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Theoretical studies on properties of some superheavy nuclei

Theoretical studies on properties of some superheavy nuclei. Zhongzhou REN Department of Physics, Nanjing University, Nanjing, China Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator, Lanzhou, China. Outline. Introduction

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Theoretical studies on properties of some superheavy nuclei

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  1. Theoretical studies on properties of some superheavy nuclei • Zhongzhou REN • Department of Physics, Nanjing University, Nanjing, China • Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator, Lanzhou, China

  2. Outline • Introduction • Nuclear structure calculations on superheavy nuclei (RMF, SHF, MM, …) • Half-lives of alpha decay: density-dependent cluster model (DDCM) • Summary

  3. 1. introduction: experiments • Z=110 (Ds), 111(Rg), 112 were produced at GSI, Hofmann, Muenzenberg, Ackermann…. Z. Phys. A, 1995-1996, …. • Z=114-116, 118, at Dubna, by Oganessian et al…. Nature, 1999; PRL, 1999;PRC, 2000-2007. • Z=110-111, new results, at Berkeley, PRL 2004…. • Z=113, RIKEN, Morita,…, J. P. S. J., 2004. • 270Hs, Duellman, Turler, …, Nature 2003, PRL 2007. • 265Bh, Lanzhou, Gan, Qin, …, EPJA 2004.

  4. 1. introduction: theory. • J. A. Wheeler, 1950s: Superheavy nuclei • Werner and Wheeler, Phys. Rev., 109 (1958) 126. • 1960s-2000s, macroscopic-microscopic model (MM): Nilsson et al, Z=114 and N=184…. • 1970s-2000s: Skyrme-Hartree-Fock (SHF) Model; Z=126? N=184? • 1990s-2000s: Relativistic Mean-Field model : • Z=120 ? N=184? • Spherical or deformed for superheavy nuclei ???

  5. Werner and Wheeler, PR, 1958: superheavy nuclei

  6. 2. Nuclear structure calculations • 2.1. RMF calculations on superheavy nuclei • Z=90-120：binding energies, deformations,… • Compare RMF with experimental data • RMF predictions on experiments • Ren et al. , PRC (2002-2005) ; NPA(2003-2005)… • 2. 2 New idea: shape coexistence and superdeformation • Ren and Toki, 2001, NPA, Ren et al,… • 2.3. Shape coexistence from other models • SHF model and MM model • Cwiok et al, Nature 433, 2005. • Goriely et al., Ato. Dat. Nucl. Dat. Tab. 77 (2001) 311 .

  7. 2.1 RMF results and discussion • Nuclei: Z =94—120; N=130—190. • Comparison of theoretical binding energy with exprimental data. • Comparison of theoretical alpha decay energy with exprimental data. • Comparison of theoretical quadrupole deformation with exprimental data.

  8. Table 1, RMF results for Pu. (TMA and NLZ2). Experimental Beta2=0.29 for 238-244Pu.

  9. Table 2, RMF results for Cm. (TMA and NLZ2) Experimental deformation Beta2=0.30 for 244-248Cm

  10. Table 5, RMF results for No. (TMA and NLZ2) Experimental deformation Beta2=0.27 for 254No

  11. Experimental B/A (MeV) is between two sets of RMF results (Z=98-108).

  12. Fig. 3 Binding energy of the Z=112, A=277 alpha-decay chain from the RMF and Moller et al.

  13. Fig. 4 Theoretical and experimental alpha decay energies for GSI Data: Z=110, 111, 112 ( +2, +1, 0 shift).

  14. Tab. 10,results for Dubna data 292116. (TMA)(Beta2=0.46, 0.45,0.44 for SHF model.)

  15. Tab. 11, results for Dubna data 292116. (NLZ2).(Beta2=0.46, 0.45,0.44 for SHF model).

  16. Fig. 9 Energy surface of Z=114, A=288.

  17. 2.2 Shape coexistence, superdeformation • Z. Ren, Shape coexistence in even-even superheavy nuclei, Phys. Rev. C65, 051304 (2002) • Z. Ren et al., Phys. Rev. C66, 064306 (2002) • Z. Ren et al., Phys. Rev. C67, 064302 (2003) • Sharma, …,Munzenberg, PRC, 2005; • ..,Stevenson, Gupta, Greiner, JPG, 2006. • Goriely, Tondeur, Pearson, SHF Model • Ato. Dat. Nucl. Dat. Tab. 77 (2001) 311. • Superdeformation for some superheavy nuclei

  18. 15. Ren, Z. Shape coexistence in even-even superheavy nuclei. Phys. Rev. C65, 051304 (2002) Cited: shape coexistence, Ref. [15] Nature, 433 (2005) 705

  19. 64. Z. Ren, Phys. Rev. C65, (2002) 051304(R) 65. Z. Ren et al., Phys. Rev. C66, (2002) 064306 Exp. Def. : 0.28, RMF Def.: 0.26-0.32,cited.

  20. Theoretical prediction: 265107 Qa and Ta Z. Ren et al, PRC 67 (2003) 064302; JNRS 3 (2002) 195. Expt: Gan et al, EPJA 2004, Qa=9.38 , Ta=0.94 s. Good agreement between theory and data.

  21. RMF prediction for 278113: Qa and Ta Z. Ren, Prog. Theor. Phys. Supplement, No. 146 (2002) 498 (YKIS01, Japan). Morita et al, JPSJ 2004, Qa=11.68, Ta=0.34 ms. Good agreement between theory and data.

  22. Oganessian et al, PRC72 2005 Predictions of SHF and RMF compare well with MM results [12,13] 南京大学

  23. Oganessian et al, PRC72 2005 SHF [12，49-51] and RMF [13，52-57] compare well with the experimental results 南京大学

  24. Siemens and Bethe: nuclei with Z>104 are prolate

  25. Siemens and Bethe: nuclei with Z>104 are prolate Conclusion : Conclusion :

  26. Sharma,… Stevenson, Gupta, Greiner agree with us:shape coexistence and superdeformation

  27. Geng, Toki, Zhao: similar results with us.

  28. Geng, Toki, Zhao JPG 32 (2006) 573:shape coexistence and superdeformation.

  29. Other RMF calculations agree with ours: superdeformation in superheavy nuclei

  30. Macroscopic-microscopic (MM) model Total Macro-E Micro-E Shell-corr. Micro-E Pairing-E

  31. Macroscopic-E: Liquid-drop model • Microscopic-E: Nilsson potential as a single particle κ, μ parameters for Nilsson potentials（T. Bengtsson, NPA,1985)．

  32. Strutinsky shell-correction: • BCS for pairing To minimize the total energy for different deformation and to obtain the ground state energy and deformation parameters

  33. Calculations based on Macroscopic-microscopic model (MM model) Even-even and odd-even nuclei： 1、Standard parameters in Nilsson model 2、BCS scheme for pairing . pairing strength:＋，– for neutrons and protons , respectively 3、no traxiality

  34. 1. Even-even nuclei(Z=94-118) ： Pu Isotopes: difference for energy is around 0.5 MeV

  35. Average binding energy ( B/A ) for other isotopic chains

  36. Comparison for MM model and RMF model (two sets)

  37. N=184 正常形 变态. 超形 变态. Z=114 附近的 核近似 球形. 形状共存

  38. Odd-A nuclei（Z=95-115) also good agreement for B and Qa (MeV)

  39. For decay chain of Z=115 and A=287 Half-life: Viola-Seaborgformula。 Together with those from RMF and Moller’s model Exp. Yu. Ts. Oganessian, et al., Phys. Rev. C72, 034611 (2005).

  40. Z=109 and Z=111: decay energy and half-lives

  41. Z=113 and Z=117: decay energy and half-lives

  42. Local formula of binding energies for heavy and superheavy nuclei PRC 72 , 2005 T. Dong and Z. Ren

  43. Local formula with subshell effect (Z>=90; N>=140) N=152 subshell

  44. Bexp—Bcal with and without subshell effect

  45. Further improvement for local formula new term Also n-p pairing

  46. Qa for even-Z nuclei

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