Skip to main content
Log in

Density and temperature in heavy-ion collisions: A test of classical and quantum approaches

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

Different methods to extract the temperature and density in heavy-ion collisions (HIC) are compared using a statistical model tailored to reproduce many experimental features at low excitation energy. The model assumes a sequential decay of an excited nucleus and a Fermi-gas entropy. We first generate statistical events as a function of excitation energy but stopping the decay chain at the first step. In such a condition the “exact” model temperature is determined from the Fermi-gas relation to the excitation energy. From these events, using quantum fluctuation (QF) and classical fluctuation (CF) methods for protons and neutrons, we derive temperature and density (quantum case only) of the system under consideration. Additionally, the same quantities are also extracted using the double ratio (DR) method for different particle combinations. A very good agreement between the “exact” model temperatures and quantum fluctuation temperatures is obtained. The role of the density is discussed. Classical methods give a reasonable estimate of the temperature when the density is very low, as expected. The effects of secondary decays of the excited fragments are discussed as well.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B.A. Li, L.W. Chen, C.M. Ko, Phys. Rep. 464, 113 (2008).

    Article  ADS  Google Scholar 

  2. G. Giuliani, H. Zheng, A. Bonasera, Progr. Part. Nucl. Phys. 76, 116 (2014).

    Article  ADS  Google Scholar 

  3. V. Baran, M. Colonna, V. Greco, M. Di Toro, Phys. Rep. 410, 335 (2005).

    Article  ADS  Google Scholar 

  4. A.W. Steiner, M. Prakash, J.M. Lattimer, P.J. Ellis, Phys. Rep. 411, 325 (2005).

    Article  ADS  Google Scholar 

  5. J.M. Lattimer, M. Prakash, Phys. Rep. 442, 109 (2007).

    Article  ADS  Google Scholar 

  6. A. Bonasera, M. Bruno, C.O. Dorso, P.F. Mastinu, Riv. Nuovo Cimento 23, 2 (2000).

    Google Scholar 

  7. J.B. Natowitz et al., Phys. Rev. C 65, 034618 (2002).

    Article  ADS  Google Scholar 

  8. A. Kelić, J.B. Natowitz, K.H. Schmidt, Eur. Phys. J. A 30, 203 (2006).

    Article  ADS  Google Scholar 

  9. M.B. Tsang, F. Zhu, W.G. Lynch, A. Aranda, D.R. Bowman, R.T. de Souza, C.K. Gelbke, Y.D. Kim, L. Phair, S. Pratt, C. Williams, H.M. Xu, W.A. Friedman, Phys. Rev. C 53, R1057 (1996).

    Article  ADS  Google Scholar 

  10. S. Albergo, S. Costa, E. Costanzo, A. Rubbino, Nuovo Cimento A 89, 1 (1985).

    Article  ADS  Google Scholar 

  11. S. Das Gupta, J. Pan, M.B. Tsang, Phys. Rev. C 54, R2820 (1996).

    Article  ADS  Google Scholar 

  12. H. Xi, W.G. Lynch, M.B. Tsang, W.A. Friedman, D. Durand, Phys. Rev. C 59, 1567 (1999).

    Article  ADS  Google Scholar 

  13. L. Qin et al., Phys. Rev. Lett. 108, 172701 (2012).

    Article  ADS  Google Scholar 

  14. K. Hagel et al., Phys. Rev. Lett. 108, 062702 (2012).

    Article  ADS  Google Scholar 

  15. R. Wada et al., Phys. Rev. C 85, 064618 (2012).

    Article  ADS  Google Scholar 

  16. A. Mekjian, Phys. Rev. Lett. 38, 640 (1977).

    Article  ADS  Google Scholar 

  17. A.Z. Mekjian, Phys. Rev. C 17, 1051 (1978).

    Article  ADS  Google Scholar 

  18. T.C. Awes, G. Poggi, C.K. Gelbke, B.B. Back, B.G. Glagola, H. Breuer, V.E. Viola, Jr., Phys. Rev. C 24, 89 (1981).

    Article  ADS  Google Scholar 

  19. L.P. Csernai, J.I. Kapusta, Phys. Rep. 131, 223 (1986).

    Article  ADS  Google Scholar 

  20. G. Röpke, S. Shlomo, A. Bonasera, J.B. Natowitz, S.J. Yennello, A.B. McIntosh, J. Mabiala, L. Qin, S. Kowalski, K. Hagel, M. Barbui, K. Schmidt, G. Giulani, H. Zheng, S. Wuenschel, Phys. Rev. C 88, 024609 (2013).

    Article  ADS  Google Scholar 

  21. S. Wuenschel et al., Nucl. Phys. A 843, 1 (2010).

    Article  ADS  Google Scholar 

  22. H. Zheng, A. Bonasera, Phys. Lett. B 696, 178 (2011).

    Article  ADS  Google Scholar 

  23. H. Zheng, A. Bonasera, Phys. Rev. C 86, 027602 (2012).

    Article  ADS  Google Scholar 

  24. H. Zheng, G. Giuliani, A. Bonasera, Nucl. Phys. A 892, 43 (2012).

    Article  ADS  Google Scholar 

  25. H. Zheng, G. Giuliani, A. Bonasera, Phys. Rev. C 88, 024607 (2013).

    Article  ADS  Google Scholar 

  26. H. Zheng, G. Giuliani, A. Bonasera, J. Phys. G: Nucl. Part. Phys. 41, 055109 (2014).

    Article  ADS  Google Scholar 

  27. M. Papa, T. Maruyama, A. Bonasera, Phys. Rev. C 64, 024612 (2001).

    Article  ADS  Google Scholar 

  28. M. Papa, G. Giuliani, A. Bonasera, J. Comput. Phys. 208, 403 (2005).

    Article  ADS  MATH  Google Scholar 

  29. J. Mabiala, A. Bonasera, H. Zheng, A.B. McIntosh, Z. Kohley, P. Cammarata, K. Hagel, L. Heilborn, L.W. May, A. Raphelt, G.A. Souliotis, A. Zarrella, S.J. Yennello, Int. J. Mod. Phys. E 22, 1350090 (2013).

    Article  ADS  Google Scholar 

  30. B.C. Stein et al., J. Phys. G: Nucl. Part. Phys. 41, 025108 (2014).

    Article  ADS  Google Scholar 

  31. J. Esteve et al., Phys. Rev. Lett. 96, 130403 (2006).

    Article  ADS  Google Scholar 

  32. T. Müller et al., Phys. Rev. Lett. 105, 040401 (2010).

    Article  Google Scholar 

  33. C. Sanner et al., Phys. Rev. Lett. 105, 040402 (2010).

    Article  ADS  Google Scholar 

  34. C.I. Westbrook, Physics 3, 59 (2010).

    Article  Google Scholar 

  35. P. Marini, in preparation.

  36. R.J. Charity, Computer code GEMINI, see http://www.chemistry.wustl.edu/~rc.

  37. J.O. Newton, D.J. Hinde, R.J. Charity, J.R. Leigh, J.J.M. Bokhorst, A. Chatterjee, G.S. Foote, S. Ogaza, Nucl. Phys. A 483, 126 (1988).

    Article  ADS  Google Scholar 

  38. R.J. Charity et al., Nucl. Phys. A 483, 371 (1988).

    Article  ADS  Google Scholar 

  39. D.R. Bowman, G.F. Peaslee, N. Colonna, R.J. Charity, M.A. McMahan, D. Delis, H. Han, K. Jing, G.J. Wozniak, L.G. Moretto, W.L. Kehoe, B. Libby, A.C. Mignerey, A. Moroni, S. Angius, I. Iori, A. Pantaleo, G. Guarino, Nucl. Phys. A 523, 386 (1991).

    Article  ADS  Google Scholar 

  40. R.J. Charity, Phys. Rev. C 53, 512 (1996).

    Article  ADS  Google Scholar 

  41. R.J. Charity, Phys. Rev. C 61, 054614 (2000).

    Article  ADS  Google Scholar 

  42. L.G. Sobotka, R.J. Charity, J.Tõke, W.U. Schröder, Phys. Rev. Lett. 93, 132702 (2004).

    Article  ADS  Google Scholar 

  43. R.J. Charity, Phys. Rev. C 82, 014610 (2010).

    Article  ADS  Google Scholar 

  44. W.D. Tian, Y.G. Ma, X.Z. Cai, D.Q. Fang, W. Guo, W.Q. Shen, K. Wang, H.W. Wang, M. Veselsky, Phys. Rev. C 76, 024607 (2007).

    Article  ADS  Google Scholar 

  45. P. Zhou, W.D. Tian, Y.G. Ma, X.Z. Cai, D.Q. Fang, H.W. Wang, Phys. Rev. C 84, 037605 (2011).

    Article  ADS  Google Scholar 

  46. L. Landau, F. Lifshits, Statistical Physics (Pergamon, New York, 1980).

  47. K. Huang, Statistical Mechanics, second edition (J. Wiley and Sons, New York, 1987).

  48. L.G. Moretto, J.B. Elliott, L. Phair, P.T. Lake, J. Phys. G: Nucl. Part. Phys. 38, 113101 (2011).

    Article  ADS  Google Scholar 

  49. J.B. Elliott, P.T. Lake, L.G. Moretto, L. Phair, Phys. Rev. C 87, 054622 (2013).

    Article  ADS  Google Scholar 

  50. J.B. Elliott et al., Phys. Rev. C 67, 024609 (2003).

    Article  ADS  Google Scholar 

  51. J. Pochodzalla et al., Phys. Rev. Lett. 75, 1040 (1995).

    Article  ADS  Google Scholar 

  52. A. Bonasera et al., Phys. Rev. Lett. 101, 122702 (2008).

    Article  ADS  Google Scholar 

  53. J. Mabiala, in preparation.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. Zheng.

Additional information

Communicated by F. Gulminelli

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, H., Bonasera, G., Mabiala, J. et al. Density and temperature in heavy-ion collisions: A test of classical and quantum approaches. Eur. Phys. J. A 50, 167 (2014). https://doi.org/10.1140/epja/i2014-14167-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/i2014-14167-9

Keywords

Navigation