Systematical calculations on superheavy nuclei

1. Systematical calculations on 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) • Alpha decay: density-dependent cluster model (DDCM) • Spontaneous Fission: new formula on half-lives of SF. • Summary

3. 1. introduction: experiments • Z=110 (Ds), 111(Rg), 112 were produced at GSI, Hofmann, Muenzenberg…. Z. Phys. A, 1995-1996 • Z=114-116, 118, at Dubna, by Oganessian et al…. Nature, 1999; PRL. 1999;PRC, 2000-2005. • Z=110-111, new results, at Berkeley, PRL 2004…. • Z=113, RIKEN, Morita,…, J. P. S. J., 2004. • 270Hs, Duellman, Turler, …, Nature 2003, EPJA 04. • 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. 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 • Nature 433, 2005. • Atom. Data. Nucl. Data Tab. 77 (2001) 311 .

6. 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.

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

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

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

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

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

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

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

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

15. 2 new: shape coexistence,superdeformation ?Ren and Toki, Nucl. Phys. A 689 (2001) 691. • 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. • S. Goriely, F. Tondeur, J. Pearson, SHF Model • Atom Data and Nucl. Data Tables 77 (2001) 311. • Superdeformation for some superheavy nuclei

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

17. 15. Ren, Z. Shape coexistence in even-even superheavy nuclei. Phys. Rev. C65, 051304 (2002) To be cited: shape coexistence, Ref. [15] Nature, 433 (2005) 475

18. 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.

19. Z. Ren et al, PRC 67 (2003) 064302; NPA 722 (2003) 543.Prediction for 265107: Qa and Ta Expt: Gan et al, EPJA 2004, Qa=9.24 , Ta=0.94 s. Good agreement between theory and data.

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. Z. Ren, Prog. Theor. Phys. Supplement, No. 146 (2002) 498 (YKIS01, Japan).RMF prediction for 278113: Qa and Ta 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. 3. Density-Dependent Cluster Model • DDCM is a new model of alpha decay: • 1) effectve potential based on the Reid potential. • 2) low density behavior included. • 3) exchange included • 4) agreement within a factor of three for half-lives • Z Ren, C Xu, Z Wang, PRC 70: 034304 (2004) • C Xu, Z Ren, NPA 753: 174 (2005) • C Xu, Z Ren, NPA 760: 303 (2005) • C. Xu, Z. Ren, PRC 73: 041301(Rapid Commun.) (2006)

25. 3. DDCM for alpha decay:agreement is within a factor of three for half-lives although experimental half-lives vary from 10-6 s to 1019 year

26. DDCM for superheavy nuclei (Z=106-118)

27. DDCM : 被PRC论文大段引用(共16处) 最近文献[7,16,18,28]研究了超重元素alpha衰变; 如图2为[7,18,28]的结果.我们的结果和[18]的结果基于不同的cluster模型. 文献[18]得到了超重核alpha衰变寿命好的符合. 文献[18]提出的结团模型理论很好描述了该区域.

28. DDCM: 被PRC论文大段引用(共16处)

30. Deformed DDCM: a spherical alpha-particle interacts with a deformed daughter nucleus with an axially symmetric deformation

31. The double-folding nuclear potential of 236U for two orientations, beta = 0◦ and beta = 90◦

32. In the multipole expansion, the density distribution of daughter nucleus is expanded as The corresponding intrinsic form factor has the form The double-folding potential can then be evaluated by a sum of different multipole components

33. The corresponding multipole components are The polar-angle dependent penetration probability of alpha decay is given by In the DDCM, thealpha-decay width has the following expression

34. The comparison of experimental alpha-decay half-lives and theoretical ones for even-even nuclei (Z= 52−104)

35. The distribution of the number of alphaemitters for different factors of agreement.

37. 4. New formula of half-lives: Ground-State and isomer spontaneous fission. • Long lifetime line of G.S. fission: N=Z+52 • Three formulas for G.S. fission. • New formula of fission half-lives of 33 isomers: • log10(T1/2) = -6 + c1(Z-92) + c2(N-Z-52)(N-146) + c3 • C Xu, Z Ren, PRC 71: 014309 (2005) • Z Ren, C Xu, NPA 759: 64 (2005),….

38. Very good agreement for SF half-lives of isomers

39. Summary • Nuclear structure calculation : • Agreement with data and new predictions • Shape coexistence: isomers of superheavy nuclei; maybe superdeformation • More and more people agree since 2005. • Density-dependent cluster model of alpha decay (spherical and deformed) • New formulas for spontaneous fission: • Ground state and isomeric state

40. Thanks

43. 国外同行对我们工作的引用和肯定

44. 国内外同行对我们工作的引用和肯定

45. Geng, Toki, Zhao JPG 32 (2006) 573:超重核有形状共存, 大形变, 与我们结果一致.

47. 编写电子和晕核散射新程序：相对论Eikonal近似编写电子和晕核散射新程序：相对论Eikonal近似 • 1. 理论结果与现有实验数据非常符合 • 2. 预言电子-丰质子核散射,能清楚探测质子晕 结构, 这是电子-质子晕核散射的第一个理论结果 • 3. 为将来的电子-丰质子核对撞实验预研 • 参考文献 • Z Wang, Z Ren, PRC 70: 034303 (2004) • Z Wang, Z Ren, PRC 71: 054323 (2005) • ……

48. 编写电子和晕核散射新程序：相对论Eikonal近似编写电子和晕核散射新程序：相对论Eikonal近似