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Volume 5, Issue 1, January 2016, Page: 15-19
Crystallization of Hard-Sphere Assembly of Fermions
Samuel Limo Chelimo, Department of Physics, University of Eldoret, Eldoret, Kenya
Khanna Mohan Kapil, Department of Physics, University of Eldoret, Eldoret, Kenya
Joel Kipkorir Tonui, Department of Physics, University of Eldoret, Eldoret, Kenya
Godfrey Sylvanous Murunga, Department of Physics, University of Eldoret, Eldoret, Kenya
Joshua Kiprotich Kibet, Department of Chemistry, Egerton University, Egerton, Kenya
Received: Jan. 17, 2016;       Accepted: Jan. 29, 2016;       Published: Feb. 17, 2016
DOI: 10.11648/j.ajmp.20160501.12      View  4332      Downloads  118
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 E, is maximum has been calculated. The values of saturation particle number densities ps for low and high densities are; 7.11x1021 particles/cm3 and 1.502x1023 particles/cm3 respectively at which the fermions close pack or crystallize. Variation of ps with hard-sphere diameter C 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, E, has been found to vary non-linearly with p at high densities and closely linear for low density. The value of E for low density is 1.435x10-22 J, and for high density it is 3.113x10-21 J. These findings are consistent with experimental and computer-simulated results obtained by others.
Fermions, Crystallization, Saturation Density
To cite this article
Samuel Limo Chelimo, Khanna Mohan Kapil, Joel Kipkorir Tonui, Godfrey Sylvanous Murunga, Joshua Kiprotich Kibet, Crystallization of Hard-Sphere Assembly of Fermions, American Journal of Modern Physics. Vol. 5, No. 1, 2016, pp. 15-19. doi: 10.11648/j.ajmp.20160501.12
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
J. G. Kirkwood, E. K. Maun and B. J. J. Adler, “Radial distribution functions and the equation of state of a fluid composed of rigid spherical molecules,” J. Chem. Phys., vol. 18, pp. 1040-1047, 1950.
K. M. Khanna, Y. K. Ayodo and T. W. A. Sakwa, “Hard Sphere Assembly of Crystalline Bosons,” Afr. Phys. Rev., 2011, 4: 0001.
L. D. Landau, “Theory of a Fermi Liquid,” Zh. Eksp. Teor. Fiz, vol. 30, pp. 1058, 1956. [Sovi. Phys. JETP vol. 3, pp. 920, 1957].
G. A. Baker, “Neutral Matter Model,” Phys. Rev., vol. C(60), 1999, 054311.
C. J. Pethick and D. G. Ravenhall, “Matter at Large Neutron Excess and the Physics of Neutron-Star Crusts,” Ann. Rev. Nucl. Part. Sci., vol. 45, pp. 429-484, 1995.
G. A. Baker Jr., “Singularity Structure of the Perturbation Series for the Ground-State Energy of a Many-Fermion System,” Rev. Mod. Phys., vol. 43, pp. 479, 1971.
G. A. Baker Jr., L. P. Benofy, M. de Llano, M. Fortes, S. M. Peltier and A. Pastino, “Hard-core square-well fermions,” Phys. Rev., vol. A26, pp. 3575, 1982.
M. A. Solìs, M. de Llano and J. W. Clark, “Kirkwood Phase Transition for Boson and Fermion Hard-Sphere Systems,” arXiv: cond-mat/0306338v1, 2003.
A. L. Fetter and J. D. Walecka, “Quantum Theory of Many-Particle System,” Mcgraw-Hill: New York, 1971, pp. 149.
S. L. Chelimo, K. M. Khanna, K. K. Sirma, J. K. Tonui, P. K. Korir, J. K. Kibet, A. J. Achieng and A. Sarai, “Quantum Hard-Sphere Assembly of Fermions,” Int. J. of Phys. and Math. Sci., vol. 5(1), pp. 47-53, 2015.
M. Solis, D. Llano, J. Clark and G. A. Baker, “Improved hard -sphere Ground state Equation of state,” Cond-Stat-Mech., 63130, 2013.
M. Viviani, E. Bundia, S. Fantoni and S. Rosati, “Spin-dependent correlations in the ground state of liquid Helium-3,” Phys. Rev., vol. B38, pp. 4523, 1988.
H. M. Zhizhong, D. Llano, E. Bundia and R. Guardiola, “Aziz fermions and liquid 3He,” Phys. Rev., vol. B43 (16), 1991.
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