Particle production at a finite potential step: Transition from Euler-Heisenberg to Klein paradox

Abstract

Spontaneous pair production for spin-$1/2$ and spin-$0$ particles is explored in a quantitative manner for a static $\tanh$-Sauter potential step (SS), evaluating the imaginary part of the effective action. We provide finite-valued per unit-surface results, including the exact sharp-edge Klein paradox (KP) limit, which is the upper bound to pair production. At the vacuum instability threshold the spin-$0$ particle production can surpass that for the spin-$1/2$ rate. Presenting the effect of two opposite sign Sauter potential steps creating a well we show that spin-$0$ pair production, contrary to the case of spin-$1/2$, requires a smoothly sloped wall.

10 pages, 6 figures

References in corpus (8)

• Dynamically assisted Schwinger mechanism
• The Schwinger mechanism revisited
• How to access QED at supercritical Coulomb field
• Universal Charge-Radius Relation for Subatomic and Astrophysical Compact Objects
• Vacuum Decay Time in Strong External Fields
• Exact Pair Production Rate for a Smooth Potential Step
• Acceleration and vacuum temperature
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Cited by in corpus (3)

• Vortex Structures and Momentum Sharing in Dynamic Sauter-Schwinger Process
• Emergence of periodic in magnetic moment effective QED action
• Dynamically assisted pair production in subcritical potential step and particle--anti-particle interpretations