Majorana dr Ettore: Search for a general expression of Rydberg corrections, valid for neutral atoms or positive ions

Abstract

It is an application, the Author says, of the statistical method devised by Fermi. In the interior of an atom with number Z, n times ionized, the potential can be put in the form

$$ V = \frac{{Ze}} {r}\varphi (x) + C, $$

where x is the distance measured in units(**)

$$ \mu = 0.47Z^{ - \tfrac{1} {3}} \left( {\frac{{Z - n}} {{Z - n - 1}}} \right)^{\tfrac{2} {3}} 10^{ - 8} cm, $$

ϕ obeys a well known differential equation and the boundary conditions

$$ \varphi (0) = 1,{\text{ }} - x_0 \varphi '(x_0 ) = \frac{{n + 1}} {Z}{\text{ }}being{\text{ }}\varphi (x_0 ) = 0, $$

and C, which is the potential at the boundary of the ion, has the value

$$ C = \frac{{(n + 1)e}} {{\mu x_0 }} \cdot $$

Talk given at the 22nd General Meeting of the Italian Physical Society, Rome, 29 December 1928. Translated from “Il Nuovo Cimento”, vol. 6 (1929) XIV–XVI, by F. Guerra and N. Robotti.

Note that in the original text of “Il Nuovo Cimento” it is erroneously printed 0.47z ^{− 1/3} instead of 0.47Z ^{− 1/3}. (Note of the Editor.)