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FIELDS, PARTICLES, AND NUCLEI
New qualitative results of the atomic theory
A. M. Dyugaeva,
E. V. Lebedevab a Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, Russia
b Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, Russia
Abstract:
The polarizability
$\alpha$ of many atoms and positive ions is related to their energy gap
$\Delta$ and valence
$m$ by the expression
$\alpha\Delta^2\cong m$ (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
$\alpha\cong(2/3\langle r^2\rangle_0)^2/m$ with the parameter
$\langle r^2\rangle_0$ 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 $\langle r^2\rangle_0=\frac{m}{2q^2}\nu_s^2( 1 + 5\nu _s^2)$. The hydrogen dependence of
$\langle r^2\rangle_0$ 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.
Received: 11.09.2016
Revised: 22.09.2016
DOI:
10.7868/S0370274X16210025
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