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Volumetto IV: 24 April 1930

  • Salvatore Esposito
  • Ettore MajoranaJr
  • Alwyn van der Merwe
  • Erasmo Recami
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 133)

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)

Keywords

Theoretical Physic Plane Wave Discrete State Spherical Function Hankel Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Salvatore Esposito
    • 1
  • Ettore MajoranaJr
    • 2
  • Alwyn van der Merwe
    • 3
  • Erasmo Recami
    • 4
  1. 1.University of Naples “Federico II”NaplesItaly
  2. 2.Italian National Institute for Nuclear PhysicsSite of PisaItaly
  3. 3.University of DenverDenverUSA
  4. 4.University of BergamoDalmine (BG)Italy

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