Rules of correspondence in atomic physics

The Smirnov method of analytic continuation (B.M. Smirnov, Sov. Phys. JETP 20, 345 (1964)) has been justified and developed for atomic physics. It has been shown that the polarizability of alkali atoms α, their van der Waals interaction constant C 6, and the oscillator strength of the transition to the first P state f 01 are related to the parameter 〈r 2〉 and gap in the spectrum \( \frac{3}{2}\frac{f}{\Delta } \approx \frac{3}{2}\alpha \Delta \approx {\left( {3{C_6}\Delta } \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}}} \approx \left\langle {{r^2}} \right\rangle \). The average square of the coordinate of the valence electron 〈r 2〉 in the first approximation has a hydrogen dependence \( {J_1} = \frac{1}{{2{v^2}}}.\) on the filling factor ν, which is defined in terms of the first ionization potential: xxxxxxxxx