有限势阶的粒子产生：从Euler-Heisenberg到Klein佯谬的转变
Particle production at a finite potential step: Transition from Euler-Heisenberg to Klein paradox
摘要：
自旋- $1/2$和自旋- $0$粒子的自发对产生以静态$\tanh$ -Sauter电位阶跃（SS）的定量方式进行探索，评估有效作用的虚部。我们提供了有限值每单位表面的结果，包括精确的锐边克莱因悖论（KP）的限制，这是对生产的上限。在真空不稳定性阈值处，自旋$0$粒子的产生率可以超过自旋$1/2$粒子的产生率.提出两个相反的符号索特潜在的步骤创建一个好的效果，我们表明，自旋$0$对生产，相反的情况下，自旋$1/2$，需要一个平滑的倾斜壁。
英文摘要：
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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