Chapter

Ettore Majorana Scientific Papers

pp 21-36

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

  • Francesco GuerraAffiliated withUniversità di Roma “La Sapienza”
  • , Nadia RobottiAffiliated withUniversità di Genova

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