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, , …. 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., Hs, Duellman, Turler, …, Nature 2003, PRL Bh, Lanzhou, Gan, Qin, …, EPJA 2004.

1. introduction: theory. J. A. Wheeler, 1950s: Superheavy nuclei Werner and Wheeler, Phys. Rev., 109 (1958) s-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= ： 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 Cwiok et al, Nature 433, 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.

NucleiB the. (1)Beta p B the. (2)Beta p B exp. (MeV) 234 Pu Pu Pu Pu Pu Pu Table 1, RMF results for Pu. (TMA and NLZ2). Experimental Beta 2 =0.29 for Pu.

NucleiB the. (1)Beta p B the. (2)Beta p B exp. (MeV) 240 Cm Cm Cm Cm Cm Cm Table 2, RMF results for Cm. (TMA and NLZ2) Experimental deformation Beta 2 =0.30 for Cm

NucleiB the. (1)Beta p B the. (2)Beta p B exp. (MeV) 252 No No No No audi 260 No audi 262 No audi Table 5, RMF results for No. (TMA and NLZ2) Experimental deformation Beta 2 =0.27 for 254 No

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

NucleiB the. Beta n Beta p Q the. Q exp * ** * ** * ** Tab. 10, results for Dubna data (TMA) (Beta 2 =0.46, 0.45,0.44 for SHF model.)

NucleiB the. Beta n Beta p Q the. Q exp * ** * ** * ** Tab. 11, results for Dubna data (NLZ2). (Beta 2 =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, (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, 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, (2002) Cited: shape coexistence, Ref. [15] Nature, 433 (2005) 705

64. Z. Ren, Phys. Rev. C65, (2002) (R) 65. Z. Ren et al., Phys. Rev. C66, (2002) Exp. Def. : 0.28, RMF Def.: ,cited.

Theoretical prediction: Q a and T a Z. Ren et al, PRC 67 (2003) ; JNRS 3 (2002) 195. AXAX B (MeV) Beta n Beta p Q a (MeV) T a (second) *10 3 Expt: Gan et al, EPJA 2004, Q a =9.38, T a =0.94 s. Good agreement between theory and data.

RMF prediction for : Q a and T a Z. Ren, Prog. Theor. Phys. Supplement, No. 146 (2002) 498 (YKIS01, Japan). AXAX B (MeV) Beta n Beta p Q a (MeV) T a (ms) Morita et al, JPSJ 2004, Q a =11.68, T a =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, PRC

南京大学 SHF [12 ， 49-51] and RMF [13 ， 52-57] compare well with the experimental results Oganessian et al, PRC

Siemens and Bethe: nuclei with Z>104 are prolate

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-EMicro-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 deformation and to obtain the ground state energy and deformation 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, respectively 3 、 no traxiality Calculations based on Macroscopic- microscopic 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=287 Half-life: Viola-Seaborg formula 。 Together with those from RMF and Moller’s model Exp. Yu. Ts. Oganessian, et al., Phys. Rev. C72, (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 heavy and superheavy nuclei

Local formula with subshell effect (Z>=90; N>=140) N=152 subshell

B exp —B cal 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

NucleiQ the. Q exp. T the. (s)T exp. (s) 256 Db Db Db Db E Db Db 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

NucleiQ the. Q exp. T the. (s)T exp. (s) 258 Bh E Bh E Bh E-20.35E Bh E E Bh E Bh E-1 Table 2, Bh (Z=107) decay energy and half-life 260 Bh : Phys. Rev. Lett. 100, (2008)

NucleiQ the. Q exp. T the. (s)T exp. (s) 264 Mt E Mt E Mt E Mt E-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: (2004) C Xu, Z Ren, NPA 753: 174 (2005) C. Xu, Z. Ren, PRC 73: (Rapid Comm.) (2006) D. Ni and Z. Ren, PRC 78 (2008); PRC 2009….

Heavy and superheavy nuclei NPA (2009)

N=126 closed-shell region nuclei PRC (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 nuclei; 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 236 U 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 s to 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

Conclusion :

Other RMF calculations: superdeformation in superheavy nuclei