New Qualitative Results of the Atomic Theory

The polarizability alpha of many atoms and positive ions is related to their energy gap Delta and valence m by the expression alpha Delta(2) congruent to m (in atomic units). The parameter Delta 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 alpha for ions of the types C++, Al++, Si++ and Si+++, P+++, As+++ has been suggested based on the approximate relation alpha congruent to (2/3 < r(2)>(0))(2)/m with the parameter < r(2)>(0) expressed in terms of the valence m, the charge number q of the atomic or ionic residue, and the ionization potential J(q)=q(2)/2v(s)(2) as < r(2)>(0)=m/2q(2)nu(2)(s)(1+5 nu(2)(s)). The hydrogen dependence of < r(2)>(0) on the parameter nu(s) has been derived by analytical continuation from the integer values nu(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.