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,
Z= , 118, at Dubna, by Oganessian et al….
Nature, 1999; PRL. 1999;PRC,
Z= , 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 ( ) ; NPA( )…
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
Table 1, RMF results for Pu. (TMA and NLZ2). Experimental Beta2=0.29 for Pu.
Nuclei
Bthe. (1)
Betap
Bthe.(2)
Bexp.(MeV)
234Pu
1775.2
0.25
1773.8
0.28
1774.8
236Pu
1788.6
1787.1
0.29
1788.4
238Pu
1801.1
0.26
1799.7
1801.3
240Pu
1813.7
0.27
1811.6
0.30
1813.5
242Pu
1825.5
1822.9
1825.0
244Pu
1836.2
1833.7
1836.1

8. Table 2, RMF results for Cm. (TMA and NLZ2)
Nuclei
Bthe. (1)
Betap
Bthe.(2)
Bexp.(MeV)
240Cm
1811.0
0.26
1809.1
0.31
1810.3
242Cm
1824.2
0.27
1822.0
1823.4
244Cm
1836.9
0.28
1834.4
1835.9
246Cm
1848.8
1845.9
1847.8
248Cm
1859.5
1856.3
1859.2
250Cm
1870.2
0.25
1866.3
1869.7
Experimental deformation Beta2=0.30 for Cm

9. Table 5, RMF results for No. (TMA and NLZ2)
Nuclei
Bthe. (1)
Betap
Bthe.(2)
Bexp.(MeV)
252No
1873.2
0.26
1870.7
0.31
1871.3
254No
1887.2
0.27
1884.1
1885.6
256No
1900.7
1897.0
1898.6
258No
1912.9
1909.6
0.30
1911.1audi
260No
1924.6
1921.7
1923.1audi
262No
1935.8
0.21
1933.1
0.29
1934.7audi
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
Tab. 10, results for Dubna data (TMA) (Beta2=0.46, 0.45,0.44 for SHF model.)
Nuclei
Bthe.
Betan
Betap
Qthe.
Qexp.
292116 * **
2080.9
2080.5
2077.7
0.49
-0.21
0.25
0.51
0.26
11.01
10.56
288114
2063.6
2062.0
2060.7
0.48
-0.18
-0.19
0.27
9.12
9.84
284112
2044.4
2043.5
2042.6
0.46
-0.17
0.47
0.29
9.83
9.17

14. Tab. 11, results for Dubna data 292116. (NLZ2). (Beta2=0. 46, 0. 45,0
Tab. 11, results for Dubna data (NLZ2). (Beta2=0.46, 0.45,0.44 for SHF model).
Nuclei
Bthe.
Betan
Betap
Qthe.
Qexp.
292116 * **
2078.7
2076.8
2076.6
0.55
0.06
-0.05
0.57
10.92
10.56
288114
2060.9
2060.3
2057.2
0.15
0.56
-0.20
0.16
0.58
9.51
9.84
284112
2042.1
2041.3
2037.8
-0.13
0.17
0.60
9.02
9.17

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, (2002)
Z. Ren et al., Phys. Rev. C66, (2002)
Z. Ren et al., Phys. Rev. C67, (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
64. Z. Ren, Phys. Rev. C65, (2002) (R) Z. Ren et al., Phys. Rev. C66, (2002)
Exp. Def. : 0.28, RMF Def.: ,cited.

19. Expt: Gan et al, EPJA 2004, Qa=9.24 , Ta=0.94 s.
Z. Ren et al, PRC 67 (2003) ; NPA 722 (2003) 543. Prediction for : Qa and Ta AX B
(MeV)
Betan
Betap Qa Ta
(second)
269109
0.22
0.23
10.21
0.069
265107
0.24
9.41
2.56
261105
0.26
9.14
3.33
257103
0.27
8.12
1.28*103
Expt: Gan et al, EPJA 2004, Qa=9.24 , Ta=0.94 s.
Good agreement between theory and data.

20. Expt: Gan et al, EPJA 2004, Qa=9.38 , Ta=0.94 s.
Theoretical prediction: Qa and Ta Z. Ren et al, PRC 67 (2003) ; JNRS 3 (2002) 195. AX B
(MeV)
Betan
Betap Qa Ta
(second)
269109
0.22
0.23
10.21
0.069
265107
0.24
9.41
2.56
261105
0.26
9.14
3.33
257103
0.27
8.12
1.28*103
Expt: Gan et al, EPJA 2004, Qa=9.38 , Ta=0.94 s.
Good agreement between theory and data.

21. Morita et al, JPSJ 2004, Qa=11.68, Ta=0.34 ms.
Z. Ren, Prog. Theor. Phys. Supplement, No. 146 (2002) 498 (YKIS01, Japan) RMF prediction for : Qa and Ta AX B
(MeV)
Betan
Betap Qa Ta
(ms)
282115
0.19
11.51
5.79
278113
0.21
11.70
0.57
274111
0.24
0.25
11.25
1.62
270109
0.27
0.28
10.20
160
Morita et al, JPSJ 2004, Qa=11.68, Ta=0.34 ms.
Good agreement between theory and data.

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

23. Oganessian et al, PRC
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: (2004)
C Xu, Z Ren, NPA 753: 174 (2005)
C Xu, Z Ren, NPA 760: 303 (2005)
C. Xu, Z. Ren, PRC 73: (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, the alpha-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 alpha emitters 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: (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
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: (2004)
Z Wang, Z Ren, PRC 71: (2005) ……

48. 编写电子和晕核散射新程序： 相对论Eikonal近似