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Symmetry energy coefficients and shell gaps from nuclear masses
Ning Wang Guangxi Normal University, Guilin, China Introduction/motivations Symmetry energy coefficients from nuclear masses Properties of nuclear matter in liquid-drop models Shell gaps in unmeasured mass region Conclusions SINAP-CUSTIPEN workshop, Shanghai, Dec. 13 – 18, 2015
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Does the “island of stability” of super-heavy elements exist?
Super-heavy nuclei To predict the ~ 4000 unknown masses based on the ~2353/2438 measured masses Does the “island of stability” of super-heavy elements exist? Or maybe just a shoal?
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The masses of neutron-rich nuclei are important for the study of r-process and nuclear symmetry energy WS4: N. Wang, M. Liu, X. Z. Wu, J. Meng, Phys. Lett. B 734, 215 (2014)
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Parabolic law for drip line nuclei?
Normal Accelerating Decelerative Higher-order terms of symmetry energy coefficients Parabolic law for drip line nuclei? From Wikipedia
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Weizsäcker-Skyrme mass model
Liquid drop Deformation Shell Residual Residual:Mirror 、pairing 、Wigner corrections... Macro-micro concept & Skyrme energy density functional N. Wang, M. Liu, et al., PRC ;PRC ;PRC
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Isospin dependence of model parameters
Symmetry energy coefficient Symmetry potential Strength of spin-orbit potential Pairing corr. term symmetry potential WS3:Phys.Rev.C84_014333
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Mass dependence of asym
Form of asym Wang_Liu, Phys. Rev. C 81 (2010) S0 P. Danielewicz et al., Nucl. Phys. A 818 (2009) 36
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M. Liu, N. Wang, Z. Li, F. Zhang, PRC82, 064306 (2010)
Wigner correction M. Liu, N. Wang, Z. Li, F. Zhang, PRC82, (2010) 广西师范大学,王 宁
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Symmetry energy coefficients of finite nuclei from Skryme energy density functional + ETF2
Second-order Fourth-order N. Wang, M. Liu, H. Jiang, J. L. Tian, Y. M. Zhao, Phys. Rev. C 91(2015)
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asymptotic behavior of asym when
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asymptotic behavior of the fourth-order term
ETF2 (MeV) SkM* -3.9 -4.4 SLy4 -4.1 -4.5 SkSC4 0.46 0.45 Binding energy per nucleon at saturation density L. W. Chen, B. J. Cai, C. M. Ko, B. A. Li, C. Shen, J. Xu, Phys. Rev. C80 (2009)
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The value of the fourth-order term is opposite for WS4 and HFB17
After removing Coulomb term, Wigner term, and asym HFB17 N. Wang, M. Liu, H. Jiang, J. L. Tian, Y. M. Zhao, Phys. Rev. C 91(2015)
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H. Jiang, N. Wang, L. W. Chen, Y. M. Zhao, A
H. Jiang, N. Wang, L. W. Chen, Y. M. Zhao, A. Arima, PRC 91 (2015) Nbound
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Properties of nuclear matter in Liquid-Drop models
Density dependence of binding energy & Esym Lublin–Strasbourg drop (LSD) formula : Pomorski, Dudek, PRC67 (2003) Through matching the liquid drop energy in LSD, one may find the best-fit Skyrme energy density functional for the LSD formula.
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N. Wang, M. Liu, L. Ou, Y. X. Zhang, Phys. Lett. B 751 (2015) 553
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Slope parameter LSD: Pomorski, Dudek, Phys. Rev. C 67, 044316 (2003).
Matching LSD LSD: Pomorski, Dudek, Phys. Rev. C 67, (2003). WS*: N. Wang, Z. Liang, M. Liu and X. Wu, Phys. Rev. C 82, (2010).
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Splitting of neutron and proton effective masses for neutron matter
from the optical potential model X. H. Li, W. J. Guo, B. A. Li, L. W. Chen, et al, Phys. Lett. B743 (2015) 408
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N. Wang, M. Liu, Chin. Sci. Bull. 60, 1145 (2015)
Magic numbers in unknown region Wienholtz, et al., Nature 498 (2013) 346 1) New magic number N=32 N. Wang, M. Liu, Chin. Sci. Bull. 60, 1145 (2015) 2) Sub-shell closure in 252Fm Mo, Liu, Wang, PRC 90, (2014)
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Contour plot of shell corrections
WS4 N. Wang, M. Liu, X. Z. Wu and J. Meng, to appear in Phys. Rev. C The super-heavy nucleus with N=184 and Z=114 deviates evidently from the line
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Conclusions After removing the Coulomb and Wigner terms, the symmetry energy coefficients of finite nuclei can be extracted from nuclear masses. The fourth-order term of symmetry energy coefficients might result in the big difference of model predictions. Through matching the Liquid-drop energy and the Skyrme energy density functional, we obtain the slope parameter L ~ 42 MeV (LSD) and 52 MeV (WS*). Many doubly-magic nuclei (N>Z) locate along the N=1.37Z+13.5, might due to the correlation between nucleons near Fermi surface, and more attentions should be paid to SHN with N=178.
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Thank you for your attention
Codes & Nuclear mass tables:
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Levels: H. Koura, S. Chiba, J. Phys. Soc. Jpn. 82, 014201 (2013)
Correlations between neutrons and protons near Fermi surface Neutron Proton Nv Zv Core 208Pb active nucleons effective ratio of neutron to proton Levels: H. Koura, S. Chiba, J. Phys. Soc. Jpn. 82, (2013) For all doubly magic nuclei along the line, one gets almost the same value of Tv
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For new masses after 2012
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Rms charge radii N. Wang, T. Li, Phys. Rev. C88, (R)
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