Electron degeneracy pressure

In astrophysics and condensed matter physics, electron degeneracy pressure is a quantum mechanical effect critical to understanding the stability of white dwarf stars and metal solids. It is a manifestation of the more general phenomenon of quantum degeneracy pressure.

The term "degenerate" here is not related to degenerate energy levels, but to Fermi–Dirac statistics close to the zero-temperature limit^[1] (temperatures much smaller than the Fermi temperature, which for metals is about 10000 K.)

In metals and in white dwarf stars, electrons can be modeled as a gas of non-interacting electrons confined to a finite volume. Although there are strong electromagnetic forces between the negatively charged electrons, these forces are approximately balanced by the positive nuclei and so can be neglected in the simplest models. The pressure exerted by the electrons is related to their kinetic energy. The degeneracy pressure is most prominent at low temperatures: If electrons were classical particles, the movement of the electrons would cease at absolute zero and the pressure of the electron gas would vanish. However, since electrons are quantum mechanical particles that obey the Pauli exclusion principle, no two electrons can occupy the same state, and it is not possible for all the electrons to have zero kinetic energy. Instead, the confinement makes the allowed energy levels quantized, and the electrons fill them from the bottom upwards. If many electrons are confined to a small volume, on average the electrons have a large kinetic energy, and a large pressure is exerted.^[2]^[3]^: 32–39

In white dwarf stars, the positive nuclei are completely ionized – disassociated from the electrons – and closely packed – a million times more dense than the Sun. At this density gravity exerts immense force pulling the nuclei together. This force is balanced by the electron degeneracy pressure keeping the star stable.^[4]

In metals, the positive nuclei are partly ionized and spaced by normal interatomic distances. Gravity has negligible effect; the positive ion cores are attracted to the negatively charged electron gas. This force is balanced by the electron degeneracy pressure.^[3]^: 410

^ Taylor, John Robert; Zafiratos, Chris D. (1991). Modern physics for scientists and engineers. Englewood Cliffs, N.J: Prentice Hall. ISBN 978-0-13-589789-8.
^ Zannoni, Alberto (1999). "On the Quantization of the Monoatomic Ideal Gas". arXiv:cond-mat/9912229. An english translation of the original work of Enrico Fermi on the quantization of the monoatomic ideal gas, is given in this paper
^ ^a ^b Cite error: The named reference AshcroftMermin was invoked but never defined (see the help page).
^ Koester, D; Chanmugam, G (1990-07-01). "Physics of white dwarf stars". Reports on Progress in Physics. 53 (7): 837–915. Bibcode:1990RPPh...53..837K. doi:10.1088/0034-4885/53/7/001. ISSN 0034-4885. S2CID 250915046.

[1] Taylor, John Robert; Zafiratos, Chris D. (1991). Modern physics for scientists and engineers. Englewood Cliffs, N.J: Prentice Hall. ISBN 978-0-13-589789-8.

[2] Zannoni, Alberto (1999). "On the Quantization of the Monoatomic Ideal Gas". arXiv:cond-mat/9912229. An english translation of the original work of Enrico Fermi on the quantization of the monoatomic ideal gas, is given in this paper

[AshcroftMermin-3] Cite error: The named reference AshcroftMermin was invoked but never defined (see the help page).

[Koester-Chanmugam-4] Koester, D; Chanmugam, G (1990-07-01). "Physics of white dwarf stars". Reports on Progress in Physics. 53 (7): 837–915. Bibcode:1990RPPh...53..837K. doi:10.1088/0034-4885/53/7/001. ISSN 0034-4885. S2CID 250915046.

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