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Symmetry energy constraints from giant resonances: A relativistic mean-field theory overview

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Abstract.

Giant resonances encapsulate the dynamic response of the nuclear ground state to external perturbations. As such, they offer a unique view of the nucleus that is often not accessible otherwise. Although interesting in their own right, giant resonances are also enormously valuable in providing stringent constraints on the equation of state of asymmetric matter. With this view in mind, we focus on two modes of excitation that are essential in reaching this goal: the isoscalar giant monopole resonance (GMR) and the isovector giant dipole resonance (GDR). GMR energies in heavy nuclei are sensitive to the symmetry energy because they probe the incompressibility of neutron-rich matter. Unfortunately, access to the symmetry energy is hindered by the relatively low neutron-proton asymmetry of stable nuclei. Thus, the measurement of GMR energies in exotic nuclei is strongly encouraged. In the case of the GDR, we find the electric dipole polarizability of paramount importance. Indeed, the electric dipole polarizability appears as one of two laboratory observables --with the neutron-skin thickness being the other-- that are highly sensitive to the density dependence of the symmetry energy. Finally, we identify the softness of skin and the nature of the pygmy resonance as important unsolved problems in nuclear structure.

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References

  1. P. Möller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995)

    ADS  Google Scholar 

  2. P. Möller, J.R. Nix, K.L. Kratz, At. Data Nucl. Data Tables 66, 131 (1996)

    Google Scholar 

  3. P. Möller, W.D. Myers, H. Sagawa, S. Yoshida, Phys. Rev. Lett. 108, 052501 (2012)

    ADS  Google Scholar 

  4. J. Duflo, Nucl. Phys. A 576, 29 (1994)

    ADS  Google Scholar 

  5. A. Zuker, Nucl. Phys. A 576, 65 (1994)

    ADS  Google Scholar 

  6. J. Duflo, A. Zuker, Phys. Rev. C 52, R23 (1995)

    ADS  Google Scholar 

  7. M.N. Harakeh, A. van der Woude, Giant Resonances-Fundamental High-frequency Modes of Nuclear Excitation (Clarendon, Oxford, 2001)

  8. N. Paar, D. Vretenar E. Khan, G. Colò, Rep. Prog. Phys. 70, 691 (2007)

    ADS  Google Scholar 

  9. H. Sagawa, S. Yoshida, X.R. Zhou, K. Yako, H. Sakai, Phys. Rev. C 76, 024301 (2007)

    ADS  Google Scholar 

  10. X. Roca-Maza et al., Phys. Rev. C 87, 034301 (2013)

    ADS  Google Scholar 

  11. J. Piekarewicz, M. Centelles, Phys. Rev. C 79, 054311 (2009)

    ADS  Google Scholar 

  12. B.A. Brown, Phys. Rev. Lett. 85, 5296 (2000)

    ADS  Google Scholar 

  13. R.J. Furnstahl, Nucl. Phys. A 706, 85 (2002)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  15. X. Roca-Maza, M. Centelles, X. Viñas, M. Warda, Phys. Rev. Lett. 106, 252501 (2011)

    ADS  Google Scholar 

  16. R. Hofstadter, Rev. Mod. Phys. 28, 214 (1956)

    ADS  Google Scholar 

  17. T. Donnelly, J. Dubach, I. Sick, Nucl. Phys. A 503, 589 (1989)

    ADS  Google Scholar 

  18. I. Angeli, K. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)

    ADS  Google Scholar 

  19. S. Abrahamyan et al., Phys. Rev. Lett. 108, 112502 (2012)

    ADS  Google Scholar 

  20. C.J. Horowitz et al., Phys. Rev. C 85, 032501 (2012)

    ADS  Google Scholar 

  21. S.J. Pollock, E.N. Fortson, L. Wilets, Phys. Rev. C 46, 2587 (1992)

    ADS  Google Scholar 

  22. T. Sil, M. Centelles, X. Viñas, J. Piekarewicz, Phys. Rev. C 71, 045502 (2005)

    ADS  Google Scholar 

  23. J. Guena, M. Lintz, M.A. Bouchiat, Mod. Phys. Lett. A 20, 375 (2005)

    ADS  Google Scholar 

  24. J. Behr, G. Gwinner, J. Phys. G 36, 033101 (2009)

    ADS  Google Scholar 

  25. M.B. Tsang et al., Phys. Rev. Lett. 92, 062701 (2004)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  27. A.W. Steiner, B.A. Li, Phys. Rev. C 72, 041601 (2005)

    ADS  Google Scholar 

  28. D.V. Shetty, S.J. Yennello, G.A. Souliotis, Phys. Rev. C 76, 024606 (2007)

    ADS  Google Scholar 

  29. M.B. Tsang et al., Phys. Rev. Lett. 102, 122701 (2009)

    ADS  Google Scholar 

  30. C.J. Horowitz, J. Piekarewicz, Phys. Rev. Lett. 86, 5647 (2001)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  32. C.J. Horowitz, J. Piekarewicz, Phys. Rev. C 66, 055803 (2002)

    ADS  Google Scholar 

  33. J. Carriere, C.J. Horowitz, J. Piekarewicz, Astrophys. J. 593, 463 (2003)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  35. B.A. Li, A.W. Steiner, Phys. Lett. B 642, 436 (2006)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  37. F.J. Fattoyev, J. Piekarewicz, Phys. Rev. C 82, 025810 (2010)

    ADS  Google Scholar 

  38. J. Piekarewicz, Phys. Rev. C 76, 064310 (2007)

    ADS  Google Scholar 

  39. A. Carbone et al., Phys. Rev. C 81, 041301 (2010)

    ADS  Google Scholar 

  40. K. Hebeler, J. Lattimer, C. Pethick, A. Schwenk, Phys. Rev. Lett. 105, 161102 (2010)

    ADS  Google Scholar 

  41. A. Steiner, S. Gandolfi, Phys. Rev. Lett. 108, 081102 (2012)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  44. J.M. Lattimer, Annu. Rev. Nucl. Part. Sci. 62, 485 (2012)

    ADS  Google Scholar 

  45. J.D. Walecka, Ann. Phys. 83, 491 (1974)

    ADS  Google Scholar 

  46. B.D. Serot, Phys. Lett. B 86, 146 (1979)

    ADS  Google Scholar 

  47. R.J. Furnstahl, B.D. Serot, Comments Nucl. Part. Phys. 2, A23 (2000)

    Google Scholar 

  48. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)

    ADS  MathSciNet  Google Scholar 

  49. W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)

    ADS  MathSciNet  Google Scholar 

  50. W. Kohn, Rev. Mod. Phys. 71, 1253 (1999)

    ADS  Google Scholar 

  51. R.J. Furnstahl, B.D. Serot, H.B. Tang, Nucl. Phys. A 615, 441 (1997)

    ADS  Google Scholar 

  52. R.J. Furnstahl, B.D. Serot, H.B. Tang, Nucl. Phys. A 618, 446 (1997)

    ADS  Google Scholar 

  53. J.J. Rusnak, R.J. Furnstahl, Nucl. Phys. A 627, 495 (1997)

    ADS  Google Scholar 

  54. R.J. Furnstahl, J.C. Hackworth, Phys. Rev. C 56, 2875 (1997)

    ADS  Google Scholar 

  55. M. Kortelainen, R.J. Furnstahl, W. Nazarewicz, M. Stoitsov, Phys. Rev. C 82, 011304 (2010)

    ADS  Google Scholar 

  56. H. Mueller, B.D. Serot, Nucl. Phys. A 606, 508 (1996)

    ADS  Google Scholar 

  57. C.J. Horowitz, B.D. Serot, Nucl. Phys. A 368, 503 (1981)

    ADS  Google Scholar 

  58. B.D. Serot, J.D. Walecka, Adv. Nucl. Phys. 16, 1 (1986)

    Google Scholar 

  59. J. Boguta, A.R. Bodmer, Nucl. Phys. A 292, 413 (1977)

    ADS  MathSciNet  Google Scholar 

  60. D.H. Youngblood, H.L. Clark, Y.W. Lui, Phys. Rev. Lett. 82, 691 (1999)

    ADS  Google Scholar 

  61. Y.W. Lui, D.H. Youngblood, Y. Tokimoto, H.L. Clark, B. John, Phys. Rev. C 70, 014307 (2004)

    ADS  Google Scholar 

  62. M. Uchida et al., Phys. Lett. B 557, 12 (2003)

    ADS  Google Scholar 

  63. M. Uchida et al., Phys. Rev. C 69, 051301 (2004)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  65. T. Li et al., Phys. Rev. C 81, 034309 (2010)

    ADS  Google Scholar 

  66. U. Garg, D. Patel, private communication

  67. N.K. Glendenning, Compact Stars (Springer-Verlag, New York, 2000)

  68. P. Demorest, T. Pennucci, S. Ransom, M. Roberts, J. Hessels, Nature 467, 1081 (2010)

    ADS  Google Scholar 

  69. J. Antoniadis et al., Science 340, 6131 (2013)

    ADS  Google Scholar 

  70. B.G. Todd, J. Piekarewicz, Phys. Rev. C 67, 044317 (2003)

    ADS  Google Scholar 

  71. A.L. Fetter, J.D. Walecka, Quantum Theory of Many Particle Systems (McGraw-Hill, New York, 1971)

  72. W.H. Dickhoff, D. Van Neck, Many-Body Theory Exposed (World Scientific Publishing Co., 2005)

  73. J.F. Dawson, R.J. Furnstahl, Phys. Rev. C 42, 2009 (1990)

    ADS  Google Scholar 

  74. J. Piekarewicz, Phys. Rev. C 62, 051304 (2000)

    ADS  Google Scholar 

  75. J. Piekarewicz, Phys. Rev. C 64, 024307 (2001)

    ADS  Google Scholar 

  76. Z.Y. Ma, A. Wandelt, N. Van Giai, D. Vretenar, P. Ring, L.G. Cao, Nucl. Phys. A 703, 222 (2002)

    ADS  Google Scholar 

  77. G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2002)

    ADS  Google Scholar 

  78. J.P. Blaizot, J.F. Berger, J. Dechargé, M. Girod, Nucl. Phys. A 591, 435 (1995)

    ADS  Google Scholar 

  79. J. Piekarewicz, Phys. Rev. C 69, 041301 (2004)

    ADS  Google Scholar 

  80. J. Piekarewicz, Phys. Rev. C 66, 034305 (2002)

    ADS  Google Scholar 

  81. P.G. Reinhard, W. Nazarewicz, Phys. Rev. C 81, 051303 (2010)

    ADS  Google Scholar 

  82. J. Piekarewicz, Phys. Rev. C 83, 034319 (2011)

    ADS  Google Scholar 

  83. J. Piekarewicz et al., Phys. Rev. C 85, 041302(R) (2012)

    ADS  Google Scholar 

  84. X. Roca-Maza et al., Phys. Rev. C 88, 024316 (2013)

    ADS  Google Scholar 

  85. A. Tamii et al., Phys. Rev. Lett. 107, 062502 (2011)

    ADS  Google Scholar 

  86. I. Poltoratska et al., Phys. Rev. C 85, 041304 (2012)

    ADS  Google Scholar 

  87. W. Satula, R.A. Wyss, M. Rafalski, Phys. Rev. C 74, 011301 (2006)

    ADS  Google Scholar 

  88. G.A. Lalazissis, J. Konig, P. Ring, Phys. Rev. C 55, 540 (1997)

    ADS  Google Scholar 

  89. G.A. Lalazissis, S. Raman, P. Ring, At. Data Nucl. Data Tables 71, 1 (1999)

    ADS  Google Scholar 

  90. B.G. Todd-Rutel, J. Piekarewicz, Phys. Rev. Lett. 95, 122501 (2005)

    ADS  Google Scholar 

  91. A.W. Steiner, J.M. Lattimer, E.F. Brown, Astrophys. J. 722, 33 (2010)

    ADS  Google Scholar 

  92. F.J. Fattoyev, C.J. Horowitz, J. Piekarewicz, G. Shen, Phys. Rev. C 82, 055803 (2010)

    ADS  Google Scholar 

  93. F.J. Fattoyev, J. Piekarewicz, Phys. Rev. Lett 111, 162501 (2013)

    ADS  Google Scholar 

  94. W.C. Chen, J. Piekarewicz, M. Centelles, Phys. Rev. C 88, 024319 (2013)

    ADS  Google Scholar 

  95. J. Piekarewicz, Phys. Rev. C 76, 031301 (2007)

    ADS  Google Scholar 

  96. H. Sagawa, S. Yoshida, G.M. Zeng, J.Z. Gu, X.Z. Zhang, Phys. Rev. C 76, 034327 (2007)

    ADS  Google Scholar 

  97. A. Avdeenkov et al., Phys. Rev. C 79, 034309 (2009)

    ADS  Google Scholar 

  98. J. Piekarewicz, J. Phys. G 37, 064038 (2010)

    ADS  Google Scholar 

  99. L.G. Cao, H. Sagawa, G. Colò, Phys. Rev. C 86, 054313 (2012)

    ADS  Google Scholar 

  100. D. Patel et al., Phys. Lett. B 718, 447 (2012)

    ADS  Google Scholar 

  101. J. Li, G. Colò, J. Meng, Phys. Rev. C 78, 064304 (2008)

    ADS  Google Scholar 

  102. E. Khan, Phys. Rev. C 80, 011307 (2009)

    ADS  Google Scholar 

  103. E. Khan, Phys. Rev. C 80, 057302 (2009)

    ADS  Google Scholar 

  104. E. Khan, J. Margueron, G. Colò, K. Hagino, H. Sagawa, Phys. Rev. C 82, 024322 (2010)

    ADS  Google Scholar 

  105. P. Vesely, J. Toivanen, B.G. Carlsson, J. Dobaczewski, N. Michel, A. Pastore, Phys. Rev. C 86, 024303 (2012)

    ADS  Google Scholar 

  106. X. Roca-Maza, G. Colò, H. Sagawa, Phys. Rev. C 86, 031306 (2012)

    ADS  Google Scholar 

  107. Y. Suzuki, K. Ikeda, H. Sato, Prog. Theor. Phys. 83, 180 (1990)

    ADS  Google Scholar 

  108. P. Van Isacker, D.D. Nagarajan, M.A. Warner, Phys. Rev. C 45, R13 (1992)

    ADS  Google Scholar 

  109. I. Hamamoto, H. Sagawa, X.Z. Zhang, Phys. Rev. C 53, 765 (1996)

    ADS  Google Scholar 

  110. I. Hamamoto, H. Sagawa, X.Z. Zhang, Phys. Rev. C 57, R1064 (1998)

    ADS  Google Scholar 

  111. D. Vretenar, N. Paar, P. Ring, G.A. Lalazissis, Phys. Rev. C 63, 047301 (2001)

    ADS  Google Scholar 

  112. D. Vretenar, N. Paar, P. Ring, G.A. Lalazissis, Nucl. Phys. A 692, 496 (2001)

    ADS  Google Scholar 

  113. N. Paar, P. Ring, T. Niksic, D. Vretenar, Phys. Rev. C 67, 034312 (2003)

    ADS  Google Scholar 

  114. N. Tsoneva, H. Lenske, C. Stoyanov, Phys. Lett. B 586, 213 (2004)

    ADS  Google Scholar 

  115. D. Sarchi, P.F. Bortignon, G. Colò, Phys. Lett. B 601, 27 (2004)

    ADS  Google Scholar 

  116. N. Paar, T. Niksic, D. Vretenar, P. Ring, Phys. Lett. B 606, 288 (2005)

    ADS  Google Scholar 

  117. J. Piekarewicz, Phys. Rev. C 73, 044325 (2006)

    ADS  Google Scholar 

  118. N. Tsoneva, H. Lenske, Phys. Rev. C 77, 024321 (2008)

    ADS  Google Scholar 

  119. A. Klimkiewicz et al., Phys. Rev. C 76, 051603 (2007)

    ADS  Google Scholar 

  120. P. Adrich et al., Phys. Rev. Lett. 95, 132501 (2005)

    ADS  Google Scholar 

  121. O. Wieland et al., Phys. Rev. Lett. 102, 092502 (2009)

    ADS  Google Scholar 

  122. D. Rossi et al., J. Phys. Conf. Ser. 420, 012072 (2013)

    ADS  Google Scholar 

  123. D. Savran, T. Aumann, A. Zilges, Prog. Part. Nucl. Phys. 70, 210 (2013)

    ADS  Google Scholar 

  124. UNEDF Collaboration, Building a universal nuclear energy density functional, http://unedf.org

  125. M. Kortelainen et al., Phys. Rev. C 82, 024313 (2010)

    ADS  Google Scholar 

  126. F.J Fattoyev, J. Piekarewicz, Phys. Rev. C 84, 064302 (2011)

    ADS  Google Scholar 

  127. F.J. Fattoyev, J. Piekarewicz, Phys. Rev. C 88, 015802 (2012)

    ADS  Google Scholar 

  128. J. Erler, C.J. Horowitz, W. Nazarewicz, M. Rafalski, P.G. Reinhard, Phys. Rev. C 87, 044320 (2013)

    ADS  Google Scholar 

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Correspondence to J. Piekarewicz.

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Communicated by A. Ramos

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

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Piekarewicz, J. Symmetry energy constraints from giant resonances: A relativistic mean-field theory overview. Eur. Phys. J. A 50, 25 (2014). https://doi.org/10.1140/epja/i2014-14025-x

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