Statistical Models of Heavy Ion Collisions and Their Parallels

  • Aram Z. Mekjian


Collisions between heavy ions produce highly fragmented nuclei, and at very high energies many new particles are produced. One approach to understanding the outcome of such collisions is based on statistical thermodynamics. This article discusses a simple statistical framework and shows its connection to several other approaches and fields. In the collision of two heavy ions or, in general, any two objects, the distribution of products and fragments is of concern. For example, the EOS collaboration1 reported a power law distribution of fragments with an exponent τ = 2.2. Namely, the number of clusters of size k falls as k −τ. This τ is related to the critical point properties of a nuclear liquid-gas phase transition, and using a percolative picture2 other critical exponents were obtained. Data on basalt-basalt collisions3 has a similar behavior: The number of fragments dN in a mass interval dm falls as dN/dm ~ m −τ with τ = 1.68, and this behavior occurs over 16 orders of magnitude in m. This feature also appears in the fragmentation of a piece of gypsum4 with an exponent τ = 1.63, and this property is used as an example of a behavior known as self-organized criticality.5 Even in the shuffling of a deck of cards, a power law can be found. Some of the specific ideas to be discussed will be illustrated with this simple example.


Spin Glass Bethe Lattice Spin Glass Model Simple Statistical Model Break Object 
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  1. 1.
    Gilkes, M. L., et al., 1994, Phys. Rev. Lett. 72:1590.ADSCrossRefGoogle Scholar
  2. 2.
    Stauffer, D., and Aharony, A., 1992, “Introduction to Percolation Theory,” Taylor and Francis, London.Google Scholar
  3. 3.
    Moore, H. J., and Gault, D. E., 1965, U. S. Geolog. Survey, Part B:127.Google Scholar
  4. 4.
    Oddershede, L., Dimon, P., and Bohr, J., 1993, Phys. Rev. Lett. 71:3107.ADSCrossRefGoogle Scholar
  5. 5.
    Bak, P., Tang, C, and Wiesenfeld, K., 1987, Phys. Rev. Lett. 59:381.MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Mekjian, A. Z., 1990, Phys. Rev. Lett. 64:2125; 1990, Phys. Rev. C41:2103.MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    Mekjian, A. Z., and Lee, S. J., 1991, Phys. Rev. A44:6294.ADSGoogle Scholar
  8. 8.
    Chase, K. C, and Mekjian, A. Z., 1996, Phys. Lett. B379:50.ADSGoogle Scholar
  9. 9.
    Chase, K. C, and Mekjian, A. Z., 1995, Phys. Rev. Lett. 75:4732.ADSCrossRefGoogle Scholar
  10. 10.
    Chase, K. C, Bhattacharya, P., and Mekjian, A. Z., 1998, Phys. Rev. C57:882.ADSGoogle Scholar
  11. 11.
    Mekjian, A. Z., and Chase, K. C, 1997, Phys. Lett. A229:340.MathSciNetADSGoogle Scholar
  12. 12.
    Bauer, W., Dean, D. R., Mosel, U., and Post, U., 1985, Phys. Lett. 150B:53.ADSGoogle Scholar
  13. 13.
    Campi, X., 1987, J. Phys. A19:L1003.Google Scholar
  14. 14.
    Pan, J., and DasGupta, S., 1995, Phys. Lett. B344:29; 1995, Phys. Rev. C51:1384.ADSGoogle Scholar
  15. 15.
    Edwards, S. F., and Anderson, P. W., 1975, J. Phys. F: Met. Phys. 5:965.ADSCrossRefGoogle Scholar
  16. 16.
    Sherrington, D., and Kirkpatrick, S., 1975, Phys. Rev. Lett. 35:1792.ADSCrossRefGoogle Scholar
  17. 17.
    Derrida, B., and Flyvbjerg, H., 1987, J. Phys. A20:5273; 1987, J. de Phys. 48:971.MathSciNetADSGoogle Scholar
  18. 18.
    Feynman, R. P., 1972, “Statistical Mechanics,” Addision-Wesley, Reading, MA.Google Scholar
  19. 19.
    Chase, K., Mekjian, A. Z., and Zamick, L., Rutgers University Report (unpublished).Google Scholar
  20. 20.
    DasGupta, S., and Mekjian, A. Z., 1998, Phys. Rev. CGoogle Scholar
  21. 21.
    Schroeder, M. R., 1991, “Fractals, Chaos, Power Laws,” Freeman, New York.zbMATHGoogle Scholar
  22. 22.
    Mandelbrot, B. B., 1982, “The Fractal Geometry of Nature,” Freeman, New York.zbMATHGoogle Scholar
  23. 23.
    Mézard, M., Parisi, G., Sourlas, N., Toulouse, G., and Virasoro, M., 1984, J. Phys. (Paris) 45:843.Google Scholar
  24. 24.
    Rajagopal, K., and Wilczek, F., 1993, Nucl. Phys. B309:395; 1993, B404:577.ADSCrossRefGoogle Scholar
  25. 25.
    Horn, D., and Silver, R., 1971, Ann. Phys. (NY) 66:509.ADSCrossRefGoogle Scholar
  26. 26.
    Kowalski, K. L., and Taylor, C. C., Case Western Reserve University Report No. 92-6 hep-ph/9211282.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Aram Z. Mekjian
    • 1
    • 2
  1. 1.Department of PhysicsRutgers UniversityPiscatawayUSA
  2. 2.Theoretical DivisionLos Alamos National LaboratoryLos AlamosUSA

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