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Relationship between the symmetry energy and the single-nucleon potential in isospin-asymmetric nucleonic matter

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Abstract

In this contribution, we review the most important physics presented originally in our recent publications. Some new analyses, insights and perspectives are also provided. We showed recently that the symmetry energy E sym (ρ) and its density slope L(ρ) at an arbitrary density ρ can be expressed analytically in terms of the magnitude and momentum dependence of the single-nucleon potentials using the Hugenholtz-Van Hove (HVH) theorem. These relationships provide new insights about the fundamental physics governing the density dependence of nuclear symmetry energy. Using the isospin and momentum (k dependent MDI interaction as an example, the contribution of different terms in the single-nucleon potential to the E sym (ρ) and L(ρ) are analyzed in detail at different densities. It is shown that the behavior of E sym is mainly determined by the first-order symmetry potential U sym,1(ρ, k) of the single-nucleon potential. The density slope L(ρ) depends not only on the first-order symmetry potential U sym,1(ρ, k) but also on the second-order one U sym,2(ρ, k). Both the U sym,1(ρ, k) and U sym,2(ρ, k) at normal density ρ 0 are constrained by the isospin- and momentum-dependent nucleon optical potential extracted from the available nucleon-nucleus scattering data. The U sym,2(ρ, k) especially at high density and momentum affects significantly the L(ρ), but it is theoretically poorly understood and currently there is almost no experimental constraints known.

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References

  1. B.A. Li, C.M. Ko, W. Bauer, Int. J. Mod. Phys. E 7, 147 (1998).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Bao-An Li, W. Udo Schröer (Editors) Isospin Physics in Heavy-Ion Collisions at Intermediate Energies (Nova Science Publishers, Inc., New York, 2001).

  4. J.M. Lattimer, M. Prakash, Science 304, 536 (2004).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. P. Danielewicz, R. Lacey, W.G. Lynch, Science 298, 1592 (2002).

    Article  ADS  Google Scholar 

  7. P.J. Siemens, Nucl. Phys. A 141, 225 (1970).

    Article  ADS  Google Scholar 

  8. C.-H. Lee, T.T. Kuo, G.Q. Li, G.E. Brown, Phys. Rev. C 57, 3488 (1998).

    Article  ADS  Google Scholar 

  9. A.W. Steiner, Phys. Rev. C 74, 045808 (2006).

    Article  ADS  Google Scholar 

  10. O. Sjöberg, Nucl. Phys. A 222, 161 (1974).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. M. Di Toro, V. Baran, M. Colonna, V. Greco, J. Phys. G: Nucl. Part. Phys. 37, 083101 (2010).

    Article  ADS  Google Scholar 

  14. K. Sumiyoshi, H. Toki, Astrophys. J. 422, 700 (1994).

    Article  ADS  Google Scholar 

  15. I. Bombaci, in Isospin Physics in Heavy-Ion Collisions at Intermediate Energies (Nova Science Publishers, Inc., New York, 2001) Chapt. 2.

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. M.B. Tsang, Yingxun Zhang, P. Danielewicz, M. Famiano, Zhuxia Li, W.G. Lynch, A.W. Steiner, Phys. Rev. Lett. 102, 122701 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong, M. Zhang, Phys. Rev. Lett. 102, 062502 (2009).

    Article  ADS  Google Scholar 

  22. C.B. Das, S. Das Gupta, C. Gale, B.A. Li, Phys. Rev. C 67, 034611 (2003).

    Article  ADS  Google Scholar 

  23. B.A. Li, C.B. Das, S. Das Gupta, C. Gale, Phys. Rev. C 69, 011603(R) (2004).

    Article  ADS  Google Scholar 

  24. B.A. Li, C.B. Das, S. Das Gupta, C. Gale, Nucl. Phys. A 735, 563 (2004).

    Article  ADS  Google Scholar 

  25. S. Ulrych, H. Müther, Phys. Rev. C 56, 1788 (1997).

    Article  ADS  Google Scholar 

  26. E.N.E. van Dalen, C. Fuchs, A. Faessler, Nucl. Phys. A 74, 227 (2004).

    Article  Google Scholar 

  27. W. Zuo, L.G. Cao, B.A. Li, U. Lombardo, C.W. Shen, Phys. Rev. C 72, 014005 (2005).

    Article  ADS  Google Scholar 

  28. S. Fritsch, N. Kaiser, W. Weise, Nucl. Phys. A 750, 259 (2005).

    Article  ADS  Google Scholar 

  29. J.A. McNeil, J.R. Shepard, S.J. Wallace, Phys. Rev. Lett. 50, 1439 (1983).

    Article  ADS  Google Scholar 

  30. L.W. Chen, C.M. Ko, B.A. Li, Phys. Rev. C 72, 064606 (2005).

    Article  ADS  Google Scholar 

  31. Z.H. Li, L.W. Chen, C.M. Ko, B.A. Li, H.R. Ma, Phys. Rev. C 74, 044613 (2006).

    Article  ADS  Google Scholar 

  32. J.R. Stone, J.C. Miller, R. Koncewicz, P.D. Stevenson, M.R. Strayer, Phys. Rev. C 68, 034324 (2003).

    Article  ADS  Google Scholar 

  33. V.R. Pandharipande, V.K. Garde, Phys. Lett. B 39, 608 (1972).

    Article  ADS  Google Scholar 

  34. R.B. Wiringa et al., Phys. Rev. C 38, 1010 (1988).

    Article  ADS  Google Scholar 

  35. M. Kutschera, Phys. Lett. B 340, 1 (1994).

    Article  ADS  Google Scholar 

  36. C. Xu, B.A. Li, L.W. Chen, Phys. Rev. C 82, 054607 (2010).

    Article  ADS  Google Scholar 

  37. C. Xu, B.A. Li, L.W. Chen, C.M. Ko, Nucl. Phys. A 865, 1 (2011).

    Article  ADS  Google Scholar 

  38. C. Xu, B.A. Li, Phys. Rev. C 81, 044603 (2010).

    Article  ADS  Google Scholar 

  39. C. Xu, B.A. Li, Phys. Rev. C 81, 064612 (2010).

    Article  ADS  Google Scholar 

  40. R. Chen, B.J. Cai, L.W. Chen, B.A. Li, X.H. Li, C. Xu, Phys. Rev. C 85, 024305 (2012).

    Article  ADS  Google Scholar 

  41. X.H. Li, B.J. Cai, L.W. Chen, R. Chen, B.A. Li, C. Xu, Phys. Lett. B 721, 101 (2013).

    Article  ADS  Google Scholar 

  42. Nuclear Density Functional Theory, Nuclear Structure Near the Limits of Stability (INT-05-3) September 26 to December 2, 2005, http://www.int.washington.edu/PROGRAMS/dft.html.

  43. B.J. Cai, L.W. Chen, Phys. Lett. B 711, 104 (2012).

    Article  ADS  Google Scholar 

  44. N.M. Hugenholtz, L. Van Hove, Physica 24, 363 (1958).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  45. L. Satpathy, V.S. Uma Maheswari, R.C. Nayak, Phys. Rep. 319, 85 (1999).

    Article  ADS  Google Scholar 

  46. K.A. Brueckner, J. Dabrowski, Phys. Rev. 134, B722 (1964).

    Article  ADS  Google Scholar 

  47. J. Dabrowski, P. Haensel, Phys. Lett. B 42, 163 (1972).

    Article  ADS  Google Scholar 

  48. J. Dabrowski, P. Haensel, Phys. Rev. C 7, 916 (1973).

    Article  ADS  Google Scholar 

  49. J. Dabrowski, P. Haensel, Can. J. Phys. 52, 1768 (1974).

    ADS  Google Scholar 

  50. A.M. Lane, Nucl. Phys. 35, 676 (1962).

    Article  Google Scholar 

  51. J. Decharge, D. Gogny, Phys. Rev. C 21, 1568 (1980).

    Article  ADS  Google Scholar 

  52. Z.H. Li, L.W. Chen, C.M. Ko, B.A. Li, H.R. Ma, Phys. Rev. C 74, 044613 (2006).

    Article  ADS  Google Scholar 

  53. D.P. Murdock, C.J. Horowitz, Phys. Rev. C 35, 1442 (1987).

    Article  ADS  Google Scholar 

  54. J.A. McNeil, L. Ray, S.J. Wallace, Phys. Rev. C 27, 2123 (1983).

    Article  ADS  Google Scholar 

  55. E.N.E. van Dalen, C. Fuchs, A. Faessler, Phys. Rev. C 72, 065803 (2005).

    Article  ADS  Google Scholar 

  56. W. Zuo, U. Lombardo, H.-J. Schulze, Z.H. Li, Phys. Rev. C 74, 014317 (2006).

    Article  ADS  Google Scholar 

  57. M.A. Preston, R.K. Bhaduri, Structure of the Nucleus (Addison-Wesley, Reading, MA, 1975) p. 191--202.

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

    Article  ADS  Google Scholar 

  59. P.E. Hodgson, The Nucleon Optical Potential (World Scientific Publishing, Sigapore, 1994) p. 7.

  60. G.R. Satchler, W.G. Love, Phys. Rep. 55, 183 (1979).

    Article  ADS  Google Scholar 

  61. C. Mahaux, R. Sartor, in Advances in Nuclear Physics, edited by J.W. Negele, E. Vogt, Vol. 20 (New York, Plenum, 1991), pp. 1-223.

  62. S. Hama, B.C. Clark, E.D. Cooper, H.S. Sherif, R.L. Mercer, Phys. Rev. C 41, 2737 (1990).

    Article  ADS  Google Scholar 

  63. A.J. Koning et al., Nucl. Phys. A 713, 231 (2003).

    Article  ADS  Google Scholar 

  64. J.-P. Jeukenne et al., Phys. Rev. C 43, 2211 (1991).

    Article  ADS  Google Scholar 

  65. J. Rapaport et al., Nucl. Phys. A 330, 15 (1979).

    Article  ADS  Google Scholar 

  66. R.P. De Vito, NSCL/MSU report-363 (1981).

  67. K. Kwiatkowski et al., Nucl. Phys. A 301, 349 (1978).

    Article  ADS  Google Scholar 

  68. D.M. Patterson et al., Nucl. Phys. A 263, 261 (1976).

    Article  ADS  Google Scholar 

  69. Y.L. Han et al., Phys. Rev. C 81, 024616 (2010).

    Article  ADS  Google Scholar 

  70. O.V. Bespalova et al., J. Phys. G 29, 1193 (2003).

    Article  ADS  Google Scholar 

  71. R.L. Varner et al., Phys. Rep. 201, 57 (1991).

    Article  ADS  Google Scholar 

  72. F.D. Becchetti, G.W. Greenlees, Phys. Rev. 182, 1190 (1969).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Nanjing University, 210008, Nanjing, China

    Chang Xu

  2. Department of Physics and Astronomy, Texas A&M University-Commerce, 75429-3011, Commerce, Texas, USA

    Bao-An Li

  3. Department of Physics and Astronomy and Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, 200240, Shanghai, China

    Lie-Wen Chen

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  1. Chang Xu
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  2. Bao-An Li
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Correspondence to Chang Xu.

Additional information

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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Xu, C., Li, BA. & Chen, LW. Relationship between the symmetry energy and the single-nucleon potential in isospin-asymmetric nucleonic matter. Eur. Phys. J. A 50, 21 (2014). https://doi.org/10.1140/epja/i2014-14021-2

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