Collisions of Electrons with Atoms and Ions: General Theory

  • G. F. Drukarev
Part of the Physics of Atoms and Molecules book series (PAMO)


The wave function of the system “electron + atom” depends upon electronic coordinates r1 ... rN and spin projections μ1 ... μN. It should be antisymmetric with respect to the permutation of any pair riμi and rkμk. Denoting by one quantity xi all variables riμi and by Pik the permutation operator, we have
$$ {p_{ik}}\Phi ( \ldots ,{x_i} \ldots ,{x_k} \ldots ) = -\Phi ( \ldots ,{x_i} \ldots ,{x_k} \ldots ). $$
The function Φ is an eigenfunction of the Hamiltonian operator H
$$ H\Phi = E\Phi $$
where H in the nonrelativistic approximation has the form
$$ H = -{1 \over 2}\mathop \sum \limits_i {\Delta _i} -\mathop \sum \limits_i {Z \over {{r_i}}} + \mathop \sum \limits_{i < j} {1 \over {\left| {{r_i} -{r_j}} \right|}}. $$


Density Matrix Total Angular Momentum Total Spin Spin Projection Spin Variable 
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

© Plenum Press, New York 1987

Authors and Affiliations

  • G. F. Drukarev
    • 1
  1. 1.Leningrad UniversityLeningradUSSR

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