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

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

2007-06-15

arxiv.org/abs/0706.2266v1

Phys. Rev. A 76, 042104 (2007)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.76.042104

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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