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Particle production at a finite potential step: transition from Euler–Heisenberg to Klein paradox

  • Regular Article - Theoretical Physics
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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.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This article is a theoretical study of the properties of relativistic wave equations, there is no experimental or simulation data associated with this work.]

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  1. Department of Physics, The University of Arizona, Tucson, AZ, 85721, USA

    Stefan Evans & Johann Rafelski

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  1. Stefan Evans
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Correspondence to Stefan Evans or Johann Rafelski.

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Communicated by Tamas Biro.

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Evans, S., Rafelski, J. Particle production at a finite potential step: transition from Euler–Heisenberg to Klein paradox. Eur. Phys. J. A 57, 341 (2021). https://doi.org/10.1140/epja/s10050-021-00654-x

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