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Symmetry energy of warm nuclear systems

  • Regular Article - Theoretical Physics
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Abstract

The temperature dependence of the symmetry energy and symmetry free energy coefficients of infinite nuclear matter and of finite nuclei is investigated. For infinite matter, both these coefficients are found to have a weaker dependence on temperature at densities close to saturation; at low but homogeneous densities, the temperature dependence becomes stronger. For finite systems, different definitions of symmetry energy coefficients are encountered in the literature yielding different values. A resolution to this problem is suggested from a global liquid-drop-inspired fit of the energies and free energies of a host of nuclei covering the entire periodic table. The hot nucleus is modeled in a subtracted finite-temperature Thomas-Fermi framework, with dynamical surface phonon coupling to nucleonic motion plugged in. Contrary to infinite nuclear matter, a substantial change in the symmetry energy coefficients is observed for finite nuclei with temperature.

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References

  1. M.B. Tsang, T.X. Liu, L. Shi, P. Danielewicz, C.K. Gelbke, X.D. Liu, W.G. Lynch, W.P. Tan, G. Verde, A. Wagner, Phys. Rev. Lett. 92, 062701 (2004).

    Article  ADS  Google Scholar 

  2. L.-W. Chen, C.M. Ko, B.-A. Li, Phys. Rev. Lett. 94, 032701 (2005).

    Article  ADS  Google Scholar 

  3. B.-A. Li, L.-W. Chen, Phys. Rev. C 72, 064611 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. M. Centelles, X. Roca-Maza, X. Viñas, M. Warda, Phys. Rev. Lett. 102, 122502 (2009).

    Article  ADS  Google Scholar 

  6. U. Garg et al., Nucl. Phys. A 788, 36 (2007).

    Article  ADS  Google Scholar 

  7. T. Li et al., Phys. Rev. Lett. 99, 162503 (2007).

    Article  ADS  Google Scholar 

  8. E. Baron, J. Cooperstein, S. Kahana, Phys. Rev. Lett. 55, 126 (1985).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. H.-Th. Janka, K. Langanke, A. Marek, G. Martínez-Pinedo, B. Müller, Phys. Rep. 442, 38 (2007).

    Article  ADS  Google Scholar 

  11. C.J. Horowitz, J. Piekarewicz, Phys. Rev. C 64, 062802 (2001).

    Article  ADS  Google Scholar 

  12. A.W. Steiner, Phys. Rev. C 77, 035805 (2008).

    Article  ADS  Google Scholar 

  13. L.F. Roberts, G. Shen, V. Cirigliano, J.A. Pons, S. Reddy, S.E. Woosley, Phys. Rev. Lett. 108, 061103 (2012).

    Article  ADS  Google Scholar 

  14. M. Dutra, O. Lourenco, J.S. Sà Martins, A. Delfinoi, J.R. Stone, P.D. Stevenson, Phys. Rev. C 85, 035201 (2012).

    Article  ADS  Google Scholar 

  15. B.K. Agrawal, J.N. De, S.K. Samaddar, Phys. Rev. Lett. 109, 262501 (2012).

    Article  ADS  Google Scholar 

  16. J. Xu, L.W. Chen, B.A. Li, H.R. Ma, Phys. Rev. C 75, 014607 (2007).

    Article  ADS  Google Scholar 

  17. J.N. De, S.K. Samaddar, Phys. Rev. C 85, 024310 (2012).

    Article  ADS  Google Scholar 

  18. S.K. Samaddar, J.N. De, X. Viñas, M. Centelles, Phys. Rev. C 76, 041602(R) (2007).

    Article  ADS  Google Scholar 

  19. Ch.C. Moustakidis, Phys. Rev. C 76, 025805 (2007).

    Article  ADS  Google Scholar 

  20. B. Friedman, V.R. Panpdharipande, Nucl. Phys. A 361, 502 (1981).

    Article  ADS  Google Scholar 

  21. G. Peilert, J. Randrup, H. Stocker, W. Greiner, Phys. Lett. B 260, 271 (1991).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. E. O’Connor, D. Gazit, C.J. Horowitz, A. Schwenk, N. Barnea, Phys. Rev. C 75, 055803 (2007).

    Article  ADS  Google Scholar 

  24. S. Mallik, J.N. De, S.K. Samaddar, S. Sarkar, Phys. Rev. C 77, 032201(R) (2008).

    Article  ADS  Google Scholar 

  25. J.N. De, S.K. Samaddar, Phys. Rev. C 78, 065204 (2008).

    Article  ADS  Google Scholar 

  26. S. K. Samaddar, J.N. De, X. Viñas, M. Centelles, Phys. Rev. C 80, 035803 (2009).

    Article  ADS  Google Scholar 

  27. J.N. De, S.K. Samaddar, B.K. Agrawal, Phys. Rev. C 82, 045201 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. J.N. De, S.K. Samaddar, X. Viñas, M. Centelles, I.N. Mishustin, W. Greiner, Phys. Rev. C 86, 024601 (2012).

    Article  ADS  Google Scholar 

  31. P. Donati, P.M. Poacher, P.F. Bortignon, R.A. Broglia, Phys. Rev. Lett. 72, 2835 (1994).

    Article  ADS  Google Scholar 

  32. R.W. Hasse, P. Schuck, Nucl. Phys. A 445, 205 (1985).

    Article  ADS  Google Scholar 

  33. M. Prakash, J. Wambach, Z.Y. Ma, Phys. Lett. B 128, 141 (1983).

    Article  ADS  Google Scholar 

  34. D.J. Dean, K. Langanke, J.M. Sampaio, Phys. Rev. C 66, 045802 (2002).

    Article  ADS  Google Scholar 

  35. S.J. Lee, A.Z. Mekjian, Phys. Rev. C 82, 064319 (2010).

    Article  ADS  Google Scholar 

  36. J.N. De, S.K. Samaddar, Phys. Rev. C 85, 024310 (2012).

    Article  ADS  Google Scholar 

  37. E. Suraud, Nucl. Phys. A 462, 109 (1987).

    Article  ADS  Google Scholar 

  38. J.N. De, S.K. Samaddar, B.K. Agrawal, Phys. Lett. B 716, 361 (2012).

    Article  ADS  Google Scholar 

  39. J. Bartel, P. Quentin, M. Brack, C. Guet, H.B. Hakansson, Nucl. Phys. A 386, 79 (1982).

    Article  ADS  Google Scholar 

  40. E. Chabanat, P. Bonche, P. Haensel, J. Meyer, R. Schaeffer, Nucl. Phys. A 635, 231 (1998).

    Article  ADS  Google Scholar 

  41. B. K. Agrawal, S. Shlomo, V. Kim Au, Phys. Rev. C 68, 031304(R) (2003).

    Article  ADS  Google Scholar 

  42. P. Bonche, S. Levit, D. vautherin, Nucl. Phys. A 436, 265 (1985) S. Shlomo, J.B. Natowitz, Phys. Lett. B 252.

    Article  ADS  Google Scholar 

  43. T. Sil, J.N. De, S.K. Samaddar, X. Viñas, M. Centelles, B.K. Agrawal, S.K. Patra, Phys. Rev. C 66, 045803 (2002).

    Article  ADS  Google Scholar 

  44. J.N. De, S. Shlomo, S.K. Samaddar, Phys. Rev. C 57, 1398 (1998).

    Article  ADS  Google Scholar 

  45. S.K. Samaddar, J.N. De, X. Viñas, M. Centelles, Phys. Rev. C 75, 054608 (2007).

    Article  ADS  Google Scholar 

  46. S. Shlomo, J.B. Natowitz, Phys. Lett. B 252, 187 (1990).

    Article  ADS  Google Scholar 

  47. W.D. Myers, W.J. Swiatecki, Ann. Phys. (N.Y.) 55, 395 (1969).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. P. Danielewicz, J. Lee, Nucl. Phys. A 818, 36 (2009).

    Article  ADS  Google Scholar 

  50. E. Lipparini, S. Stringari, Phys. Lett. B 112, 421 (1982).

    Article  ADS  Google Scholar 

  51. H. Jiang, G.J. Fu, Y.M. Zhao, A. Arima, Phys. Rev. C 85, 024301 (2012).

    Article  ADS  Google Scholar 

  52. P.-G. Reinhard et al., Phys. Rev. C 73, 014309 (2006).

    Article  ADS  Google Scholar 

  53. M. Stoitsov, R.B. Cakirli, R.F. Casten, W. Nazarewicz, W. Satula, Phys. Rev. Lett. 98, 132502 (2007).

    Article  ADS  Google Scholar 

  54. M. Liu, N. Wang, Z.X. Li, F.S. Zhang, Phys. Rev. C 82, 064306 (2010).

    Article  ADS  Google Scholar 

  55. J.N. De, S.K. Samaddar, Phys. Rev. C 78, 065204 (2008).

    Article  ADS  Google Scholar 

  56. P. Klüpfel, P.-G. Reinhard, T.J. Bürnevich, J.A. Maruhn, Phys. Rev. C 79, 034310 (2009).

    Article  ADS  Google Scholar 

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Correspondence to B. K. Agrawal.

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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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Agrawal, B.K., De, J.N., Samaddar, S.K. et al. Symmetry energy of warm nuclear systems. Eur. Phys. J. A 50, 19 (2014). https://doi.org/10.1140/epja/i2014-14019-8

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  • DOI: https://doi.org/10.1140/epja/i2014-14019-8

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