https://doi.org/10.1140/epja/s10050-021-00654-x
Regular Article - Theoretical Physics
Particle production at a finite potential step: transition from Euler–Heisenberg to Klein paradox
Department of Physics, The University of Arizona, 85721, Tucson, AZ, USA
a
evanss@email.arizona.edu
b
rafelski@email.arizona.edu
Received:
8
November
2021
Accepted:
18
December
2021
Published online:
31
December
2021
Spontaneous pair production for spin-1/2 and spin-0 particles is explored in a quantitative manner for a static 
-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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
