Klein Tunnelling and the Klein Paradox

Details Klein Tunnelling and the Klein Paradox Klein Tunnelling and the Klein Paradox

1998-06-15

arxiv.org/abs/quant-ph/9806052v1

Int.J.Mod.Phys. A14 (1999) 631-644

Physics

Quantum Physics

17 pages

Scientific paper

10.1142/S0217751X99000312

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 a property of relativistic wave equations, not necessarily connected to particle emission. The Coulomb potential is investigated in this context: it is shown that a heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly, it is expected that as $Z$ increases the Coulomb barrier will become increasingly transparent to positrons. This is an example of Klein tunnelling.

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