American Journal of Modern Physics

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Crystallization of Hard-Sphere Assembly of Fermions

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 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.

DOI 10.11648/j.ajmp.20160501.12
Published in American Journal of Modern Physics (Volume 5, Issue 1, January 2016)
Page(s) 15-19
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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), 2024. Published by Science Publishing Group

Keywords

Fermions, Crystallization, Saturation Density

References
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[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.
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Author Information
  • Department of Physics, University of Eldoret, Eldoret, Kenya

  • Department of Physics, University of Eldoret, Eldoret, Kenya

  • Department of Physics, University of Eldoret, Eldoret, Kenya

  • Department of Physics, University of Eldoret, Eldoret, Kenya

  • Department of Chemistry, Egerton University, Egerton, Kenya

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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://download.sciencepg.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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    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
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    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
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    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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