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

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