Few-Body Systems

, Volume 41, Issue 3–4, pp 201–210 | Cite as

Relativistic versus nonrelativistic solution of the N-fermion problem in a hyperradius-confining potential

Article

Abstract

We investigate the quantum system of N identical fermions in the relativistic limit. In this article the considered potential is a combination of Coulombic, linear confining and harmonic oscillator terms. By using Jacobi coordinates and introducing the hyperradius quantity we obtain the wave functions of the system as well as the corresponding energy eigenvalues. Assuming that all particles are confined within a hypersphere we calculate the corresponding xbag. In particular we consider the case N = 3 which corresponds to baryonic systems. By using the experimental values of the charge radius of each baryon we calculate the potential coefficients. Within our treatment the results of the MIT bag model are recovered for N = 1. Finally we compare the results obtained by the Dirac equation with the corresponding results of the Schrödinger equation and we find that the energy spectra obtained by the former are much closer to experimental values.

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References

  1. Giannini, MM, Santopinto, E, Vassallo, A 2003Prog Part Nucl Phys50263CrossRefADSGoogle Scholar
  2. Rajabi, AA 2005Iran J Phys Res537Google Scholar
  3. Giannini, MM, Santopinto, E, Vassallo, A 2001Eur Phys J A12447CrossRefADSGoogle Scholar
  4. Fabre de la Ripelle, M 1988Phys Lett B20597CrossRefADSGoogle Scholar
  5. Capstick, S, Keister, BD 1995Phys Rev D513598CrossRefADSGoogle Scholar
  6. Close, FE 1979An introduction to quarks and partonsAcademic PressNew YorkGoogle Scholar
  7. Zhong, L, Song, HQ, Su, RK 1997J Phys G23557CrossRefADSGoogle Scholar
  8. Tegen, R, Schedl, M, Weise, W 1983Phys Lett B1259CrossRefADSGoogle Scholar
  9. Aiello, M, Giannini, MM, Santopinto, E 1998J Phys G24753CrossRefADSGoogle Scholar
  10. Strobel, GL 1998Int J Theor Phys372001CrossRefGoogle Scholar
  11. Aiello, M, Giannini, MM, Frerris, M, Pizoo, M, Santopinto, E 1996Phys Lett B387215CrossRefADSGoogle Scholar
  12. Giannini, MM, Santopinto, E, Vassallo, A 2001Eur Phys J A12447CrossRefADSGoogle Scholar
  13. Santopinto, E, Iachello, F, Giannini, MM 1998Eur Phys J A1307CrossRefADSGoogle Scholar
  14. Santopinto, E, Iachello, F, Giannini, MM 1997Nucl Phys A623100cCrossRefADSGoogle Scholar
  15. Rajabi, AA 2005Few Body Syst37197CrossRefADSGoogle Scholar
  16. Giannini, MM, Santopinto, E, Vassallo, A 2002Nucl Phys A699308CrossRefADSGoogle Scholar
  17. Fabre de la Ripelle, M 1983Ann Phys NY147281MATHCrossRefADSMathSciNetGoogle Scholar
  18. Aquilanti, V, Tonzani, S 2004J Chem Phys1264066CrossRefADSGoogle Scholar
  19. Tolstikhin, OI, Nakamura, H 1998J Chem Phys1088899CrossRefADSGoogle Scholar
  20. Chapuisat, X 1992Phys Rev A454277CrossRefADSGoogle Scholar
  21. Giannini, MM, Santopinto, E, Iachello, F 1995Gruber, B eds. Symmetries in ScienceVIIPlenum PressNew York445Google Scholar
  22. Fabre de la Ripelle, M, Navarro, J 1979Ann Phys NY123185MATHCrossRefADSGoogle Scholar
  23. Fabre de la Ripelle, M, Fiedeldey, H, Sofianos, SA 1988Phys Rev C38449CrossRefADSGoogle Scholar
  24. Bell, J, Ruegg, H 1975Nucl Phys B98151CrossRefADSGoogle Scholar
  25. Gruber, BJ, Marmo, G, Yoshinaga, N 2005The relativistic many-body problem in quantum mechanicsSpringerBerlin HeidelbergGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Physics DepartmentShahrood University of TechnologyShahroodIran

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