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≈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.