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Nuclear collective dynamics within Vlasov approach

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Abstract

We discuss, in an investigation based on Vlasov equation, the properties of the isovector modes in nuclear matter and atomic nuclei in relation with the symmetry energy. We obtain numerically the dipole response and determine the strength function for various systems, including a chain of Sn isotopes. We consider for the symmetry energy three parameterizations with density providing similar values at saturation but which manifest very different slopes around this point. In this way we can explore how the slope affects the collective response of finite nuclear systems. We focus first on the dipole polarizability and show that while the model is able to describe the expected mass dependence, A 5/3, it also demonstrates that this quantity is sensitive to the slope parameter of the symmetry energy. Then, by considering the Sn isotopic chain, we investigate the emergence of a collective mode, the Pygmy Dipole Resonance (PDR), when the number of neutrons in excess increases. We show that the total energy-weighted sum rule exhausted by this mode has a linear dependence with the square of isospin I = (N − Z)/A, again sensitive to the slope of the symmetry energy with density. Therefore the polarization effects in the isovector density have to play an important role in the dynamics of PDR. These results provide additional hints in the investigations aiming to extract the properties of symmetry energy below saturation.

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References

  1. J.H. Jeans, Mon. Not. R. Astron. Soc. 76, 71 (1913)

    Google Scholar 

  2. A.A. Vlasov, Zh. Eksp. Teor. Fiz. 8, 291 (1938)

    MATH  Google Scholar 

  3. C.K. Birdsall, A.B. Langdon, Plasma Physics via Computer Simulations (Taylor and Francis, 1991)

  4. P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer, New York, 1980)

  5. M. Di Toro, U. Lombardo, G. Russo, Workshop on Fluid Dynamical Approaches to the Many-Body Problem: Fundamental and Mathematical Aspects, Catania, Italy, 1984, Nuovo Cimento A 87, 174 (1985)

    Google Scholar 

  6. F. Calvayrac, P.-G. Reinhard, E. Suraud, Ann. Phys. 225, 125 (1997)

    Article  ADS  Google Scholar 

  7. A. Dellafiore, F. Matera, F.A. Brieva, Phys. Rev. B 61, 2316 (2000)

    Article  ADS  Google Scholar 

  8. Th. Fennel et al., Rev. Mod. Phys. 82, 1793 (2010)

    Article  ADS  Google Scholar 

  9. G. Manfredi, P.A. Hervieux, Phys. Rev. B 70, 201402 (2004)

    Article  ADS  Google Scholar 

  10. N. Crouseilles, P.A. Hervieux, G. Manfredi, Phys. Rev. B 78, 155412 (2008)

    Article  ADS  Google Scholar 

  11. D.M. Brink, M. Di Toro, Nucl. Phys. A 372, 151 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  12. J.E. Moyal, Proc. Cambridge Phil. Soc. 45, 99 (1949)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. G. Manfredi, Fields Inst. Commun. 46, 263 (2005)

    MathSciNet  Google Scholar 

  14. G.F. Bertsch, Prog. Part. Nucl. Phys. 4, 483 (1980)

    Article  ADS  Google Scholar 

  15. P.-G. Reinhard, E. Suraud, Ann. Phys. 239, 193 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. P.-G. Reinhard, E. Suraud, Ann. Phys. 239, 216 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  17. H. Kohl, P. Schuck, S. Stringari, Nucl. Phys. A 459, 265 (1986)

    Article  ADS  Google Scholar 

  18. A. Bonasera, V.N. Kondratyev, A. Smerzi, E.A. Remler, Phy. Rev. Lett. 71, 505 (1993)

    Article  ADS  Google Scholar 

  19. A. Dellafiore, F. Matera, D.M. Brink, Phys. Rev. A 51, 914 (1995)

    Article  ADS  Google Scholar 

  20. B.K. Jennings, A.D. Jackson, Phys. Rep. 66, 141 (1980)

    Article  ADS  Google Scholar 

  21. D.M. Brink, A. Dellafiore, M. Di Toro, Nucl. Phys. A 456, 205 (1986)

    Article  ADS  Google Scholar 

  22. A. Dellafiore, F. Matera, Nucl. Phys. A 460, 245 (1986)

    Article  ADS  Google Scholar 

  23. F. Burgio, M. Di Toro, Nucl. Phys. A 476, 189 (1988)

    Article  ADS  Google Scholar 

  24. V.I. Abrosimov, M. Di Toro, V. Strutinsky, Nucl. Phys. A 562, 41 (1993)

    Article  ADS  Google Scholar 

  25. V.I. Abrosimov, A. Dellafiore, F. Matera, Phys. Part. Nucl. 36, 699 (2005)

    Google Scholar 

  26. E.B. Balbutsev, P. Schuck, Ann. Phys. 322, 489 (2007)

    Article  ADS  MATH  Google Scholar 

  27. M. Urban, Phys. Rev. C 85, 034322 (2012)

    Article  ADS  Google Scholar 

  28. M. Di Toro, V.M. Kolomietz, Z. Phys. A 328, 285 (1987)

    ADS  Google Scholar 

  29. M. Urban, P. Schuck, Phys. Rev. A 73, 013621 (2006)

    Article  ADS  Google Scholar 

  30. V.I. Abrosimov, D.M. Brink, A. Dellafiore, F. Matera, Nucl. Phys. A 800, 1 (2008)

    Article  ADS  Google Scholar 

  31. V.I. Abrosimov, D.M. Brink, A. Dellafiore, F. Matera, Nucl. Phys. A 864, 205 (2011)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. D.M. Rossi et al., Phys. Rev. Lett. 111, 242503 (2013)

    Article  ADS  Google Scholar 

  35. B. Jacquot, A. Guarnera, Ph. Chomaz, M. Colonna, Phys. Rev. C 54, 3025 (1996)

    Article  ADS  Google Scholar 

  36. V. Baran, M. Colonna, M. Di Toro, A.B. Larionov, Nucl. Phys. A 632, 287 (1998)

    Article  ADS  Google Scholar 

  37. V. Baran, M. Colonna, M. Di Toro, V. Greco, Phys. Rev. Lett. 86, 4492 (2001)

    Article  ADS  Google Scholar 

  38. S.S. Avancini, L. Brito, D.P. Menezes, C. Providencia, Phys. Rev. C 71, 044323 (2005)

    Article  ADS  Google Scholar 

  39. C. Ducoin, J. Margueron, Ph. Chomaz, Nucl. Phys. A 809, 30 (2008)

    Article  ADS  Google Scholar 

  40. G. Fabbri, F. Matera, Phys. Rev. C 58, 1345 (1998)

    Article  ADS  Google Scholar 

  41. A.B. Larionov, M. Cabibbo, V. Baran, M. Di Toro, Nucl. Phys. A 648, 157 (1999)

    Article  ADS  Google Scholar 

  42. V. Baran, M. Colonna, M. Di Toro, A.B. Larionov, Proceedings of the 6th International Topical Conference on Giant Resonances, Varenna, Italy, 1998, Nucl. Phys. A 649, 185 (1999)

  43. E.A. Uehling, G.E. Uhlenbeck, Phys. Rev. 43, 552 (1933)

    Article  ADS  Google Scholar 

  44. G.F. Bertsch, S. Das Gupta, Phys. Rep. 160, 189 (1988)

    Article  ADS  Google Scholar 

  45. A. Bonasera, F. Gulminelli, J. Molitoris, Phys. Rep. 243, 1 (1994)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  47. V. Baran et al., Nucl. Phys. A 679, 373 (2001)

    Article  ADS  Google Scholar 

  48. V. Baran, D.M. Brink, M. Colonna, M. Di Toro, Phys. Rev. Lett. 87, 182501 (2001)

    Article  ADS  Google Scholar 

  49. V.N. Kondratyev, A. Bonasera, A. Iwamoto, Phys. Rev. C 61, 044613 (2000)

    Article  ADS  Google Scholar 

  50. A.B. Larionov, I.N. Mishustin, L.M. Safarov, W. Greiner, Phys. Rev. C 78, 014604 (2008)

    Article  ADS  Google Scholar 

  51. S. Plumari et al., Phys. Lett. B 689, 18 (2010)

    Article  ADS  Google Scholar 

  52. C. Gregoire et al., Nucl. Phys. A 465, 77 (1987)

    Article  Google Scholar 

  53. P. Schuck et al., Prog. Part. Nucl. Phys. 22, L81 (1989)

    Article  Google Scholar 

  54. A.B. Langdon, C.K. Birdsall, Phys. Fluids 13, 2115 (1970)

    Article  ADS  Google Scholar 

  55. D. Idier, B. Benhassine, M. Farine, B. Remaud, F. Sebille, Nucl. Phys. A 564, 204 (1993)

    Article  ADS  Google Scholar 

  56. V. Baran, M. Colonna, M. Di Toro, A. Croitoru, D. Dumitru, Phys. Rev. C 88, 044610 (2013)

    Article  ADS  Google Scholar 

  57. V. Baran, B. Frecus, M. Colonna, M. Di Toro, Phys. Rev. C 85, 051601 (2012)

    Article  ADS  Google Scholar 

  58. V. Baran et al., Rom. J. Phys. 57, 36 (2012)

    Google Scholar 

  59. P.-G. Reinhard, P.D. Stevenson, D. Almehed, J.A. Maruhn, M.R. Strayer, Phys. Rev. E 73, 036709 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  61. A. Migdal, J. Phys. 8, 331 (1944)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  63. V.I. Abrosimov, O.I. Davydovs’ka, Ukr. J. Phys. 54, 1068 (2009)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  65. T. Aumann, T. Nakamura, Phys. Scr. T 152, 014012 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  67. N. Paar, J. Phys. G 37, 064014 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  70. D.P. Arteaga, E. Khan, P. Ring, Phys. Rev. C 79, 034311 (2009)

    Article  ADS  Google Scholar 

  71. I. Daoutidis, S. Goriely, Phys. Rev. C 86, 034328 (2012)

    Article  ADS  Google Scholar 

  72. P. Papakonstantinou, H. Hergert, V.Yu. Ponomarev, R. Roth, Phys. Rev. C 89, 034306 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  74. N. Paar, Y.F. Niu, D. Vretenar, J. Meng, Phys. Rev. Lett. 103, 032502 (2009)

    Article  ADS  Google Scholar 

  75. N. Tsoneva, H. Lenske, Ch. Stoyanov, Phys. Lett. B 586, 213 (2004)

    Article  ADS  Google Scholar 

  76. E. Litvinova, P. Ring, V. Tselyaev, K. Langanke, Phys. Rev. C 79, 054312 (2009)

    Article  ADS  Google Scholar 

  77. M.P. Brine, P.D. Stevenson, J.A. Mahrun, P.-G. Reinhard, Int. J. Mod. Phys. E 15, 1417 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Physics, University of Bucharest, 077125, Bucharest-Măgurele, Romania

    Virgil Baran, Bogdan Frecus, Andreea Croitoru & Daniel Dumitru

  2. Laboratori Nazionali del Sud, INFN, 95123, Catania, Italy

    Maria Colonna

  3. Physics and Astronomy Department, University of Catania, 95124, Catania, Italy

    Massimo Di Toro

Authors
  1. Virgil Baran
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  2. Maria Colonna
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  3. Massimo Di Toro
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  4. Bogdan Frecus
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  5. Andreea Croitoru
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  6. Daniel Dumitru
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Correspondence to Virgil Baran.

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Baran, V., Colonna, M., Di Toro, M. et al. Nuclear collective dynamics within Vlasov approach. Eur. Phys. J. D 68, 356 (2014). https://doi.org/10.1140/epjd/e2014-50171-x

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  • DOI: https://doi.org/10.1140/epjd/e2014-50171-x

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