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

• Nuclear structure calculations on superheavy nuclei (RMF, SHF, MM, …)

• Half-lives of alpha decay: density-dependent cluster model (DDCM)

• Summary

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.

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 ???

Werner and Wheeler, PR, 1958: 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• Cwiok et al, Nature 433, 2005. • Goriely et al., Ato. Dat. Nucl. Dat. 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).

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

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

15. Ren, Z. Shape coexistence in even-even superheavy nuclei. Phys. Rev. C65, 051304 (2002)

Cited: shape coexistence, Ref. [15]

Nature, 433 (2005) 705

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.

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.

RMF prediction for 278113 : Qa and Ta Z. Ren, Prog. Theor. Phys. Supplement,

No. 146 (2002) 498 (YKIS01, Japan).

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

Siemens and Bethe: nuclei with Z>104 are prolate

Siemens and Bethe: nuclei with Z>104 are prolate

Conclusion :

Conclusion :

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

Geng, Toki, Zhao: similar results with us.

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

Other RMF calculations agree with ours: superdeformation in superheavy nuclei

Macro-E Micro-ETotal

Micro-E Shell-corr.

Macroscopic-microscopic (MM) model

Pairing-E

Liquid-drop model

Macroscopic-E:

Microscopic-E:Nilsson potential as a single particle

κ, μ parameters for Nilsson potentials （ T. Bengtsson, NPA,1985) ．

To minimize the total energy for different deform

ation and to obtain the ground state energy and defo

rmation parameters

BCS for pairing

Strutinsky shell-correction:

Even-even and odd-even nuclei ：

1 、 Standard parameters in Nilsson model

2 、 BCS scheme for pairing . pairing strength: ＋，– for neutrons and protons , respectively3 、 no traxiality

, 0 1

0 1

1( )

19.2, 7.4

p n

N ZG g g

A Ag g

Calculations based on Macroscopic-miCalculations based on Macroscopic-microscopic model (MM model)croscopic model (MM model)

1. Even-even nuclei(Z=94-118) ：

Pu Isotopes: difference for energy is around 0.5 MeV

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

Comparison for MM model and RMF model

(two sets)

N=184

Z=114附近的核近似球形 .

正常形变态 .

超形变态 .

形状共存

also good agreement for B and Qa (MeV)

Odd-A nuclei （ Z=95-115)

For decay chain of Z=115 and A=287Half-life: Viola-Seaborg formula。

Together with those from RMF and Moller’s model

Exp. Yu. Ts. Oganessian, et al., Phys. Rev. C72, 034611 (2005).

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

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

PRC 72 , 2005 T. Dong and Z. Ren

Local formula of binding energies for Local formula of binding energies for heavy and superheavy nucleiheavy and superheavy nuclei

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

N=152

subshell

Bexp—Bcal with and without subshell effect

Further improvement for local formula

new term Also n-p pairing

Qa for even-Z nuclei

Qa for odd-Z nuclei

Nuclei Q the. Q exp. T the. (s) T exp. (s)256Db 9.550 0.408 2.5257Db 9.407 9.230 0.443 1.53-1.63258Db 9.529 0.465 7.03259Db 9.655 9.620 0.903E-1 0.51260Db 9.494 9.380 0.585 1.52-1.68261Db 9.337 0.699 1.8-2.20

Good agreement is achieved ! For 259 Db theoretical alpha decay energies are almost equal to experimental value.

Table 1, Db (Z=105) decay energy and half-life

Nuclei Q the. Q exp. T the. (s) T exp. (s)258Bh 10.446 0.819E-2259Bh 10.309 0.777E-2260Bh 10.437 10.364 0.863E-2 0.35E-1261Bh 10.568 10.560 0.177E-2 0.137E-1262Bh 10.412 10.300 0.994E-2263Bh 10.263 0.101E-1

Table 2, Bh (Z=107) decay energy and half-life

260Bh : Phys. Rev. Lett. 100, 022501 (2008)

Nuclei Q the. Q exp. T the. (s) T exp. (s)264Mt 11.306 0.315E-3265Mt 11.162 0.286E-3266Mt 11.010 10.996 0.149E-2267Mt 10.864 0.141E-2

Table 3, Mt (Z=109) decay energy and half-life

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, PRC 73: 041301(Rapid Comm.) (2006)

• D. Ni and Z. Ren, PRC 78 (2008); PRC 2009….

Heavy and superheavy nucleiNPA 825 145-158 (2009)

N=126 closed-shell region nucleiPRC 80 014314 (2009)

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.

Summary

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

lei; maybe superdeformation• RMF, MM, and Local formula for Energy

• Density-dependent cluster model of alpha decay half-lives (spherical and deformed)

• New version of DDCM

Thanks

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

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

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

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

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 )

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 .

Siemens and Bethe: Nuclei with Z>104 are prolate

Siemens and Bethe: Nuclei with Z>104 are prolate

Siemens and Bethe: Nuclei with Z>104 are prolate

Siemens and Bethe: Nuclei with Z>104 are prolate

Conclusion :

Conclusion :

Other RMF calculations: superdeformation in superheavy nuclei