New qualitative results of the atomic theory

Abstract

The polarizability α of many atoms and positive ions is related to their energy gap Δ and valence m by the expression αΔ² ≅ m (in atomic units). The parameter Δ corresponds to a dipolar transition from the ground state to the first excited P state without a change in the principal quantum number n. This relation holds for univalent (m = 1) Na, K, Rb, Cs, Fr and bivalent (m = 2) Mg, Ca, Zn, Sr, Cd, Ba, Yb, Hg atoms. The above relation agrees with the experiment for positive ions Mg⁺ and Ca⁺ (m = 1) and Al⁺ and Ga⁺ (m = 2). The polarizability has been found for atoms and ions of the type Zn⁺, In⁺, Tl⁺, for which experimental data are unavailable. A method of calculating α for ions of the types C⁺⁺, Al⁺⁺, Si⁺⁺ and Si⁺⁺⁺, P⁺⁺⁺, As⁺⁺⁺ has been suggested based on the approximate relation α ≅(2/3〈r²〉₀)²/m with the parameter 〈r²〉₀ expressed in terms of the valence m, the charge number q of the atomic or ionic residue, and the ionization potential ${J_q} = \frac{{{q^2}}}{{2v_s^2}}$ as ${\left\langle {{r^2}} \right\rangle _0} = \frac{m}{{2{q^2}}}\nu _s^2\left( {1 + 5\nu _s^2} \right)$. The hydrogen dependence of 〈r²〉₀ on the parameter ν_s has been derived by analytical continuation from the integer values ν_s = 1 and 2. A variational estimate of the van der Waals constant characterizing the interaction of two spherically symmetric atoms at large distances has been given.