The vacuum charge, Klein tunnelling and the Klein paradox

The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the potential is strong enough. The vacuum charge and lifetime of the well are estimated. If the well is wide enough, a seemingly constant current is emitted. These phenomena are transient whereas the tunnelling first calculated by Klein is time independent. Klein tunnelling is an intrinsic property of relativistic wave equations. These ideas could in principle be tested in positron-heavy nucleus scattering. It is also possible that they have analogues in superfluid helium. (C) 1998 Elsevier Science B.V. All rights reserved.