dorsal/arxiv
View SchemaHistory and Physics of the Klein Paradox
| Authors | A Calogeracos, N Dombey |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9905076 |
| URL | https://arxiv.org/abs/quant-ph/9905076 |
| DOI | 10.1080/001075199181387 |
| Journal | Contemp.Phys. 40 (1999) 313-321 |
Abstract
The early papers by Klein, Sauter and Hund which investigate scattering off a high step potential in the context of the Dirac equation are discussed to derive the 'paradox' first obtained by Klein. The explanation of this effect in terms of electron-positron production is reassessed. It is shown that a potential well or barrier in the Dirac equation can become supercritical and emit positrons or electrons spontaneously if the potential is strong enough. If the well or barrier is wide enough, a seemingly constant current is emitted. This phenomenon is transient whereas the tunnelling first calculated by Klein is time-independent. It is shown that tunnelling without exponential suppression occurs when an electron is incident on a high barrier, even when the barrier is not high enough to radiate. Klein tunnelling is therefore a property of relativistic wave equations and is not necessarily connected to particle emission. The Coulomb potential is investigated and it is shown that a heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly, as $Z$ increases the Coulomb barrier should become increasingly transparent to positrons. This is an example of Klein tunnelling. Phenomena akin to supercritical positron emission may be studied experimentally in superfluid $^3$He
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"abstract": "The early papers by Klein, Sauter and Hund which investigate scattering off a\nhigh step potential in the context of the Dirac equation are discussed to\nderive the \u0027paradox\u0027 first obtained by Klein. The explanation of this effect in\nterms of electron-positron production is reassessed. It is shown that a\npotential well or barrier in the Dirac equation can become supercritical and\nemit positrons or electrons spontaneously if the potential is strong enough. If\nthe well or barrier is wide enough, a seemingly constant current is emitted.\nThis phenomenon is transient whereas the tunnelling first calculated by Klein\nis time-independent. It is shown that tunnelling without exponential\nsuppression occurs when an electron is incident on a high barrier, even when\nthe barrier is not high enough to radiate. Klein tunnelling is therefore a\nproperty of relativistic wave equations and is not necessarily connected to\nparticle emission. The Coulomb potential is investigated and it is shown that a\nheavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly,\nas $Z$ increases the Coulomb barrier should become increasingly transparent to\npositrons. This is an example of Klein tunnelling. Phenomena akin to\nsupercritical positron emission may be studied experimentally in superfluid\n$^3$He",
"arxiv_id": "quant-ph/9905076",
"authors": [
"A Calogeracos",
"N Dombey"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/001075199181387",
"journal_ref": "Contemp.Phys. 40 (1999) 313-321",
"title": "History and Physics of the Klein Paradox",
"url": "https://arxiv.org/abs/quant-ph/9905076"
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