Positron Tunnelling through the Coulomb Barrier of Superheavy Nuclei

We study beams of medium-energy electrons and positrons which obey the Dirac equation and scatter from nuclei with $Z > 100.$ At small distances the potential is modelled to be that of a charged sphere. A large peak is found in the probability of positron penetration to the origin for $Z \approx 184.$ This may be understood as an example of Klein tunnelling through the Coulomb barrier: it is the analogue of the Klein Paradox for the Coulomb potential.