Klein Tunnelling and the Klein Paradox

Abstract

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.

17 pages

Cited by in corpus (30)

• Klein tunneling in graphene: optics with massless electrons
• The Woods-Saxon Potential in the Dirac Equation
• Negative Refraction Gives Rise to the Klein Paradox
• Probes of the vacuum structure of quantum fields in classical backgrounds
• Supercriticality and Transmission Resonances in the Dirac equation
• Rapid Tunneling and Percolation in the Landscape
• Low Momentum Scattering in the Dirac Equation
• Spin-dependent Klein tunneling in polariton graphene with photonic spin-orbit interaction
• Amplification of coupling for Yukawa potentials
• Scattering state of Klein-Gordon Particles by q-parameter hyperbolic Poschl-Teller potential
• An Investigation of the Bound State Solutions of the Klein-Gordon Equation for the Generalized Woods-Saxon Potential in Spin Symmetry and Pseudo-spin Symmetry Limits
• Scattering of a spinless particle by an asymmetric Hulth{é}n potential within the effective mass formalism
• Stationary phase method and delay times for relativistic and non-relativistic tunneling particles
• Resolution of the Klein Paradox
• Klein tunnelling and Hartman effect in graphene junctions with proximity exchange field
• Delay time computation for relativistic tunneling particles
• A Comparative Interpretation of the Thermodynamic Functions of a Relativistic Bound State problem proposed with an Attractive or a Repulsive Surface Effect
• Klein tunneling of two correlated bosons
• On the Role of Differentiation Parameter in a Bound State Solution of the Klein-Gordon Equation
• Positron Tunnelling through the Coulomb Barrier of Superheavy Nuclei
• Fermions in the background of mixed vector-scalar-pseudoscalar square potentials
• Study of superradiance in the Lambert-W potential barrier
• Relation between phase and dwell times for quantum tunneling of a relativistically propagating particle
• Relativistic tunneling and accelerated transmission
• Probing Klein tunneling through quantum quenches
• Klein Paradox for Optical Scattering from Excited Targets
• Confined Neutrino Oscillation
• Relativistic two-body system in (1+1)-dimensions
• Klein paradox for bound states - A puzzling phenomenon
• Dynamically assisted pair production in subcritical potential step and particle--anti-particle interpretations