Simple Formula for the Ionization Rate of Rydberg States in Static Electric Fields

With use of a full three-turning-point WKB analysis, a simple formula is obtained for the ionization rate of hydrogenic atoms. Contrary to current belief, WKB ionization rates are found to be excellent approximations to exact numerical calculations. In addition, the symmetries of the WKB solution are explored and it is shown that the resonance parameters can all be written as simple functions of three objects, ${I_{\xi }}^{\mathrm{}\left(j\right)\mathrm{}}$, ${I_{\eta }}^{\mathrm{}\left(j\right)\mathrm{}}$, and ${\theta }^{\mathrm{}\left(j\right)\mathrm{}}$, which can easily be calculated on programmable pocket calculators.