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arXiv · 0706.2266

The role of the slope of `realistic' potential barriers in preventing relativistic tunnelling in the Klein zone

Paolo Christillin·Emilio d'Emilio
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Abstract

The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e. supporting an infinite electric field), of height U> E + m - due to the many-body nature of the Dirac equation evidentiated by the Klein paradox - has been widely studied. We exploit here the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunnelling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelenght of the particle - the latter circumstance being hardly escapable in most realistic cases.

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Paolo Christillin, Emilio d'Emilio. 2007-06-15. The role of the slope of `realistic' potential barriers in preventing relativistic tunnelling in the Klein zone. https://doi.org/10.1103/physreva.76.042104

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