Theory of Radiative-Stark Mixing

The theory of Stark mixing $n\ell-n\ell'$ transitions in atomic hydrogen $H(n\ell)$ induced by ion impact has been exactly solved analytically [1] by considering the full array of $\ell$-changing transitions only within the $n$-shell. We now incorporate the effect of radiative transitions $n\ell-n'\ell\pm1$. By considering the rates of radiative decay and Stark mixing, the region where radiative decay becomes competitive with Stark mixing can be identified. The Stark frequency $(s^{-1})$ is $\nu_S \sim v\sigma_{\ell\ell'}N^+\sim n^3/\tilde{v}$ where $N^+$ is the concentration of ions and $\tilde{v}$ is ratio of ion velocity and average orbital electron velocity. The radiative frequency $(s^{-1})$ is $A_{n\ell}=1.071\times10^{11} n^{-3}(\ell+1/2)^{-2}$. For typical laboratory conditions $N^+\sim 10^8 cm^{-3}$ and $\tilde{v}\sim 1$ the two frequencies become comparable for $n\approx 17$. In this paper, we present a phenomenological approach to the theory of Stark mixing with the radiative coupling incorporated. We call this coupled process Radiative-Stark mixing to differentiate from pure Stark mixing. \begin{thebibliography}{99} \bibitem{1} D.~Vrinceanu and M.~R.~Flannery, Phys. Rev. A, {\bf 63}, 032701 (2001) \end{thebibliography}