We consider a onecomponent plasma model of neutron star crusts, assuming a single species of nuclei at a given density . We restrict ourselves to matter composed of atomic nuclei immersed in a nearly ideal and uniform, strongly degenerate electron gas of number density . This model is valid at . A neutron gas is also present at densities greater than neutron drip density .
For an ideal, fully degenerate, relativistic electron gas, the Fermi energy (using the letter F to denote quantities evaluated at the Fermi level and the letter for electrons) is given by
where is a dimensionless relativity parameter defined in terms of the Fermi momentum by and is the electron effective mass at the Fermi surface. The Fermi velocity is Electrons are strongly degenerate for , where the electron Fermi temperature is defined by is the Boltzmann constant and Let the mass number of nuclei be and their proton number be . The electric charge neutrality of matter implies that the number density of ions (nuclei) is For , the quantities and are related to the mass density of the crust by where is the atomic mass unit, . For , one has to replace in Equation (8) by , where is the number of nucleons bound in the nucleus and is the number of free (unbound) neutrons per ion. is, thus, the number of nucleons per ion. The electron relativity parameter can be expressed as where .The ion plasma temperature is defined, in terms of the the ion plasma frequency
by Quantum effects for ions become very important for . The electron plasma frequency is so that the electron plasma temperature which can be rewritten as


The crystallization of a Coulomb plasma of ions occurs at the temperature
where the ion sphere (also called the unit cell or Wigner–Seitz cell) radius is For classical ions () one has . For the zeropoint quantum vibrations of ions becomes important and lead to crystal melting at lower .http://www.livingreviews.org/lrr200810 
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