# Fermi Gas

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## Fermi gas

[′fer·mē ‚gas]## Fermi Gas

a gas that consists of particles with half-integral spin and obeys Fermi-Dirac statistics. Fermi gas that consists of noninteracting particles is called ideal Fermi gas. Fermi gases include electrons in metals and semiconductors, electrons in atoms with large atomic numbers, nucleons in heavy atomic nuclei, and gases consisting of quasiparticles with half-integral spin.

At a temperature *T* = 0°K, an ideal Fermi gas is in the ground state, and the particles of the gas occupy all quantum states with energy up to a certain maximum value, which depends on the gas density and is called the Fermi level (*E _{F}*). Quantum states with energy

*E*>

*E*are empty; such a distribution of occupied and empty states corresponds to complete degeneracy of the Fermi gas. At

_{F}*T*≠ 0°K, the mean occupation number for a quantum state of an ideal Fermi gas is described by the Fermi-Dirac distribution function.

A Fermi level also exists for a nonideal Fermi gas, although the particles of such a gas do not occupy specific quantum states. In a nonideal Fermi gas consisting of electrons in a metal, the formation of pairs of correlated electrons (the Cooper effect) and the transition of the metal to the superconducting state may occur at very low temperatures because of the attraction of electrons with equal but oppositely directed momenta and spins. A Fermi gas consisting of electrons in heavy atoms is described by the Thomas-Fermi model (*see*SELF-CONSISTENT FIELD).

D. N. ZUBAREV