Abstract
Crystallization of a hard-sphere system of fermions with densities ranging from low to high values has been studied. Saturation densities at which the total energy <i>E</i>, is maximum has been calculated. The values of saturation particle number densities <i>p<sub>s</sub></i> for low and high densities are; 7.11<i>x</i>10<sup>21</sup> particles/<i>cm</i><sup>3</sup> and 1.502<i>x</i>10<sup>23</sup> particles/<i>cm</i><sup>3</sup> respectively at which the fermions close pack or crystallize. Variation of <i>p<sub>s</sub></i> with hard-sphere diameter <i>C</i> is not linear and it is more or less the same for both low and high density since crystallization occurs in both the cases. The total energy, <i>E</i>, has been found to vary non-linearly with <i>p</i> at high densities and closely linear for low density. The value of <i>E</i> for low density is 1.435<i>x</i>10<sup>-22</sup> <i>J</i>, and for high density it is 3.113<i>x</i>10<sup>-21</sup> <i>J</i>. These findings are consistent with experimental and computer-simulated results obtained by others.
Highlights
For physical systems, whether molecular or nuclear, the interaction potential is composed of repulsive part and attractive part
We study the properties of a hard-sphere assembly of fermions
A gas or a liquid composed of fermions in which pairs of particles interact via hard-sphere interaction has been studied to obtain the total energy E of the system and to obtain the saturation density ρs, leading to crystallization of the system
Summary
For physical systems, whether molecular or nuclear, the interaction potential is composed of repulsive part and attractive part. When the two-particle scattering length is large (weak interactions), these short range interactions can modify the gas properties sufficiently Such examples are low density neutron matter that may occur in the inner crust of neutron stars [4]. A hard-sphere system of fermions with densities ranging from very low to very high values will be considered to obtain an expression for the energy per particle E/N. It was found that in hard-sphere system, freezing transition from a fluid to a crystalline phase occurs as the density is increased It is, possible that the same phenomena may occur in quantum systems, whether of bosons or fermions [7]. Saturation densities leading to crystallization of hard-sphere fermions, and the energy per particle E/N, have been calculated
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