Theoretical study of structure & synthesis mechanism of superheavy nuclei

Transcription

1 Humboldt Kolleg Interfacing Structure & Reaction Dynamics in the Synthesis of the Heaviest Nuclei, ECT*, Trento, Sep. 1-4, 2015 Theoretical study of structure & synthesis mechanism of superheavy nuclei Shan-Gui Zhou ( 周善贵 ) State Key Laboratory of Theoretical Physics & Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing Supported by: NSFC & MOST; HPC Cluster of SKLTP/ITP-CAS ScGrid of CNIC-CAS

2 Introduction Contents Structure properties of heaviest nuclei Low-lying spectra of nuclei w/ Z~100 Fission barriers & potential energy surfaces Synthesis mechanism of heaviest nuclei The capture process: 1) A new formula for barrier penetration; 2) An empirical coupled channel model & a systematic study; 3) Breakup effects The CN formation process: 1) A DNS model with a dynamical PES; 2) Microscopic study with ImQMD simulations The survival process: A systematic study of the stability of excited SHN Summary & perspectives

3 Structure properties of heaviest nuclei Ground state properties Binding energy (separation energy, Q value) Deformation; exotic shapes? Single particle level (shell) structure location of the island Spectroscopy Saddle point properties Potential energy surface fission path & fission barrier Shell structure Isomeric states Longer half-life? A step stone toward the island of stability? Excited compound nucleus Level density Quenching of shell effects w/ temperature...

4 Magicity in SHN from the RCHB theory Zhang_Meng_Zhang_Geng_Toki 2005_NPA

5 Spectroscopy of nuclei with Z~100 Synthesis of SHN Decay modes & energies; X-sections,... Spectroscopy of SHN Detailed structure & stability Spectroscopy of deformed nuclei with Z ~ 100 & N ~ 152 Of interest in itself --- occurrence of deformation & K-isomerism Orbitals around the Fermi level in these nuclei stem from those connected to the spherical shell gaps in SHN (1/2 - [521]) Herzberg_Greenlees_Butler _Nature

6 Experimental facilities & status Data from ENSDF (Apr., 2012) by Zhen-Hua Zhang ( 张振华 )

7 Theoretical study of low-lying spectra Self-consistent approaches Macroscopic-Microscopic models Projected shell model Cranking shell model Egido_Robledo2000_PRL Delaroche _NPA Adamian _PRC Afanasjev _PRC Bender _NPA Cwiok _NPA Muntian _PRC R Sobiczewski _PRC Parkhomenko_Sobiczewski2004_APPB Parkhomenko_Sobiczewski2005_APPB Adamian _PRC Sun _PRC Al-Khudair _PRC He _NPA Liu... PRC R Chen _PRC Zhang _PRC R Zhang _PRC85_ Zhang _PRC

8 MOIs from a cranked Nilsson model w/ pairing treated by a particle number conserving method Zhang_He_Zeng_Zhao_SGZ2012_PRC85_014324

9 MOIs from a cranked Nilsson model w/ pairing treated by a particle number conserving method Expt.! Zhang_He_Zeng_Zhao_SGZ2012_PRC85_014324

10 246 Fm: g.s. band Jyvaskyla Piot PRC85_041301R

11 246 Fm: g.s. band Jyvaskyla Piot PRC85_041301R

12 256 Rf: g.s. band Jyvaskyla

13 256 Rf: g.s. band Jyvaskyla Zhang_Meng_Zhao_SGZ2013_PRC

14 Z = 120 w/ new Nilsson parameters Zhang_He_Zeng_Zhao_SGZ2013_NPR30-268

15 Survival probability & nuclear structure Nuclear structure inputs for W sur : S n, B f, level densities,

16 Survival probability & nuclear structure Nuclear structure inputs for W sur : S n, B f, level densities, W sur with S n & B f from various models differ a lot! Nasirov 2011_PRC

17 Survival probability & nuclear structure Nuclear structure inputs for W sur : S n, B f, level densities, W sur with S n & B f from various models differ a lot! Nasirov 2011_PRC Mic-Mac models Moller & Nix Sobiczewski et al.

18 Nuclear fission Fission barrier is crucial for the description of fission E Z = 92 b 2 Courtesy of Bing-Nan Lu ( 吕炳楠 )

19 Nuclear fission Fission barrier is crucial for the description of fission Various shapes may appear during fission E Z = 92 b 2 Courtesy of Bing-Nan Lu ( 吕炳楠 )

20 Nuclear fission Fission barrier is crucial for the description of fission Various shapes may appear during fission E Z = 92 b 2 To include as many shape degrees of freedom as possible Courtesy of Bing-Nan Lu ( 吕炳楠 )

21 Covariant Density Functional Theory (CDFT) Serot_Walecka1986_ANP16-1 Reinhard1989_RPP Ring1996_PPNP Vretenar_Afanasjev_Lalazissis_Ring2005_PR Meng_Toki_SGZ_Zhang_Long_Geng2006_PPNP57-470

22 MDC-CDFT (b 20, b 22, b 30, b 32, b 40, ) ph channel Non-linear Density-dependent Meson exchange NL3, NL3*, PK1,... DD-ME1, DD-ME2,... Point Coupling PC-F1, PC-PK1,... DD-PC1,... MDC-RMF MDC-RHB pp channel BCS Bogoliubov Constant gap Constant strength Delta force Separable force Lu_Zhao_SGZ 2011_PRC Zhao_Lu_Zhao_SGZ 2012_PRC Lu_Zhao_SGZ 2012_PRC R Lu_Zhao_Zhao_SGZ 2014_PRC

23 240 Pu: 3-dim. PES (b 20, b 22, b 30 ) AS & RS for g.s. & isomer, the latter is stiffer Triaxial & octupole shape around the outer barrier Triaxial deformation crucial around barriers Lu_Zhao_SGZ 2012_PRC R

24 B f of actinide nuclei inner barriers Influence of triaxiality Inner fission barriers lowered by 1~2 MeV Outer fission barriers lowered by 0.5~1 MeV Problems Th: out barriers primary 238 U:? 248 Cm: two fission paths outer barriers Empirical values: RIPL-3 (NDS2010) Lu_Zhao_SGZ 2012_PRC R

25 Three steps to a SHN Capture M. Schaedel Formation of CN Deexcitation of CN Capture CN formation neutron(s) emission

26 What we have done The capture process A new formula for barrier penetration An empirical coupled channel model & a systematic study Breakup effects The CN formation process A DNS model with a dynamical PES Microscopic study with ImQMD simulations The survival process A systematic study of the stability of excited SHN Fission barriers, separation energies, etc.

27 The capture process Path integral method WKB approximation Hill-Wheeler formula New formula by Li et al.... Hill_Wheeler1953_PR

28 Channel coupling effects Coupling effects due to rotation, vibration, nucleon transfer, W. Q. Shen, et al., 1987 Phys. Rev. C36, 115 Dasgupta _ARNPS48-401

29 Channel coupling effects Coupling effects due to rotation, vibration, nucleon transfer, W. Q. Shen, et al., 1987 Phys. Rev. C36, ,2 +, Dasgupta _ARNPS48-401

30 Barrier distribution Coupling effects due to rotation, vibration, nucleon transfer, are taken into account empirically by introducing a barrier distribution

31 Barrier distribution Coupling effects due to rotation, vibration, nucleon transfer, are taken into account empirically by introducing a barrier distribution

32 Barrier distribution Coupling effects due to rotation, vibration, nucleon transfer, are taken into account empirically by introducing a barrier distribution

33 Barrier distribution Coupling effects due to rotation, vibration, nucleon transfer, are taken into account empirically by introducing a barrier distribution

34 Two examples of barrier distribution Asymmetric Gaussian distribution Zagrebaev2001_PRC Zagrebaev 2001_PRC Superposition of two Gaussian functions Liu_Wang_Li_Wu_Zhao2006_NPA768-80

35 The present empirical CC approach Capture cross section Wang, Wen, Zhao, Zhao & SGZ arxiv: [nucl-th] Barrier distribution Parameters

36 Fusion reactions w/ well bound projectiles 217 reactions with 182 Z P Z T 1640 Wang, Wen, Zhao, Zhao & SGZ arxiv: [nucl-th]

37 Good examples Wang, Wen, Zhao, Zhao & SGZ arxiv: [nucl-th]

38 Bad examples Wang, Wen, Zhao, Zhao & SGZ arxiv: [nucl-th]

39 Breakup effects of weakly bound projectiles CF TF ICF Canto, Gomes, Donangelo & Hussein Phys. Rep., 2006, 424, 1-111

40 Suppression of CF: example 1 CF suppression for the reactions involving 6 Li, 7 Li, & 10 B projectiles almost independent of the target charge A correlation of CF suppression with the breakup threshold energy With targets of 208 Pb & 209 Bi Gasques, Hinde, Dasgupta, Mukherjee & Thomas Phys. Rev. C, 2009, 79,

41 Suppression of CF: example 2 A trend of systematic behavior for CF suppression as a function of the target charge & bombarding energy is not achieved

42 Suppression of CF: example 3 A trend of systematic behavior for CF suppression as a function of the target charge is not achieved either

43 What we aim at To explore the influence of the breakup on CF cross section at energies above the Coulomb barrier To perform a systematic study by comparing the fusion data with a uniform standard reference

44 What we aim at To explore the influence of the breakup on CF cross section at energies above the Coulomb barrier To perform a systematic study by comparing the fusion data with a uniform standard reference ECT* Workshop on Low-Energy Reaction Dynamics of Heavy-Ions & Exotic Nuclei, May 26-30, 2014

45 Reduction of fusion cross sections To eliminate the geometrical factors and static effects of the potential between the two nuclei, the fusion cross section & the collision energy are reduced to a dimensionless fusion function F(x) & a dimensionless variable x Canto, Gomes, Lubian, Chamon & Crema J. Phys. G, 2009, 36, Nucl. Phys. A, 2009, 821, Double folding & parameter-free Sao Paulo potential (SPP) Candido Ribeiro et al. Phys. Rev. Lett., 1997, 78, Chamon et al. Phys. Rev. Lett., 1998, 79,

46 Universal fusion function (UFF) Wong s formula UFF Wong Phys. Rev. Lett., 1973, 31, Canto, Gomes, Lubian, Chamon & Crema J. Phys. G, 2009, 36, Nucl. Phys. A, 2009, 821, 51-71

47 Fusion reactions w/ weakly bound projectiles 37 reactions: 8 projectiles including weakly bound & tightly bound nuclei Wang, Zhao, Gomes, Zhao & SGZ PRC 90 (2014)

48 CF functions of reactions with 6 Li as projectile Breakup channel: a+d, E B.U. = MeV, F B.U. = 0.6

49 CF functions of reactions with 7 Li as projectile Breakup channel: a+t, E B.U. = MeV, F B.U. = 0.67

50 CF functions of reactions with 9 Be as projectile Breakup channel: a+a+n, E B.U. = MeV, F B.U. = 0.68

51 CF functions of reactions with 10 B as projectile Breakup channel: a+ 6 Li, E B.U. = MeV, F B.U. = 0.8

52 CF functions of reactions with 11 B as projectile Breakup channel: a+ 7 Li, E B.U. = MeV, F B.U. = 0.91

53 CF functions of reactions with 12 C as projectile Breakup channel: a+ 8 Be, E B.U. = MeV, F B.U. = 0.88

54 CF functions of reactions with 13 C as projectile Breakup channel: a+ 9 Be, E B.U. = MeV, F B.U. = 0.94

55 CF functions of reactions with 16 O as projectile Breakup channel: a+ 12 C, E B.U. = MeV, F B.U. = 0.87

56 Systematics of CF suppression by breakup An exponential relation between suppression factor & threshold energy of the breakup channel 9 Be a bit out of the systematic trend, why? a = b = MeV c = MeV -1 Physics behind this relation?

57 Suppression of CF due to breakup probability CF cross section calculated as with breakup probability Diaz-Torres_Hinde_Tostevin_Dasgupta_Gasques 2007_PRL Two parameters: An intuitive guess for the factor A = Z P Z T & a obtained by fitting Wang, et al., in preparation

58 CF functions of reactions with 9 Be as projectile Preliminary A = Z P Z T & a = fm -1 for reactions with 9 Be as projectile Wang, et al., in preparation

59 CF functions of reactions with 6 Li as projectile Preliminary A = Z P Z T & a = fm -1 for reactions with 6 Li as projectile Wang, et al., in preparation

60 The 2nd exponential relation: One more step Preliminary a = b = MeV c = MeV -1 Wang, et al., in preparation

61 Summary & perspectives Structure of heaviest nuclei Low-lying spectra of nuclei w/ Z~100 Fission barriers & potential energy surfaces Detailed study of three steps for producing an SHN Capture: New penetration formula, systematics & breakup effects Fusion: Phenomenological & microscopic studies Survival: Systematics & nuclear structure Still far away from a comprehensive understanding Structure of SHN: Location of the island? Shapes, PES, & B f, Fusion mechanism: Adiabatic OR diabatic?

62 Zhou, Shan-Gui ITP/CAS Beijing Thanks 谢谢 URL: