Stark effect of hydrogenic ions

Considering Stark-effect applications in atomic physics and especially in plasma spectroscopy, we established several formulas for spectral line intensity, energy level, and ionization rate. In particular, by means of the systematic numerical check on an intermediate formula [Eq. (36d) in the text], we show that the ionization rate may be expressed completely in terms of the energy level according to ${Γ}({n}₁,{n}₂,m,{λ})={1}{2{π}}{{∂}E({n}₁,{n}₂,m,{λ})}{{∂}{n}₂}exp[{-}K({n}₁,{n}₂,m,{λ})],$ where ${λ}={({n}₁+{n}₂+m+1)}³{F}{4{Z}³}$, and $K({n}₁,{n}₂,m,{λ})={1}{6{λ}}+ln{{{λ}}^{2{n}₂+m+1}{n}₂!({n}₂+m)!}{2{π}}+3({n}₂{-}{n}₁){-}1/6{∫}{0}^{{λ}}[{n}³{{∂}E({n}₁,{n}₂,m,{{λ}}^{{'}})}{{∂}{n}₂}{-}1+6(2{n}₂+m+1){{λ}}^{{'}}]{d{{λ}}^{{'}}}{{{λ}}^{{'}2}}.$ The two factors on the right-hand side of (i) are interpreted, respectively, as the atomic-electron-collision frequency and transmission coefficient through the potential barrier created by the electric field F. By using the ninth-order perturbation series for resonance energy E(n₁,n₂,m,λ) it is found that (i) is in fairly good agreement with the most recent numerical solutions of the Schr\"odinger equation. A discussion follows in connection with other analytical and empirical formulas.