Symmetry energy: nuclear masses and neutron stars

  • J. M. Pearson
  • N. Chamel
  • A. F. Fantina
  • S. Goriely
Regular Article - Theoretical Physics
Part of the following topical collections:
  1. Topical issue on Nuclear Symmetry Energy


We describe the main features of our most recent Hartree-Fock-Bogoliubov nuclear mass models, based on 16-parameter generalized Skyrme forces. They have been fitted to the data of the 2012 Atomic Mass Evaluation, and favour a value of 30MeV for the symmetry coefficient J , the corresponding root-mean square deviation being 0.549MeV. We find that this conclusion is compatible with measurements of neutron-skin thickness. By constraining the underlying interactions to fit various equations of state of neutron matter calculated ab initio our models are well adapted to a realistic and unified treatment of all regions of neutron stars. We use our models to calculate the composition, the equation of state, the mass-radius relation and the maximum mass. Comparison with observations of neutron stars again favours a value of J = 30 MeV.


Neutron Star Symmetry Energy Drip Line Skyrme Force Neutron Drip Line 
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  1. 1.
    G. Audi, M. Wang, A.H. Wapstra, F.G. Kondev, M. MacCormick, X. Xu, B. Pfeiffer, Chin. Phys. C 36, 1287 (2012).CrossRefGoogle Scholar
  2. 2.
    J.M. Pearson, Hyperfine Interact. 132, 59 (2001).ADSCrossRefGoogle Scholar
  3. 3.
    N. Chamel, P. Haensel, Living Rev. Relativ. 11, 10 (2008) Scholar
  4. 4.
    S. Goriely, N. Chamel, J.M. Pearson, Phys. Rev. C 82, 035804 (2010).ADSCrossRefGoogle Scholar
  5. 5.
    M.B. Tsang, J.R. Stone, F. Camera, P. Danielewicz, S. Gandolfi, K. Hebeler, C.J. Horowitz, J. Lee, W.G. Lynch, Z. Kohley, R. Lemmon, P. Möller, T. Murakami, S. Riordan, X. Roca-Maza, F. Sammarruca, A.W. Steiner, I. Vidaña, S.J. Yennello, Phys. Rev. C 86, 015803 (2012).ADSCrossRefGoogle Scholar
  6. 6.
    Bao-An Li, Àngels Ramos, Giuseppe Verde, Isaac Vidaña, Eur. Phys. J. A 50, 9 (2014).ADSCrossRefGoogle Scholar
  7. 7.
    S.B. Rüster, M. Hempel, J. Schaffner-Bielich, Phys. Rev. C 73, 035804 (2006).ADSCrossRefGoogle Scholar
  8. 8.
    J.M. Pearson, S. Goriely, N. Chamel, Phys. Rev. C 83, 065810 (2011).ADSCrossRefGoogle Scholar
  9. 9.
    S. Goriely, N. Chamel, J.M. Pearson, Phys. Rev. C 88, 024308 (2013).ADSCrossRefGoogle Scholar
  10. 10.
    R.N. Wolf, D. Beck, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, N. Chamel, S. Goriely, F. Herfurth, M. Kowalska, S. Kreim, D. Lunney, V. Manea, E. Minaya Ramirez, S. Naimi, D. Neidherr, M. Rosenbusch, L. Schweikhard, J. Stanja, F. Wienholtz, K. Zuber, Phys. Rev. Lett. 110, 041101 (2013).ADSCrossRefGoogle Scholar
  11. 11.
    J.W. Negele, D. Vautherin, Nucl. Phys. A 207, 298 (1973).ADSCrossRefGoogle Scholar
  12. 12.
    M. Baldo, E. E. Saperstein, S. V. Tolokonnikov, Eur. Phys. J. A 32, 97 (2007).ADSCrossRefGoogle Scholar
  13. 13.
    F. Grill, J. Margueron, N. Sandulescu, Phys. Rev. C 84, 065801 (2011).ADSCrossRefGoogle Scholar
  14. 14.
    N. Chamel, S. Naimi, E. Khan, J. Margueron, Phys. Rev. C 75, 055806 (2007).ADSCrossRefGoogle Scholar
  15. 15.
    P. Magierski, P.-H. Heenen, Phys. Rev. C 65, 045804 (2002).ADSCrossRefGoogle Scholar
  16. 16.
    P. Gögelein, E.N.E. van Dalen, C. Fuchs, H. Müther, Phys. Rev. C 77, 025802 (2008).ADSCrossRefGoogle Scholar
  17. 17.
    W.G. Newton, J.R. Stone, Phys. Rev. C 79, 055801 (2009).ADSCrossRefGoogle Scholar
  18. 18.
    M. Onsi, A.K. Dutta, H. Chatri, S. Goriely, N. Chamel, J.M. Pearson, Phys. Rev. C 77, 065805 (2008).ADSCrossRefGoogle Scholar
  19. 19.
    J.M. Pearson, N. Chamel, S. Goriely, C. Ducoin, Phys. Rev. C 85, 065803 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    J.M. Pearson, Y. Aboussir, A.K. Dutta, R.C. Nayak, M. Farine, F. Tondeur, Nucl. Phys. A 528, 1 (1991).ADSCrossRefGoogle Scholar
  21. 21.
    J.M. Lattimer, Annu. Rev. Nucl. Part. Sci. 62, 485 (2012).ADSCrossRefGoogle Scholar
  22. 22.
    N. Chamel, S. Goriely, J.M. Pearson, Phys. Rev. C 80, 065804 (2009).ADSCrossRefGoogle Scholar
  23. 23.
    N. Chamel, S. Goriely, Phys. Rev. C 82, 045804 (2010).ADSCrossRefGoogle Scholar
  24. 24.
    B. Friedman, V.R. Pandharipande, Nucl. Phys. A 361, 502 (1981).ADSCrossRefGoogle Scholar
  25. 25.
    A. Akmal, V.R. Pandharipande, D.G. Ravenhall, Phys. Rev. C 58, 1804 (1998).ADSCrossRefGoogle Scholar
  26. 26.
    Z.H. Li, H.-J. Schulze, Phys. Rev. C 78, 028801 (2008).ADSCrossRefGoogle Scholar
  27. 27.
    G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003).ADSCrossRefGoogle Scholar
  28. 28.
    N. Chamel, A.F. Fantina, J.M. Pearson, S. Goriely, Phys. Rev. C 84, 062802(R) (2011).ADSCrossRefGoogle Scholar
  29. 29.
    R.C. Tolman, Phys. Rev. 55, 364 (1939).ADSCrossRefGoogle Scholar
  30. 30.
    J.R. Oppenheimer, G.M. Volkoff, Phys. Rev. 55, 374 (1939).ADSCrossRefMATHGoogle Scholar
  31. 31.
    P.B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, J.W.T. Hessels, Nature 467, 1081 (2010).ADSCrossRefGoogle Scholar
  32. 32.
    J. Antoniadis, P.C.C. Freire, N. Wex, T.M. Tauris, R.S. Lynch, M.H. van Kerkwijk, M. Kramer, C. Bassa, V.S. Dhillon, T. Driebe, J.W.T. Hessels, V.M. Kaspi, V.I. Kondratiev, N. Langer, T.R. Marsh, M.A. McLaughlin, T.T. Pennucci, S.M. Ransom, I.H. Stairs, J. van Leeuwen, J.P.W. Verbiest, D.G. Whelan, Science 340, 1233232 (2013).CrossRefGoogle Scholar
  33. 33.
    N. Chamel, A.F. Fantina, J.M. Pearson, S. Goriely, Astron. Astrophys. 553, A22 (2013).ADSCrossRefGoogle Scholar
  34. 34.
    J. Jastrzebski, A. Trzcińska, P. Lubiński, B. Clos, F.J. Hartmann, T. von Egidy, S. Wycech, Int. J. Mod. Phys. E 13, 343 (2004).ADSCrossRefGoogle Scholar
  35. 35.
    P. Möller, J.R. Nix, At. Data Nucl. Data Tables 39, 213 (1988).ADSCrossRefGoogle Scholar
  36. 36.
    M. Farine, J.M. Pearson, B. Rouben, Nucl. Phys. A 304, 317 (1978).ADSCrossRefGoogle Scholar
  37. 37.
    J. Dong, W. Zuo, J. Gu, U. Lombardo, Phys. Rev. C 85, 034308 (2012).ADSCrossRefGoogle Scholar
  38. 38.
    S. Goriely, M. Samyn, J.M. Pearson, M. Onsi, Nucl. Phys. A 750, 425 (2005).ADSCrossRefGoogle Scholar
  39. 39.
    E. Gourgoulhon, lectures given at the Compstar 2010 School, arXiv:1003.5015v1.
  40. 40.
    A.W. Steiner, J.M. Lattimer, E.F. Brown, Astrophys. J. 722, 33 (2010).ADSCrossRefGoogle Scholar
  41. 41.
    P.G. Jonker, D. Steeghs, D. Chakrabarty, A.M. Juett, Astrophys. J. 665, L147 (2007).ADSCrossRefGoogle Scholar
  42. 42.
    C.O. Heinke, P.G. Jonker, R. Wijnands, C.J. Deloye, R.E. Taam, Astrophys. J. 691, 1035 (2009).ADSCrossRefGoogle Scholar
  43. 43.
    D. Page, J.M. Lattimer, M. Prakash, A.W. Steiner, Astrophys. J. 707, 1131 (2009).ADSCrossRefGoogle Scholar
  44. 44.
    D.L. Kaplan, D.A. Frail, B.M. Gaensler, E.V. Gotthelf, S.R. Kulkarni, P.O. Slane, A. Nechita, Astrophys. J. Suppl. 153, 269 (2004).ADSCrossRefGoogle Scholar
  45. 45.
    D.L. Kaplan, B.M. Gaensler, S.-R. Kulkarni, P.O. Slane, Astrophys. J. Suppl. 163, 344 (2006).ADSCrossRefGoogle Scholar
  46. 46.
    P.S. Shternin, D.G. Yakovlev, Astron. Lett. 34, 675 (2008).ADSCrossRefGoogle Scholar
  47. 47.
    T. Klähn, D. Blaschke, S. Typel, E.N. E.van Dalen, A. Faessler, C. Fuchs, T. Gaitanos, H. Grigorian, A. Ho, E.E. Kolomeitsev, M.C. Miller, G. Röpke, J. Trümper, D.N. Voskresensky, F. Weber, H.H. Wolter, Phys. Rev. C 74, 035802 (2006).ADSCrossRefGoogle Scholar
  48. 48.
    G.T. Garvey, W.J. Gerace, R.L. Jaffe, I. Talmi, I. Kelson, Rev. Mod. Phys. 41, S1 (1969).ADSCrossRefGoogle Scholar
  49. 49.
    J. Barea, A. Frank, J.G. Hirsch, P. Van Isacker, S. Pittel, V. Velazquez, Phys. Rev. C 77, 041304(R) (2008).ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • J. M. Pearson
    • 1
  • N. Chamel
    • 2
  • A. F. Fantina
    • 2
  • S. Goriely
    • 2
  1. 1.Dépt. de PhysiqueUniversité de MontréalMontréalCanada
  2. 2.Institut d’Astronomie et d’AstrophysiqueUniversité Libre de BruxellesBrusselsBelgium

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