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International Journal of Theoretical Physics

, Volume 45, Issue 1, pp 152–175 | Cite as

Spin-Polarized 3He–HeII Mixtures in the Static Fluctuation Approximation

  • A. S. Sandouqa
  • M. K. Al-Sugheir
  • H. B. Ghassib
Article

Abstract

We have used the so-called static fluctuation approximation (SFA) to calculate the thermodynamic properties of spin-polarized 3He–HeII mixtures at low temperature, T < 0.025 K. This approximation is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for spin-up and spin-down systems. This set is solved numerically by an iteration method for a realistic interhelium potential. The mean internal energy per unit volume, the pressure, the entropy per unit volume, and the specific heat per unit volume increase with increasing temperature. The mean internal energy per unit volume, the pressure increase with increasing spin polarization; while the entropy per unit volume and the specific heat per unit volume are weakly–dependent on spin polarization.

Key Words

spin-polarized system static fluctuation approximation 3He-HeII mixtures 

References

  1. Ali, S. N. (1997). The Helium–Helium Interaction in Vacuum: A Reconsideration, MSc Thesis, University of Jordan, Amman, Jordan.Google Scholar
  2. Al-Sugheir, M. K. (2004). International Journal of Theoretical Physics 43, 1527.CrossRefMATHADSGoogle Scholar
  3. Al-Sugheir, M. K., Ghassib, H. B., and Nigmatullin, R. R. (2001). International Journal of Theoretical Physics 40, 1033.CrossRefMATHGoogle Scholar
  4. Al-Sugheir, M. K. and Ghassib, H. B. (2002). International Journal of Theoretical Physics 41, 705.CrossRefMATHGoogle Scholar
  5. Aziz, R. A., Nain, V. P. S., Carley, J. S., Taylor, W. L., and McConville, G. T. (1979). Journal of Chemical Physics 70, 4330.CrossRefADSGoogle Scholar
  6. Bradley, J. R. (1997). Reports on Progress in Physics 60, 1173.CrossRefADSGoogle Scholar
  7. Bishop, R. F., Ghassib, H. B., and Strayer, M. R. (1977). Journal of Low Temperature Physics 26, 669.CrossRefADSGoogle Scholar
  8. Burden, R. L. and Faires, J. D. (1993). Numerical Analysis, 5th edn., PWS Publishing Company, Boston.MATHGoogle Scholar
  9. Campbell, L. J. (1967). Physical Review Letters 19, 154.CrossRefADSGoogle Scholar
  10. Candela, D., McAllaster, S. R., and Wei, L. J. (1991). Physical Review B 44, 7510.CrossRefADSGoogle Scholar
  11. Candela, D., Hayden, M. E., and Nacher, P. J. (1994). Physical Review Letters 73, 2587.CrossRefPubMedADSGoogle Scholar
  12. Fetter, A. L. and Walecka, J. D. (1971). Quantum Theory of Many-Particle Systems, McGraw-Hill, New York.Google Scholar
  13. Ghassib, H. B., Bishop, R. F., and Strayer, M. R. (1976). Journal of Low Temperature Physics 23, 393.CrossRefADSGoogle Scholar
  14. Hampson, T. M. M., McHale, G., and Rowley, R. M. (1988). Conference on Spin Polarized Quantum System, Word Scientific, Singapore.Google Scholar
  15. Huang, K. (1987). Statistical Mechanics, 2nd edn., Wiley, New York.MATHGoogle Scholar
  16. Janzen, A. R. and Aziz, R. A. (1995). Journal of Chemical Physics 103, 9626.CrossRefADSGoogle Scholar
  17. Kelly, D. C. (1973). Thermodynamics and Statistical Physics, Academic Press, New York.Google Scholar
  18. Kittel, C. and Kroemer, H. (1995). Thermal Physics, 2nd edn., Freeman, New York.Google Scholar
  19. Meyerovich, A. E. (1978). Physics Letters 69A, 279.ADSGoogle Scholar
  20. Meyerovich, A. E. (1980). Physics Letters 76A, 297.ADSGoogle Scholar
  21. Nigmatullin, R. R., Khamzin, A. A., and Ghassib, H. B. (2000a). Solid State Communications 113, 257.CrossRefGoogle Scholar
  22. Nigmatullin, R. R., Khamzin, A. A., and Ghassib, H. B. (2000b). Physical Review E 61, 3441.CrossRefADSGoogle Scholar
  23. Nigmatullin, R. R., Khamzin, A. A., and Ghassib, H. B. (2000c). International Journal of Theoretical Physics 39, 405.CrossRefMATHGoogle Scholar
  24. Nigmatullin, R. R. and Toboev, V. A. (1989). Theoretical and Mathematical Physics 80, 94.CrossRefMathSciNetGoogle Scholar
  25. Nunes, G. J., Jin, C., Hawthorne, D. L., Putnam, A. M., and Lee, D. M. (1992). Physical Review B 46, 9082.CrossRefADSGoogle Scholar
  26. Pathria, R. K. (2004). Statistical Mechanics, 4th edn., Pergamon Press, Oxford.Google Scholar
  27. Stoof, H. C., Bijlsma, M., and Houbiers, M. (1996). Journal of Research of the National Institute of Standards and Technology 101, 443.Google Scholar
  28. Villard, B., Nacher, P. N., and Tastevn, G. (2000). Physica B 284–288, 178.CrossRefGoogle Scholar
  29. Wilks, J. (1967). The Properties of Liquid and Solid Helium, Clarendon, Oxford.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • A. S. Sandouqa
    • 1
  • M. K. Al-Sugheir
    • 2
  • H. B. Ghassib
    • 1
    • 3
  1. 1.Department of PhysicsUniversity of JordanAmmanJordan
  2. 2.Department of PhysicsThe Hashemite UniversityZarqaJordan
  3. 3.Department of Physics, Faculty of ScienceUniversity of JordanAmmanJordan

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