Systematical calculations on superheavy nuclei
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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

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Systematical calculations on superheavy nuclei

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

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


1 introduction experiments

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

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. 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

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.


Table 1 rmf results for pu tma and nlz2 experimental beta 2 0 29 for 238 244 pu

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


Table 2 rmf results for cm tma and nlz2

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

Experimental deformation Beta2=0.30 for 244-248Cm


Table 5 rmf results for no tma and nlz2

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

Experimental deformation Beta2=0.27 for 254No


Experimental b a mev is between two sets of rmf results z 98 108

Experimental B/A (MeV) is between two 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. 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

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


Tab 10 results for dubna data 292 116 tma beta 2 0 46 0 45 0 44 for shf model

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


Tab 11 results for dubna data 292 116 nlz2 beta 2 0 46 0 45 0 44 for shf model

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


2 new shape coexistence superdeformation

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


Fig 9 energy surface of z 114 a 288

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


15 ren z shape coexistence in even even superheavy nuclei phys rev c65 051304 2002

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

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 265 107 q a and t a

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.


Theoretical prediction 265 107 q a and t a z ren et al prc 67 2003 064302 jnrs 3 2002 195

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.


Systematical calculations on superheavy nuclei

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.


Oganessian et al prc72 2005

Oganessian et al, PRC72 2005

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

南京大学


Oganessian et al prc72 20051

Oganessian et al, PRC72 2005

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

南京大学


3 density dependent cluster model

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)


Systematical calculations on superheavy nuclei

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 for superheavy nuclei (Z=106-118)


Ddcm prc 16

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 prc 161

DDCM: 被PRC论文大段引用(共16处)


Systematical calculations on superheavy nuclei

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


Systematical calculations on superheavy nuclei

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


Systematical calculations on superheavy nuclei

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


Systematical calculations on superheavy nuclei

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


Systematical calculations on superheavy nuclei

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


Systematical calculations on superheavy nuclei

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


4 new formula of half lives ground state and isomer spontaneous fission

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

Very good agreement for SF half-lives of isomers


Summary

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


Thanks

Thanks


Systematical calculations on superheavy nuclei

国外同行对我们工作的引用和肯定


Systematical calculations on superheavy nuclei

国内外同行对我们工作的引用和肯定


Geng toki zhao jpg 32 2006 573

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.


Eikonal

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)

  • ……


Eikonal1

编写电子和晕核散射新程序:相对论Eikonal近似


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