like   nucleus with Z>137 with Z>137
  The main concepts of the recently developed approach to singular problems of quantum mechanics are extended to the Dirac particle in the Coulomb field of a point-like nucleus with its charge Z>137. The reflection and transmission coefficients, which describe, respectively, the reflection of electron by the singularity and its falling onto it, are analytically calculated, using the exact solutions of the Dirac equation. The superradiation phenomenon is found. It suppresses the widely discussed effect of spontaneous electron- positron pair creation. 
A.E.Shabad