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The Degenerate Electron Gas

  • Rudolf Kippenhahn
  • Alfred Weigert
Chapter
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Part of the Astronomy and Astrophysics Library book series (AAL)

Abstract

We consider a gas of sufficiently high density in the volume dV so that it is practically fully pressure ionized (§14.6). Here we shall deal with the free electrons, of number density ne. If the velocity distribution of the electrons is given by Boltz-mann statistics, then their mean kinetic energy is 3kT/2. In momentum space p x , p y , p z each electron of a given volume dV in local space is represented by a point and these points form a “cloud” which is spherically symmetric around the origin. If p is the absolute value of the momentum \( \left( {{p^2} = p_x^2 + p_y^2 + p_z^2} \right) \), then the number of electrons in the spherical shell [p, p + dp] is, according to the Boltzmann distribution function,
$$ f(p)dpdV = {n_e}\frac{{4\pi {p^2}}}{{{{\left( {2\pi {m_e}kT} \right)}^{{3/2}}}}}\exp \left( { - \frac{{{p^2}}}{{2{m_e}kT}}} \right)dp\,dV $$
(15.1)
.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Rudolf Kippenhahn
    • 1
  • Alfred Weigert
  1. 1.GöttingenGermany

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