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Isospin effects in nuclear mass models

Ning Wang 1 , Min Liu 1 , Xi-Zhen Wu 2 , Jie Meng 3. Isospin effects in nuclear mass models. 1 Guangxi Normal University, Guilin, China 2 China Institute of Atomic Energy, Beijing, China 3 Peking University, Beijing, China.

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Isospin effects in nuclear mass models

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  1. Ning Wang1, Min Liu1, Xi-Zhen Wu2, Jie Meng3 Isospin effects in nuclear mass models 1 Guangxi Normal University, Guilin, China 2 China Institute of Atomic Energy, Beijing, China 3 Peking University, Beijing, China XXII Nuclear Physics Workshop “Marie & Pierre Curie” Kazimierz Dolny, September 22-27, 2015

  2. Outline • Introduction • Macroscopic-microscopic mass models • Symmetry energy coefficients and shell gaps 1. Why is there so large discrepancy between predictions of HFB and those of WS for neutron drip-line nuclei? 2. Can we obtain the properties of asymmetric nuclear matter from the liquid drop models? 3. Where is the central position of “island of stability”? • Conclusions

  3. 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?

  4. Wang, Liang, Liu, Wu, Phys. Rev. C 82 (2010) 044304 Courtesy of Qiu-Hong Mo Yu. Oganessian. SKLTP/CAS - BLTP/JINR July 16, 2014, Dubna Central position of the island for SHE？ neutrons → Mass models with rms error of ~400-600keV

  5. The masses of neutron-rich nuclei are important for the study of r-process and nuclear symmetry energy N. Wang, M. Liu, X. Z. Wu, J. Meng, Phys. Lett. B 734, 215 (2014)

  6. Macroscopic-Microscopic • Strutinsky type: (shell corrections) • Finite range droplet model (FRDM): [M, β, Bf,…] • Extended Thomas-Fermi+SI (ETFSI): [M, EOS, β, Bf,…] • Lublin-Strasbourg Drop (LSD) model: [M, β, Bf,…] • Weizsäcker-Skyrme (WS) model:[M, β, Rch,…]… … • Others : • Esh from valence-nucleons: Kirson, NPA798 (2008) 29 Dieperink & Isacker, EPJA 42 (2009) 269 • Wigner-Kirkwood method: Centelles, Schuck, Vinas, Anna. Phys. 322 (2007) 363; Bhagwat, et al.,PRC81_044321 • KUTY model: Koura, Uno, Tachibana, Yamada, NPA674(2000)47… …

  7. Macro-micro mass models 1. Nuclear liquid drop with sharp surface Myers & Swiatecki, Nucl. Phys. 81 (1966) 1 Volume term Surface term Coulomb term Parabolic approximation for small deformations

  8. Nuclear surface diffuseness and its isospin dependence make the deformation energies much more complicated The values of g1 and g2 can be obtained by known masses

  9. 2. Strutinsky shell correction Woods-Saxon potential symmetry potential WSBETA: Cwoik, Dudek, et al., Comput. Phys. Commun. 46(1987) 379

  10. 3. Weizsäcker-Skyrme mass model Liquid drop Deformation Shell Residual Residual：Mirror 、pairing 、Wigner corrections... Macro-microconcept& Skyrme energy density functional N. Wang, M. Liu, et al., PRC81-044322；PRC82-044304；PRC84-014333

  11. symmetry potential Isospin dependence of model parameters • Symmetry energy coefficient • Symmetry potential • Strength of spin-orbit potential • Pairing corr. term WS3：Phys.Rev.C84_014333

  12. 5.Isospin dependence ofsurface diffuseness Neutron-rich N. Wang, M. Liu, X. Z. Wu, and J. Meng, Phys. Lett. B 734 (2014) 215

  13. WS Potential energy surface around ground state deformations To obtain g.s. energy, one needs to find the minimum on the PES are considered

  14. M(WS3) – M(exp.) Predictive power for new massesAME2012

  15. For new masses after 2012 http://nuclearmasses.org

  16. Question 1 HFB17 & WS4 symmetry energy coefficients NormalAcceleratingDecelerative Parabolic law for drip line nuclei? From Wikipedia

  17. Symmetry energy coefficients of finite nuclei from Skryme energy density functional + ETF

  18. The value of the fourth-order term is opposite for WS4 and HFB17 After removing Coulomb term, Wigner term, and asym N. Wang, M. Liu, H. Jiang, J. L. Tian, Y. M. Zhao, Phys. Rev. C 91, 044308 (2015)

  19. coefficient of fourth-order term vs model rms error Jiang, Wang, et al., Phys. Rev.C91_054302 Nbound

  20. Question 2Properties of asymmetric nuclear matter With an rms error of only 8 keV To match the liquid drop energy in LSD for a series of nuclei with “macroscopic” energy from the Skyrme energy density functional +ETF, one can find the best-fit functionals for the LSD formula.

  21. Slope parameter Matching LSD LSD: Pomorski, Dudek, Phys. Rev. C 67, 044316 (2003). WS*: N. Wang, Z. Liang, M. Liu and X. Wu, Phys. Rev. C 82, 044304 (2010).

  22. Question 3 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, 024320 (2014)

  23. Contour plot of shell corrections WS4 What is the reason that these doubly-magic nuclei locate at the same line? The super-heavy nucleus with N=184 and Z=114 deviates evidently from the line

  24. Neutron Proton Nv Zv Core Correlations between neutrons and protons near Fermi surface 208Pb active nucleons effective ratio of neutron to proton Levels: H. Koura, S. Chiba,J. Phys. Soc. Jpn. 82, 014201 (2013) For all doubly magic nuclei along the line, one gets almost the same value of Tv

  25. The discrepancy between the theoretical masses and the recently evaluated experimental ones in the region of heavy nuclei Litvinov, Palczewski, Cherepanov, Sobiczewski, Acta Phys. Polo. B 45 (2014) 1979

  26. Conclusions • We proposed a macro-micro mass model with an rms error of 298 keV. The isospin dependence of model parameters influences strongly the masses of super-heavy nuclei and neutron-rich nuclei. • 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.

  27. Thank you for your attention Codes & Nuclear mass tables：www.ImQMD.com/mass Guilin, China

  28. Comparison of Qa

  29. Convergence test for the higher order terms

  30. Quadrupole Deformations Oblate Prolate

  31. Deformation energies

  32. Rms charge radii N. Wang, T. Li, Phys. Rev. C88, 011301(R)

  33. reduces rms error by ~10% with the same mass but withthe numbers of protons and neutrons interchanged Residual –Mirror corr. charge-symmetry / independence of nuclear force

  34. Residual – Wigner corr. of heavy nuclei (N,Z) N=Z K. Mazurek, J. Dudek，et al., J. Phys. Conf. Seri. 205 (2010) 012034

  35. Radial Basis Function (RBF) corrections Revised masses leave-one-out cross-validation Wang & Liu, Phys. Rev. C 84, 051303(R) (2011)

  36. The systematic error of a global model could be evaluated by the RBF method N. Wang and M. Liu, J. Phys: Conf. Seri. 420 (2013) 012057

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