Parameters of the Free-Electron Gas

The volume of unit ceU that contains two electrons in fe-space is (2ji/ I). Consequently, the total number of electrons N can be expressed as 

The value kp is called the Fermi momentum. It depends on the electron density. It is seen from (5.17) that for large N the occupied region in fe-space is indistinguishable from a sphere. 

Substituting (5.17) into (5.15) we arrive at the next equation for the Fermi energy 

the Fermi energy of the free-electron gas is dependent on the density of electrons as n l.  

A dimensionless parameter tg is universally used to describe properties of the electron gas. By definition, tg is the radius in atomic units of the sphere, which encloses one unit of the electron charge. It may be found from the equaUty 

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