The vacuum charge, Klein tunnelling and the Klein paradox

The Klein paradox is reassessed by considering the properties of a finite s quare well or barrier in the Dirac equation. It is shown that spontaneous p ositron emission occurs for a well if the potential is strong enough. The v acuum charge and lifetime of the well are estimated. If the well is wide en ough, a seemingly constant current is emitted. These phenomena are transien t whereas the tunnelling first calculated by Klein is time independent. Kle in tunnelling is an intrinsic property of relativistic wave equations. Thes e 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.