Crystallization of Hard-Sphere Assembly of Fermions

Samuel Limo Chelimo; Khanna Mohan Kapil; Joel Kipkorir Tonui; Godfrey Sylvanous Murunga; Joshua Kiprotich Kibet

doi:doi:10.11648/j.ajmp.20160501.12

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Crystallization of Hard-Sphere Assembly of Fermions

Samuel Limo Chelimo, Khanna Mohan Kapil, Joel Kipkorir Tonui, Godfrey Sylvanous Murunga, Joshua Kiprotich Kibet

Published in American Journal of Modern Physics (Volume 5, Issue 1)

Received: 17 January 2016 Accepted: 29 January 2016 Published: 17 February 2016

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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 E, is maximum has been calculated. The values of saturation particle number densities p_s 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 p_s 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.

Published in	American Journal of Modern Physics (Volume 5, Issue 1)
DOI	10.11648/j.ajmp.20160501.12
Page(s)	15-19
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Fermions, Crystallization, Saturation Density

References

[1]	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.
[2]	K. M. Khanna, Y. K. Ayodo and T. W. A. Sakwa, “Hard Sphere Assembly of Crystalline Bosons,” Afr. Phys. Rev., 2011, 4: 0001.
[3]	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].
[4]	G. A. Baker, “Neutral Matter Model,” Phys. Rev., vol. C(60), 1999, 054311.
[5]	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.
[6]	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.
[7]	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.
[8]	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.
[9]	A. L. Fetter and J. D. Walecka, “Quantum Theory of Many-Particle System,” Mcgraw-Hill: New York, 1971, pp. 149.
[10]	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.
[11]	M. Solis, D. Llano, J. Clark and G. A. Baker, “Improved hard -sphere Ground state Equation of state,” Cond-Stat-Mech., 63130, 2013.
[12]	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.
[13]	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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Samuel Limo Chelimo, Khanna Mohan Kapil, Joel Kipkorir Tonui, Godfrey Sylvanous Murunga, Joshua Kiprotich Kibet. (2016). Crystallization of Hard-Sphere Assembly of Fermions. American Journal of Modern Physics, 5(1), 15-19. https://doi.org/10.11648/j.ajmp.20160501.12

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ACS Style

Samuel Limo Chelimo; Khanna Mohan Kapil; Joel Kipkorir Tonui; Godfrey Sylvanous Murunga; Joshua Kiprotich Kibet. Crystallization of Hard-Sphere Assembly of Fermions. Am. J. Mod. Phys. 2016, 5(1), 15-19. doi: 10.11648/j.ajmp.20160501.12

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AMA Style

Samuel Limo Chelimo, Khanna Mohan Kapil, Joel Kipkorir Tonui, Godfrey Sylvanous Murunga, Joshua Kiprotich Kibet. Crystallization of Hard-Sphere Assembly of Fermions. Am J Mod Phys. 2016;5(1):15-19. doi: 10.11648/j.ajmp.20160501.12

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@article{10.11648/j.ajmp.20160501.12,
  author = {Samuel Limo Chelimo and Khanna Mohan Kapil and Joel Kipkorir Tonui and Godfrey Sylvanous Murunga and Joshua Kiprotich Kibet},
  title = {Crystallization of Hard-Sphere Assembly of Fermions},
  journal = {American Journal of Modern Physics},
  volume = {5},
  number = {1},
  pages = {15-19},
  doi = {10.11648/j.ajmp.20160501.12},
  url = {https://doi.org/10.11648/j.ajmp.20160501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20160501.12},
  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 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.},
 year = {2016}
}

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TY  - JOUR
T1  - Crystallization of Hard-Sphere Assembly of Fermions
AU  - Samuel Limo Chelimo
AU  - Khanna Mohan Kapil
AU  - Joel Kipkorir Tonui
AU  - Godfrey Sylvanous Murunga
AU  - Joshua Kiprotich Kibet
Y1  - 2016/02/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmp.20160501.12
DO  - 10.11648/j.ajmp.20160501.12
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 15
EP  - 19
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20160501.12
AB  - 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.
VL  - 5
IS  - 1
ER  -

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Author Information

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

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APA Style

Samuel Limo Chelimo, Khanna Mohan Kapil, Joel Kipkorir Tonui, Godfrey Sylvanous Murunga, Joshua Kiprotich Kibet. (2016). Crystallization of Hard-Sphere Assembly of Fermions. American Journal of Modern Physics, 5(1), 15-19. https://doi.org/10.11648/j.ajmp.20160501.12

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ACS Style

Samuel Limo Chelimo; Khanna Mohan Kapil; Joel Kipkorir Tonui; Godfrey Sylvanous Murunga; Joshua Kiprotich Kibet. Crystallization of Hard-Sphere Assembly of Fermions. Am. J. Mod. Phys. 2016, 5(1), 15-19. doi: 10.11648/j.ajmp.20160501.12

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AMA Style

Samuel Limo Chelimo, Khanna Mohan Kapil, Joel Kipkorir Tonui, Godfrey Sylvanous Murunga, Joshua Kiprotich Kibet. Crystallization of Hard-Sphere Assembly of Fermions. Am J Mod Phys. 2016;5(1):15-19. doi: 10.11648/j.ajmp.20160501.12

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@article{10.11648/j.ajmp.20160501.12,
  author = {Samuel Limo Chelimo and Khanna Mohan Kapil and Joel Kipkorir Tonui and Godfrey Sylvanous Murunga and Joshua Kiprotich Kibet},
  title = {Crystallization of Hard-Sphere Assembly of Fermions},
  journal = {American Journal of Modern Physics},
  volume = {5},
  number = {1},
  pages = {15-19},
  doi = {10.11648/j.ajmp.20160501.12},
  url = {https://doi.org/10.11648/j.ajmp.20160501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20160501.12},
  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 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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Crystallization of Hard-Sphere Assembly of Fermions
AU  - Samuel Limo Chelimo
AU  - Khanna Mohan Kapil
AU  - Joel Kipkorir Tonui
AU  - Godfrey Sylvanous Murunga
AU  - Joshua Kiprotich Kibet
Y1  - 2016/02/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ajmp.20160501.12
DO  - 10.11648/j.ajmp.20160501.12
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 15
EP  - 19
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20160501.12
AB  - 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.
VL  - 5
IS  - 1
ER  -

Copy | Download