Effect of Wigner energy on the symmetry energy coefficient in nuclei

  • The nuclear symmetry energy coefficient (including the coefficient asym(4) of the I4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei. It is found that the extracted symmetry energy coefficient asym*(A,I) decreases with increasing isospin asymmetry I, which is mainly caused by Wigner correction, since esym* is the summation of the traditional symmetry energy esym and the Wigner energy eW. We obtain the optimal values J=30.25±0.10 MeV, ass=56.18±1.25 MeV, asym(4)=8.33±1.21 MeV and the Wigner parameter x=2.38±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with 20≤A≤261 with an rms deviation of 23.42 keV. We also find that the volume symmetry coefficient J≈30 MeV is insensitive to the value x, whereas the surface symmetry coefficient ass and the coefficient asym(4) are very sensitive to the value of x in the range 1≤x≤4. The contribution of the asym(4) term increases rapidly with increasing isospin asymmetry I. For very neutron-rich nuclei, the contribution of the asym(4) term will play an important role.
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Jun-Long Tian, Hai-Tao Cui, Teng Gao and Ning Wang. Effect of Wigner energy on the symmetry energy coefficient in nuclei[J]. Chinese Physics C, 2016, 40(9): 094101. doi: 10.1088/1674-1137/40/9/094101
Jun-Long Tian, Hai-Tao Cui, Teng Gao and Ning Wang. Effect of Wigner energy on the symmetry energy coefficient in nuclei[J]. Chinese Physics C, 2016, 40(9): 094101.  doi: 10.1088/1674-1137/40/9/094101 shu
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Received: 2016-04-13
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    Supported by National Natural Science Foundation of China (11475004, 11275052, 11305003, 11375094 and 11465005), Natural Science Foundation of He'nan Educational Committee (2011A140001 and 2011GGJS-147), Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences (Y4KF041CJ1)

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Effect of Wigner energy on the symmetry energy coefficient in nuclei

    Corresponding author: Jun-Long Tian,
    Corresponding author: Ning Wang,
Fund Project:  Supported by National Natural Science Foundation of China (11475004, 11275052, 11305003, 11375094 and 11465005), Natural Science Foundation of He'nan Educational Committee (2011A140001 and 2011GGJS-147), Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences (Y4KF041CJ1)

Abstract: The nuclear symmetry energy coefficient (including the coefficient asym(4) of the I4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei. It is found that the extracted symmetry energy coefficient asym*(A,I) decreases with increasing isospin asymmetry I, which is mainly caused by Wigner correction, since esym* is the summation of the traditional symmetry energy esym and the Wigner energy eW. We obtain the optimal values J=30.25±0.10 MeV, ass=56.18±1.25 MeV, asym(4)=8.33±1.21 MeV and the Wigner parameter x=2.38±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with 20≤A≤261 with an rms deviation of 23.42 keV. We also find that the volume symmetry coefficient J≈30 MeV is insensitive to the value x, whereas the surface symmetry coefficient ass and the coefficient asym(4) are very sensitive to the value of x in the range 1≤x≤4. The contribution of the asym(4) term increases rapidly with increasing isospin asymmetry I. For very neutron-rich nuclei, the contribution of the asym(4) term will play an important role.

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