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

Outline

• Introduction• Nuclear structure calculations on superheavy n

uclei (RMF, SHF, MM)• Alpha decay: density-dependent cluster model

(DDCM)• Spontaneous Fission: new formula on half-lives

of SF.• Summary

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.

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 ???

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 .

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.

Nuclei Bthe. (1) Betap Bthe.(2) Betap Bexp.(MeV)

234Pu 1775.2 0.25 1773.8 0.28 1774.8

236Pu 1788.6 0.25 1787.1 0.29 1788.4

238Pu 1801.1 0.26 1799.7 0.29 1801.3

240Pu 1813.7 0.27 1811.6 0.30 1813.5

242Pu 1825.5 0.28 1822.9 0.30 1825.0

244Pu 1836.2 0.26 1833.7 0.30 1836.1

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

Nuclei Bthe. (1) Betap Bthe.(2) Betap Bexp.(MeV)

240Cm 1811.0 0.26 1809.1 0.31 1810.3

242Cm 1824.2 0.27 1822.0 0.31 1823.4

244Cm 1836.9 0.28 1834.4 0.31 1835.9

246Cm 1848.8 0.27 1845.9 0.31 1847.8

248Cm 1859.5 0.26 1856.3 0.31 1859.2

250Cm 1870.2 0.25 1866.3 0.31 1869.7

Table 2, RMF results for Cm. (TMA and NLZ2)

Experimental deformation Beta2=0.30 for 244-248Cm

Nuclei Bthe. (1) Betap Bthe.(2) Betap Bexp.(MeV)

252No 1873.2 0.26 1870.7 0.31 1871.3

254No 1887.2 0.27 1884.1 0.31 1885.6

256No 1900.7 0.27 1897.0 0.31 1898.6

258No 1912.9 0.27 1909.6 0.30 1911.1audi

260No 1924.6 0.26 1921.7 0.30 1923.1audi

262No 1935.8 0.21 1933.1 0.29 1934.7audi

Table 5, RMF results for No. (TMA and NLZ2)

Experimental deformation Beta2=0.27 for 254No

Experimental B/A (MeV) is between t

wo sets of RMF results (Z=98-108).

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

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

Nuclei Bthe. Betan Betap Qthe. Qexp.

292116

*

**

2080.9

2080.5

2077.7

0.49

-0.21

0.25

0.51

-0.21

0.26

11.01 10.56

288114

*

**

2063.6

2062.0

2060.7

0.48

-0.18

0.26

0.49

-0.19

0.27

9.12 9.84

284112

*

**

2044.4

2043.5

2042.6

0.46

0.27

-0.17

0.47

0.29

-0.17

9.83 9.17

Tab. 10, results for Dubna data 292116. (TMA) (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

0.06

-0.05

10.92 10.56

288114

*

**

2060.9

2060.3

2057.2

0.15

0.56

-0.20

0.16

0.58

-0.20

9.51 9.84

284112

*

**

2042.1

2041.3

2037.8

0.16

0.58

-0.13

0.17

0.60

-0.13

9.02 9.17

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

2 new: shape coexistence,superdeformation

? Ren and Toki, Nucl. Phys. A 689 (2001) 691.• Z. Ren, Shape coexistence in even-even superhe

avy 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

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

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

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.

Z. Ren et al, PRC 67 (2003) 064302; NPA 722 (2003) 543.Prediction for 265107 : Qa and Ta

AX B

(MeV)

Betan Betap Qa

(MeV)

Ta

(second)269109 1960.17 0.22 0.23 10.21 0.069265107 1942.08 0.23 0.24 9.41 2.56261105 1923.19 0.26 0.26 9.14 3.33257103 1904.03 0.26 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.

Theoretical prediction: 265107 Qa and Ta

Z. Ren et al, PRC 67 (2003) 064302; JNRS 3 (2002) 195.

AX B

(MeV)

Betan Betap Qa

(MeV)

Ta

(second)269109 1960.17 0.22 0.23 10.21 0.069265107 1942.08 0.23 0.24 9.41 2.56261105 1923.19 0.26 0.26 9.14 3.33257103 1904.03 0.26 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.

Z. Ren, Prog. Theor. Phys. Supplement, No. 146 (2002) 498 (YKIS01, Japan).

RMF prediction for 278113 : Qa and Ta

AX B

(MeV)

Betan Betap Qa

(MeV)

Ta

(ms)282115 2015.03 0.19 0.19 11.51 5.79278113 1998.24 0.21 0.21 11.70 0.57274111 1981.64 0.24 0.25 11.25 1.62270109 1964.59 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.

南京大学

Predictions of SHF and RMF compare well with MM results [12,13]

Oganessian et al, PRC72 2005

南京大学

SHF [12， 49-51] and RMF [13， 52-57] compare well with the experimental results

Oganessian et al, PRC72 2005

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.) (200

6)

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

DDCM for superheavy nuclei (Z=106-118)

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 .

DDCM: 被 PRC 论文大段引用 ( 共 16处 )

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

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

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

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

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

The distribution of the number of alpha emitters for different factors of agreement.

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),….

Very good agreement for SF half-lives of isomers

Summary

• Nuclear structure calculation :• Agreement with data and new predictions• Shape coexistence: isomers of superheavy nuc

lei; 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

Thanks

国外同行对我们工作的引用和肯定

国内外同行对我们工作的引用和肯定

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 .

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)• ……

编写电子和晕核散射新程序：相对论 Eikonal 近似