Theoretical study of structure & synthesis mechanism of superheavy nuclei

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

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

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...

Magicity in SHN from the RCHB theory Zhang_Meng_Zhang_Geng_Toki 2005_NPA753-106

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... 2006_Nature442-896

Experimental facilities & status RITU@JYFL SHIP@GSI VASSILISSA@FLNR FMA@ANL LISE3@GANIL RMS@JAEA HIRFL@IMP... Data from ENSDF (Apr., 2012) by Zhen-Hua Zhang ( 张振华 )

Theoretical study of low-lying spectra Self-consistent approaches Macroscopic-Microscopic models Projected shell model Cranking shell model Egido_Robledo2000_PRL85-1198 Delaroche...2006_NPA771-103 Adamian...2011_PRC84-024324 Afanasjev...2003_PRC67-024309 Bender...2003_NPA723-354 Cwiok...1994_NPA573-356 Muntian...1999_PRC60-041302R Sobiczewski...2001_PRC63-034306 Parkhomenko_Sobiczewski2004_APPB35-2447 Parkhomenko_Sobiczewski2005_APPB36-3115 Adamian...2011_PRC84-024324 Sun...2008_PRC77-044307 Al-Khudair...2009_PRC79-034320 He...2009_NPA817-45 Liu... PRC86-011301R Chen...2008_PRC77-061305 Zhang...2011_PRC83-011304R Zhang...2012_PRC85_014324 Zhang...2013_PRC87-054308

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

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

246 Fm: g.s. band observed @ Jyvaskyla Piot...2012 PRC85_041301R

256 Rf: g.s. band observed @ Jyvaskyla

256 Rf: g.s. band observed @ Jyvaskyla Zhang_Meng_Zhao_SGZ2013_PRC87-054308

Z = 120 w/ new Nilsson parameters Zhang_He_Zeng_Zhao_SGZ2013_NPR30-268

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

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_PRC84-044612

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_PRC84-044612 Mic-Mac models Moller & Nix Sobiczewski et al.

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

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 )

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 )

Covariant Density Functional Theory (CDFT) Serot_Walecka1986_ANP16-1 Reinhard1989_RPP52-439 Ring1996_PPNP37-193 Vretenar_Afanasjev_Lalazissis_Ring2005_PR409-101 Meng_Toki_SGZ_Zhang_Long_Geng2006_PPNP57-470

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_PRC84-014328 Zhao_Lu_Zhao_SGZ 2012_PRC86-057304 Lu_Zhao_SGZ 2012_PRC85-011301R Lu_Zhao_Zhao_SGZ 2014_PRC89-014323

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_PRC85-011301R

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 230-232 Th: out barriers primary 238 U:? 248 Cm: two fission paths outer barriers Empirical values: RIPL-3 (NDS2010) Lu_Zhao_SGZ 2012_PRC85-011301R

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

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.

The capture process Path integral method WKB approximation Hill-Wheeler formula New formula by Li et al.... Hill_Wheeler1953_PR089-1102

Channel coupling effects Coupling effects due to rotation, vibration, nucleon transfer, W. Q. Shen, et al., 1987 Phys. Rev. C36, 115 Dasgupta...1998_ARNPS48-401

Channel coupling effects Coupling effects due to rotation, vibration, nucleon transfer, W. Q. Shen, et al., 1987 Phys. Rev. C36, 115 0 +,2 +,4 + 2 + 0 + 6 + 4 + 2 + 0 + Dasgupta...1998_ARNPS48-401

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

Two examples of barrier distribution Asymmetric Gaussian distribution Zagrebaev2001_PRC64-034606 Zagrebaev 2001_PRC65-014607 Superposition of two Gaussian functions Liu_Wang_Li_Wu_Zhao2006_NPA768-80

The present empirical CC approach Capture cross section Wang, Wen, Zhao, Zhao & SGZ arxiv:1504.00756 [nucl-th] Barrier distribution Parameters

Fusion reactions w/ well bound projectiles 217 reactions with 182 Z P Z T 1640 Wang, Wen, Zhao, Zhao & SGZ arxiv:1504.00756 [nucl-th]

Good examples Wang, Wen, Zhao, Zhao & SGZ arxiv:1504.00756 [nucl-th]

Bad examples Wang, Wen, Zhao, Zhao & SGZ arxiv:1504.00756 [nucl-th]

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

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, 034605-8

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

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

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

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, 015109 Nucl. Phys. A, 2009, 821, 51-71 Double folding & parameter-free Sao Paulo potential (SPP) Candido Ribeiro et al. Phys. Rev. Lett., 1997, 78, 3270-3273 Chamon et al. Phys. Rev. Lett., 1998, 79, 5218-5221

Universal fusion function (UFF) Wong s formula UFF Wong Phys. Rev. Lett., 1973, 31, 766-769 Canto, Gomes, Lubian, Chamon & Crema J. Phys. G, 2009, 36, 015109 Nucl. Phys. A, 2009, 821, 51-71

Fusion reactions w/ weakly bound projectiles 37 reactions: 8 projectiles including weakly bound & tightly bound nuclei Wang, Zhao, Gomes, Zhao & SGZ PRC 90 (2014) 034612

CF functions of reactions with 6 Li as projectile Breakup channel: a+d, E B.U. = 1.474 MeV, F B.U. = 0.6

CF functions of reactions with 7 Li as projectile Breakup channel: a+t, E B.U. = 2.467 MeV, F B.U. = 0.67

CF functions of reactions with 9 Be as projectile Breakup channel: a+a+n, E B.U. = 1.573 MeV, F B.U. = 0.68

CF functions of reactions with 10 B as projectile Breakup channel: a+ 6 Li, E B.U. = 4.461 MeV, F B.U. = 0.8

CF functions of reactions with 11 B as projectile Breakup channel: a+ 7 Li, E B.U. = 8.665 MeV, F B.U. = 0.91

CF functions of reactions with 12 C as projectile Breakup channel: a+ 8 Be, E B.U. = 7.367 MeV, F B.U. = 0.88

CF functions of reactions with 13 C as projectile Breakup channel: a+ 9 Be, E B.U. = 10.648 MeV, F B.U. = 0.94

CF functions of reactions with 16 O as projectile Breakup channel: a+ 12 C, E B.U. = 7.162 MeV, F B.U. = 0.87

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 = 0.330 b = 0.290 MeV c = 0.087 MeV -1 Physics behind this relation?

Suppression of CF due to breakup probability CF cross section calculated as with breakup probability Diaz-Torres_Hinde_Tostevin_Dasgupta_Gasques 2007_PRL98-152701 Two parameters: An intuitive guess for the factor A = Z P Z T & a obtained by fitting Wang, et al., in preparation

CF functions of reactions with 9 Be as projectile Preliminary A = Z P Z T & a = 0.603 fm -1 for reactions with 9 Be as projectile Wang, et al., in preparation

CF functions of reactions with 6 Li as projectile Preliminary A = Z P Z T & a = 0.585 fm -1 for reactions with 6 Li as projectile Wang, et al., in preparation

The 2nd exponential relation: One more step Preliminary a = 0.604 b = 0.116 MeV c = 0.194 MeV -1 Wang, et al., in preparation

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?

Zhou, Shan-Gui ITP/CAS Beijing Thanks 谢谢 Email: sgzhou@itp.ac.cn URL: www.itp.ac.cn/~sgzhou