Abstract
Spin-half fermions are considered to be limited in a spherical potential well with periodic boundary conditions. The whole system is treated like a relativistic Fermi Gas. Solving the corresponding Dirac equation, the density of states, the Fermi energy, the average energy, the density of states of nucleons and the total energy of the ground-state are obtained.
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Greiner, W., Maruhn, J.A.: Nuclear Models. Springer, Berlin (1996)
Men, F.D., Liu, H.: The instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field. Chin. Phys. 15, 2856–2860 (2006)
Suzuki, M., Suzuki, I.S.: Free electron Fermi gas model: specific heat and Pauli paramagnetism. In: Lecture Note on Solid State Physic Department of Physics, State University of New York at Binghamton, Binghamton, New York pp. 13902–6000 (2006, June 15).
Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Holt, Rinehart and Winston, New York (1976). ISBN 0-03-083993-9.
Ginocchio, J.N.: Relativistic symmetries in nuclei and hadrons. Phys. Rep. 414, 165–261 (2005)
Ginocchio, J.N., Leviatan, A.: Relativistic Symmetry in Nuclei. Phys. Lett. B 425, 1–5 (1998)
Ginocchio, J.N.: Pseudospin as a relativist symmetry. Phys. Rev. Lett 78(436), 436–439 (1997)
Zhang, F.L., Fu, B., Chen, J.L.: Higgs algebraic symmetry in two-dimensional Dirac equation. Phys. Rev. A 80, 054102–4 (2009)
Geim, A.K., Novoselov, K.S.: The rise of graphene. Nature Mater. 6, 183–191 (2007)
Bagchi, B., Ganguly, A.: A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials. J. Phys A Math. Gen. 36, 161–167 (2003)
Alonso, V., De Vincenzo, S.: General boundary conditions for a Dirac particle in a box and their non-relativistic limits. J. Phys. A 30, 8573–8585 (1997)
Roy, S.M., Singh, V.: Fractional total-charge Eigenvalues for a fermion in a finite one-dimensional box. Phys. Lett B. 143, 179–182 (1984)
Rajaraman, R., Bell, J.S.: On solitons with half integral charge. Phys. Lett. 116, 151–154 (1982)
Alhaidari, A.D.: Dirac particle in a square well and in a box. In: Proceedings of the Fifth Saudi Physical Society Conference (SPS5), A. Al-Hajry et al. (ed.), AIP Conference Proceedings, American Institute of Physics, Melville, New York, vol. 1370, pp. 21–25 (2011).
Springford, M.: Electrons at the Fermi Surface. Cambridge University Press, Cambridge (1980).
Ziman, J.: Electrons in Metals: A Short Guide to the Fermi Surface. Taylor & Francis, London (1964)
Hassanabadi, H., Maghsoodi, E., Zarrinkamar, S.: Dirac equation with vector and scalar cornell potentials and an external magnetic field. Ann. Phys. 525(12), 944–950 (2013).
Alberto, P., Fiolhais, C., Gil, V.M.S.: Relativistic particle in a box. Eur. J. Phys. 17, 19–24 (1996)
Zwerger, W.: The BCS-BEC Crossover and the Unitary Fermi Gas. Springer, Berlin (2011).
Wei, G.F., Dong, S.H.: Pseudospin symmetry in the relativistic Manning–Rosen potential including a Pekeris-type approximation to the pseudo-centrifugal term. Phys. Lett. B 686, 288–292 (2010)
Maruhn, J.A., Reinhard, P.G., Suraud, E.: Simple Models of Many-Fermion Systems. Springer, Berlin (1977).
Greiner, W., Müller, B.: Quantum Mechanics. Symmetries, Springer, New York (1994)
Moniz, E.J.: Pion electroproduction from nuclei. Phys. Rev. 184, 1154–1161 (1969)
Miller, G.A.: Fermi gas model. Nucl. Phys. B 112, 223–225 (2002). (Proc. Suppl.)
Mengoli, A., Nakajima, Y.: Fermi-gas model parametrization of nuclear level density. J. Nucl. Sci. Tech. 31, 151–162 (1994)
Meyerhof, W.E.: Elements of Nuclear Physics. McGraw-Hill, New York (1967)
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Hassanabadi, H., Armat, A. & Naderi, L. Relativistic Fermi-Gas Model for Nucleus. Found Phys 44, 1188–1194 (2014). https://doi.org/10.1007/s10701-014-9836-7
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DOI: https://doi.org/10.1007/s10701-014-9836-7