Seventy years of the Klein paradox

The Klein paradox is examined. Its explanation in terms of electron–positron production is reassessed. It is shown that a potential well or barrier in the Dirac equation can produce positron or electron emission spontaneously if the potential is strong enough. The vacuum charge and lifetime of the w...

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Bibliographic Details
Published in:Physics reports 1999-07, Vol.315 (1), p.41-58
Main Authors: Dombey, N., Calogeracos, A.
Format: Article
Language:English
Subjects:
Klein paradox
Positron production
Quantum tunnelling
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Summary:The Klein paradox is examined. Its explanation in terms of electron–positron production is reassessed. It is shown that a potential well or barrier in the Dirac equation can produce positron or electron emission spontaneously if the potential is strong enough. The vacuum charge and lifetime of the well/barrier are calculated. 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. Furthermore, tunnelling without exponential suppression occurs when an electron is incident on a high barrier, even when it is not high enough to radiate. Klein tunnelling is therefore a property of relativistic wave equations and 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.
ISSN:0370-1573
1873-6270
DOI:10.1016/S0370-1573(99)00023-X