类氢及碱金属原子激发态寿命的半经典计算公式

Semiclassical formula for the radiative lifetimes of excited states of the hydrogenlike and alkali metal atoms

根据对应原理,得到了类氢原子能态平均寿命半经典的计算公式τ(n,l),然后利用相对论单通道量子数亏损理论进行推广,得到用来计算考虑总角动量J的激发态寿命公式τ(n,l,l+1／2)和τ(n,l,l-1／2),利用单通道量子数亏损理论得到了碱金属原子n、l远大于1时激发态寿命的半经典公式τ(n,l)=τ0(m+M/nm/v+M)2v7l(l+1/2)/n4,其计算结果和实验数据符合的很好。

Based on the correspondence principle, a simple semiclassical formula for the radiative lifetimes r ( n, l) of hydrogen-like states is presented. By using the relativistic one-channel theory, we have obtained the radiative lifetimes τ(n,l,l + 1/2) and τ(n,l,l-1/2) of hydrogen-like states. According to the one-channel quantum defect theory, the radiative lifetimes formula τ(n,l) = τ0(m+M/nm/v+M)2v7l(l+1/2)n4 ofalkali-metal atoms is presented as the function of the main quantum number n and orbital angular momentum l.