Electron degeneracy pressure
Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli exclusion principle disallows two identical half-integer spin particles (electrons and all other fermions) from simultaneously occupying the same quantum state. The result is an emergent pressure against compression of matter into smaller volumes of space. Electron degeneracy pressure results from the same underlying mechanism that defines the electron orbital structure of elemental matter. For bulk matter with no net electric charge, the attraction between electrons and nuclei exceeds (at any scale) the mutual repulsion of electrons plus the mutual repulsion of nuclei; so in absence of electron degeneracy pressure, the matter would collapse into a single nucleus. In 1967, Freeman Dyson showed that solid matter is stabilized by quantum degeneracy pressure rather than electrostatic repulsion. Because of this, electron degeneracy creates a barrier to the gravitational collapse of dying stars and is responsible for the formation of white dwarfs.
From the Fermi gas theory
Electrons are members of a family of particles known as fermions. Fermions, like the proton or the neutron, follow Pauli's principle and Fermi–Dirac statistics. In general, for an ensemble of non-interacting fermions, also known as a Fermi gas, each particle can be treated independently with a single-fermion energy given by the purely kinetic term,
The degeneracy pressure at zero temperature can be computed as
When particle energies reach relativistic levels, a modified formula is required. The relativistic degeneracy pressure is proportional to ρe4/3.
For the case of electrons in crystalline solid, several approximations are carefully justified to treat the electrons as independent particles. Usual models are the free electron model and the nearly free electron model. In the appropriate systems, the electron degeneracy pressure can be calculated; it can be shown that this pressure is an important contributor to the compressibility or bulk modulus of metals.
Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar limit (1.44 solar masses). This is the pressure that prevents a white dwarf star from collapsing. A star exceeding this limit and without significant thermally generated pressure will continue to collapse to form either a neutron star or black hole, because the degeneracy pressure provided by the electrons is weaker than the inward pull of gravity.
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