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Classical calculation of radiative decay rates of hydrogenic Stark states
Journal of Physics B: Atomic, Molecular and Optical Physics ( IF 1.6 ) Pub Date : 2021-04-26 , DOI: 10.1088/1361-6455/abe0a5
Michael Horbatsch , Marko Horbatsch

The Kepler–Coulomb problem is solved in parabolic coordinates and the Larmor radiation problem is analyzed to complement a previous study performed for the usual representation in spherical polar coordinates. The problem is then extended to include a weak electric field and a solution in terms of action-angle variables is provided. A comparison with quantum spontaneous decay rates shows that for azimuthal quantum number m = 0 states only transitions to nearby n −Δn principal quantum number states are described properly by the Wentzel–Kramers–Brillouin (WKB) quantized classical motions, but that for m > 0 reasonable results emerge for many values of Δn. A simple approximate expression for the lifetime of m ≠ 0 states emerges from the semi-classical analysis.



中文翻译:

氢斯塔克态辐射衰变率的经典计算

Kepler-Coulomb 问题在抛物线坐标系中求解,Larmor 辐射问题被分析以补充先前针对球面极坐标中的常用表示进行的研究。然后将问题扩展到包括弱电场,并提供关于动作角变量的解决方案。与量子自发衰减率的比较表明,对于方位角量子数m = 0 状态,只有到附近的nn主量子数状态的跃迁才能被 Wentzel-Kramers-Brillouin (WKB) 量子化经典运动正确描述,但对于m > 0 出现了许多 Δ n值的合理结果。生命周期的简单近似表达式m ≠ 0 状态来自半经典分析。

更新日期:2021-04-26
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