Volumetto IV: 24 April 1930

Abstract

Let us consider an atom with n electrons in the ground state, which we will assume is an s level described by the eigenfunction ψ ₀ corresponding to the eigenvalue E ₀. The component of the electric moment along the z axis is given by

$$ M = - e({z_1} + {z_2} + ... + {z_n}) = - ez $$

((4.1))

with z = z ₁ +z ₂+...+z _n . An electric field of intensity E acting along the z axis induces a perturbation of the atom that depends on the potential EM = H. Assuming that the ground state is not degenerate or, more precisely, that no p levels correspond to the eigenvalue E ₀, the element M ₀₀ of the perturbation matrix certainly vanishes. Consequently, for weak fields the variation of the eigenvalue is given by the second-order formula

$$ \delta {E_0} = \sum\limits_1^\infty {\frac{{{{\left| {{M_{0k}}} \right|}^2}}}{{{E^0} - {E_k}}}} = \sum\limits_1^\infty {{e^2}} {E^2}\frac{{{{\left| {{z_k}} \right|}^2}}}{{{E^0} - {E_k}}} $$

((4.2))

where

$$ z\psi 0 = \sum\limits_k {{z_k}} $$

((4.3))