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Effects of the liquid-gas phase transition and cluster formation on the symmetry energy

  • Regular Article - Theoretical Physics
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Abstract

Various definitions of the symmetry energy are introduced for nuclei, dilute nuclear matter below saturation density and stellar matter, which is found in compact stars or core-collapse supernovae. The resulting differences are exemplified by calculations in a theoretical approach based on a generalized relativistic density functional for dense matter. It contains nucleonic clusters as explicit degrees of freedom with medium-dependent properties that are derived for light clusters from a quantum statistical approach. With such a model the dissolution of clusters at high densities can be described. The effects of the liquid-gas phase transition in nuclear matter and of cluster formation in stellar matter on the density dependence of the symmetry energy are studied for different temperatures. It is observed that correlations and the formation of inhomogeneous matter at low densities and temperatures causes an increase of the symmetry energy as compared to calculations assuming a uniform uncorrelated spatial distribution of constituent baryons and leptons.

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References

  1. W. Heisenberg, Z. Phys. 77, 1 (1932).

    Article  ADS  MathSciNet  Google Scholar 

  2. E. Wigner, Phys. Rev. C 51, 106 (1937).

    Article  ADS  Google Scholar 

  3. C.F. von Weizsäcker, Z. Phys. 96, 431 (1935).

    Article  ADS  MATH  Google Scholar 

  4. H.A. Bethe, R.F. Bacher, Rev. Mod. Phys. 8, 82 (1936).

    Article  ADS  Google Scholar 

  5. B.K. Agrawal, J.N. De, S.K. Samaddar, G.Colò, A. Sulaksono, Phys. Rev. C 87, 051306 (2013).

    Article  ADS  Google Scholar 

  6. J.M. Lattimer, Y. Lim, Astrophys. J. 771, 51 (2013).

    Article  ADS  Google Scholar 

  7. Bao-An Li, Xiao Han, Phys. Lett. B 727, 276 (2013).

    Article  ADS  Google Scholar 

  8. H. Sotani, K. Nakazato, K. Iida, K. Oyamatsu, Mon. Not. R. Astron. Soc. 434, 2060 (2013).

    Article  ADS  Google Scholar 

  9. Ning Wang, Li Ou, Min Liu, Phys. Rev. C 87, 034327 (2013).

    Article  ADS  Google Scholar 

  10. K. Hebeler, J.M. Lattimer, C.J. Pethick, A. Schwenk, Astrophys. J. 773, 11 (2013).

    Article  ADS  Google Scholar 

  11. Zhen Zhang, Lie-Wen Chen, Phys. Lett. B 726, 234 (2013).

    Article  ADS  Google Scholar 

  12. Jianmin Dong, Wei Zuo, Jianzhong Gu, Phys. Rev. C 87, 014303 (2013).

    Article  Google Scholar 

  13. Lie-Wen Chen, arXiv:1212.0284 [nucl-th].

  14. P. Marini et al., Phys. Rev. C 87, 024603 (2013).

    Article  ADS  Google Scholar 

  15. F.J. Fattoyev, J. Carvajal, W.G. Newton, Bao-An Li, Phys. Rev. C 87, 015806 (2013).

    Article  ADS  Google Scholar 

  16. P. Russotto et al., J. Phys. Conf. Ser. 420, 012092 (2013).

    Article  ADS  Google Scholar 

  17. F.J. Fattoyev, W.G. Newton, Jun Xu, Bao-An Li, J. Phys. Conf. Ser. 420, 012108 (2013).

    Article  ADS  Google Scholar 

  18. Jianmin Dong, Wei Zuo, Jianzhong Gu, Umberto Lombardo, Phys. Rev. C 85, 034308 (2012).

    Article  Google Scholar 

  19. S. Gandolfi, J. Phys. Conf. Ser. 420, 012150 (2013).

    Article  ADS  Google Scholar 

  20. W. Trautmann, H.H. Wolter, Int. J. Mod. Phys. E 21, 1230003 (2013).

    Article  ADS  Google Scholar 

  21. M.B. Tsang et al., Phys. Rev. C 86, 015803 (2012).

    Article  ADS  Google Scholar 

  22. K. Hagel, contribution to this Topical Issue, arXiv:1401.2074 [nucl-ex].

  23. S. Kowalski et al., Phys. Rev. C 75, 014601 (2007).

    Article  ADS  Google Scholar 

  24. J. Natowitz et al., Phys. Rev. Lett. 104, 202501 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Ad.R. Raduta, F. Gulminelli, Phys. Rev. C 80, 024606 (2009).

    Article  ADS  Google Scholar 

  27. S. Typel, G. Röpke, T. Klähn, D. Blaschke, H.H. Wolter, Phys. Rev. C 81, 015803 (2010).

    Article  ADS  Google Scholar 

  28. A.S. Botvina, I.N. Mishustin, Nucl. Phys. A 843, 98 (2010).

    Article  ADS  Google Scholar 

  29. M. Hempel, J. Schaffner-Bielich, Nucl. Phys. A 837, 210 (2010).

    Article  ADS  Google Scholar 

  30. M. Hempel, J. Schaffner-Bielich, S. Typel, G. Röpke, Phys. Rev. C 84, 055804 (2011).

    Article  ADS  Google Scholar 

  31. M.D. Voskresenskaya, S. Typel, Nucl. Phys. A 887, 42 (2012).

    Article  ADS  Google Scholar 

  32. G. Röpke, N.-U. Bastian, D. Blaschke, T. Klähn, S. Typel, H.H. Wolter, Nucl. Phys. A 897, 70 (2013).

    Article  ADS  Google Scholar 

  33. N. Buyukcizmeci et al., Nucl. Phys. A 907, 1354 (2013).

    Article  Google Scholar 

  34. H. Müller, B.D. Serot, Phys. Rev. C 52, 2072 (1995).

    Article  ADS  Google Scholar 

  35. F. Gulminelli, Ad.R. Raduta, J. Margueron, P. Papakonstantinou, M. Oertel, J. Phys. Conf. Ser. 420, 012079 (2013).

    Article  ADS  Google Scholar 

  36. M. Hempel, V. Dexheimer, S. Schramm, I. Iosilevskiy, Phys. Rev. C 88, 014906 (2013).

    Article  ADS  Google Scholar 

  37. Guang-Hua Zhang, Wei-Zhou Jiang, Phys. Lett. B 720, 148 (2013).

    Article  ADS  Google Scholar 

  38. P. Danielewicz, J. Lee, Nucl. Phys. A 922, 1 (2014).

    Article  ADS  Google Scholar 

  39. D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75, 1021 (2003).

    Article  ADS  Google Scholar 

  40. P. Danielewicz, Nucl. Phys. A 727, 233 (2003).

    Article  ADS  Google Scholar 

  41. M. Wang, G. Audi, A.H. Wapstra, F.G. Kondev, M. MacCormick, X. Xu, B. Pfeiffer, Chin. Phys. 36, 1603 (2012).

    Article  Google Scholar 

  42. J. Duflo, A.P. Zuker, Phys. Rev. C 52, R23 (1995) and private communication to AMDC, http://amdc.in2p3.fr.

    Article  ADS  Google Scholar 

  43. X. Viñas, M. Centelles, X. Roca-Maza, M. Warda, arXiv:1308.1008 [nucl-th], contribution to this Topical Issue.

  44. A. Carbone, A. Polls, C. Providência, A. Rios, I. Vidaña, arXiv:1308.1416 [nucl-th], contribution to this Topical Issue.

  45. M. Colonna, V. Baran, M. Di Toro, H.H. Wolter, Phys. Rev. C 78, 064618 (2008).

    Article  ADS  Google Scholar 

  46. T. Klähn et al., Phys. Rev. C 74, 035802 (2006).

    Article  ADS  Google Scholar 

  47. C.J. Horowitz, A. Schwenk, Phys. Lett. B 638, 153 (2006).

    Article  ADS  Google Scholar 

  48. C.J. Horowitz, A. Schwenk, Nucl. Phys. A 776, 55 (2006).

    Article  ADS  Google Scholar 

  49. E. OConnor, D. Gazit, C.J. Horowitz, A. Schwenk, N. Barnea, Phys. Rev. C 77, 055803 (2007).

    Article  ADS  Google Scholar 

  50. C. Ducoin, Ph. Chomaz, F. Gulminelli, Nucl. Phys. A 771, 68 (2006).

    Article  ADS  Google Scholar 

  51. G. Röpke, Phys. Rev. C 79, 014002 (2009).

    Article  ADS  Google Scholar 

  52. G. Röpke, Nucl. Phys. A 867, 66 (2011).

    Article  ADS  Google Scholar 

  53. G. Audi, F.G. Kondev, M. Wang, B. Pfeiffer, X. Sun, J. Blachot, M. MacCormick, Chin. Phys. 36, 1157 (2012).

    Article  Google Scholar 

  54. M.K. Grossjean, H. Feldmeier, Nucl. Phys. A 444, 113 (1985).

    Article  ADS  Google Scholar 

  55. H.A. Bethe, Phys. Rev. 50, 332 (1936).

    Article  ADS  Google Scholar 

  56. H.A. Bethe, Rev. Mod. Phys. 9, 69 (1937).

    Article  ADS  MATH  Google Scholar 

Download references

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Correspondence to S. Typel.

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Communicated by A. Ramos

Contribution to the Topical Issue “Nuclear Symmetry Energy” edited by Bao-An Li, Ángels Ramos, Giuseppe Verde, Isaac Vidaña.

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Typel, S., Wolter, H.H., Röpke, G. et al. Effects of the liquid-gas phase transition and cluster formation on the symmetry energy. Eur. Phys. J. A 50, 17 (2014). https://doi.org/10.1140/epja/i2014-14017-x

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  • DOI: https://doi.org/10.1140/epja/i2014-14017-x

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