One model that estimates the properties of an electron gas at absolute zero in metals is the Fermi gas.

The green curve uses the general pressure law for an ideal Fermi gas, while the blue curve is for a non-relativistic ideal Fermi gas.

( 43 )</ sup > gives the following expression, based on the equation of state for an ideal Fermi gas:

In 1930, Stoner derived the internal energy-density equation of state for a Fermi gas, and was then able to treat the mass-radius relationship in a fully relativistic manner, giving a limiting mass of approximately ( for μ < sub > e </ sub >= 2. 5 ) 2. 19 · 10 < sup > 30 </ sup > kg.

where the Indian physicist Subrahmanyan Chandrasekhar worked on the calculation of the statistics of a degenerate Fermi gas.

the hydrostatic equation together with the nonrelativistic Fermi gas equation of state, and also treated the case of a relativistic Fermi gas, giving rise to the value of the limit shown above.

Fermions, on the other hand, are forbidden from sharing quantum states, giving rise to systems such as the Fermi gas.

In both of these models the electrons are seen as a gas traveling through the lattice of the solid with an energy that is essentially isotropic in that it depends on the square of the magnitude, not the direction of the momentum vector k. In three-dimensional k-space, the set of points of the highest filled levels ( the Fermi surface ) should therefore be a sphere.

* the ideal quantum Fermi gas, composed of fermions.

The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas and quantum Fermi gas in the limit of high temperature to specify these additive constants.

Here, the electrons are modelled as a Fermi gas, a gas of particles which obey the quantum mechanical Fermi-Dirac statistics.

Degenerate matter is also called a Fermi gas or a degenerate gas.

In the special case of a noninteracting Fermi gas ( or " jellium "), the temperature dependence is:

But Fermi also participated in preliminary work on the hydrogen bomb at Los Alamos as a consultant, and along with Stanislaw Ulam, calculated that the amount of tritium needed for Edward Teller's model of a thermonuclear weapon would be prohibitive, and a fusion reaction could not be assured to propagate even with this large quantity of tritium.

" The nuclear Thomas – Fermi model ", Lawrence Berkeley National Laboratory ( LBNL ), United States Department of Energy, ( August 1, 1994 ).

The Thomas – Fermi model was developed independently by Thomas and Fermi in 1927.

Indeed, Enrico Fermi proposed in 1949 a model for the acceleration of cosmic rays through particle collisions with magnetic clouds in the interstellar medium.

A later model to produce Fermi Acceleration was generated by a powerful shock front moving through space.

One of these introduced the Fermi – Ulam model, which is an extension of Fermi's theory of the acceleration of cosmic rays.

In the free electron model non-interacting electrons bounce around inside a potential well of depth U. The Fermi Level is the highest energy level that is occupied by electrons.

* 1927 Thomas and Fermi develop the Thomas-Fermi model

* 1934 Enrico Fermi publishes a very successful model of beta decay in which neutrinos were produced.

An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions.

Fermi liquid theory ( also known as Landau-Fermi liquid theory ) is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures.

Although density functional theory has its conceptual roots in the Thomas – Fermi model, DFT was put on a firm theoretical footing by the two Hohenberg – Kohn theorems ( H – K ).

The simplest approximation is the local-density approximation ( LDA ), which is based upon exact exchange energy for a uniform electron gas, which can be obtained from the Thomas – Fermi model, and from fits to the correlation energy for a uniform electron gas.

Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension.

In the Stoner model, a high density of states at the Fermi level makes the nonmagnetic state unstable.

Main predictions of the free-electron model are derived by the Sommerfeld expansion of the Fermi-Dirac occupancy for energies around the Fermi level.

The Fermi ball calculation we have used above, based on the liquid drop model

This simple model can be used to describe the classical ideal gas as well as the various quantum ideal gases such as the ideal massive Fermi gas, the ideal massive Bose gas as well as black body radiation which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the photons with an equilibrated mass.

The Fermi liquid model of correlated electrons in metals is able to explain the temperature dependence of resistivity by electron-electron interactions.

* Fermi – Ulam model ( billiards with oscillating walls )

The key ingredient was Leon Neil Cooper's calculation of the bound states of electrons subject to an attractive force in his 1956 paper, " Bound Electron Pairs in a Degenerate Fermi Gas ".

Demonstration of a self-sustaining nuclear chain reaction was accomplished by Enrico Fermi and others, in the successful operation of Chicago Pile-1, the first artificial nuclear reactor, in late 1942.

Enrico Fermi (; 29 September 1901 – 28 November 1954 ) was an Italian physicist, naturalized American later in his life, particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics.

Enrico Fermi was born in Rome to Alberto Fermi, a Chief Inspector of the Ministry of Communications, and Ida de Gattis, an elementary school teacher.

In Pisa, Fermi was advised by the director of the physics laboratory, Luigi Puccianti, who acknowledged that there was little that he could teach Fermi, and frequently asked Fermi to teach him something.

In 1923, while writing the appendix for the Italian edition of the book The Mathematical Theory of Relativity by A. Kopff, Enrico Fermi pointed out, for the first time, that hidden inside the famous Einstein equation (), there was an enormous amount of nuclear potential energy to be exploited.

At age 24, Fermi took a professorship at the University of Rome ( one of the first three in theoretical physics in Italy ) which he won in a competition whose selection committee was chaired by Professor Orso Mario Corbino, director of the Institute of Physics.

Corbino helped Fermi in selecting his team, which soon was joined by notable minds like Edoardo Amaldi, Bruno Pontecorvo, Franco Rasetti and Emilio Segrè.

Thus Fermi saw the theory published in Italian and in German before it was published in English.

Fermi went home for lunch one day and returned with the explanation: the increased activity was due to hydrogen atoms in the wood slowing down neutrons ( later called moderation ) and this slowing caused them to be more active in nuclear reactions.

Fermi was well known for his simplicity in solving problems.

From the time he was a boy, Fermi meticulously recorded his calculations in notebooks, and later used them to solve many new problems that he encountered based on these earlier known problems.

On 25 January 1939, a Columbia University team conducted the first nuclear fission experiment in the United States, which was done in the basement of Pupin Hall ; the members of the team were Herbert L. Anderson, Eugene T. Booth, John R. Dunning, Enrico Fermi, G. Norris Glasoe, and Francis G. Slack.

Eventually Fermi and Szilárd's reactor work was folded into the Manhattan Project.

To continue the research where it would not pose a public health hazard, the reactor was disassembled and moved to a wooded site outside Chicago, where Fermi directed research on reactors and other fundamental sciences.

Fermi moved to what was to become Los Alamos National Laboratory in the later stages of the Manhattan Project to serve as a general consultant.

Fermi was present as an observer of the Trinity test on July 16, 1945.