Possibility of Synthesizing Doubly Magic Superheavy Nucleus Y. Aritomo Department of Electric and Electronic Engineering, Faculty of Science and Engineering, Kindai University, Higashi-Osaka, Osaka, Japan RISP, Daejeon, Korea 16 th February (2016)
Way to synthesize new SHE 1) Ti, Cr, Fe etc. beams 48 Ca beams Actinide target cf. Pb, Bi targets Z=113 RIKEN 2) Secondary beams 3) Transfer reaction U+Th, U+Cm
1. Introduction 2. Model Dynamical model with Langevin equation Two center shell model 3. Results Synthesis of Superheavy Elements (land at the center of Island of Stability) 4. Summary Contains
LvFl May 2012 IUPAC f lerovium livermorium Periodic Table Менделеев( ) 1869 Super Heavy Elements less stable Jan IUPAC
1. Introduction Nuclear Chart and Stability of Nuclei
Our Interest ・ Next magic number Z=82, N=126 ・ Verification of ‘Island of Stability’ （ predicted by macroscopic-microscopic model in 1960’s ） ・ Synthesis of new elements 1. Introduction N Z Nuclear Chart Stability of nuclei
G. Flerov and K. Petrjzak Leningrad 1940 N. Bohr and J.A. Wheeler (1939) Mayer and Jensen (1949) Magic numbers Models: Macro-microscopic Hartry-Fock-Bogolubov Relativistic-mean-field
Quadrupole deformation β 2 LD Potential energy / MeV LD + shell 超重元素領域における核分裂障壁 Shell correction energies in the macroscopic-microscopic model N Z
fissility parameter Spherical nucleus Surface energy Coulomb energy 超重元素領域の原子核の安定性 Ys.Ts. Oganessian, Yu.A. Lazarev Treatise on Heavy-Ion Science vol.4 (1985) Z= LDM 10
Experimental setup for synthesis of SHE LabCountryCityAcceleratorSeparator FLNRRussiaDubnaU400 U400M DGFRS VASSILISSA GSIGermanyDarmstadtUNILACSHIP TASCA RIKENJapanWakoRILACGALIS LBNLUSABerkeley88-inch CyclotronBGS GANILFranceCaenSPIRAL2's LINAC accelerator S3 (Super Separator Spectrometer) Gas-filled separator Electromagnetic separator
G.N. Flerov ( ) Yu.Ts. Oganessian (1933-) P. Armbruster (1931-) S. Hofmann (1943-) G. Muenzenberg (1940-) K. Morita (1957-)
Fusion process in Superheavy mass region FUSION TRANSFER, QUASI-FISSION Nuclear Molecule Compound Nucleus (CN) Evaporation Residue (ER) FUSION-FISSION Fission Fragments 90~99%
„Cold“ and „Hot“ Fusion Reactions Cold Fusion → doubly magic target nuclei: Pb, Bi; E*(CN) = 10 – 20 MeV; evaporation of 1 – 2 neutrons; up to now successful for Z ≤ 113 Hot Fusion → actinide targets (U, Cm, …) and 48 Ca projectiles; E*(CN) = 30 – 40 MeV; evaporation of 3 – 4 neutrons; up to now successful for Z ≤ 118 reaction Q-value large reaction Q-value small
Y. Aritomo et al. PRC 59, 796 (1999) Cold fusion Hot fusion formation survival formation survival
Cold fusion reaction Hot fusion reaction Ds 62 Ni Pb n (GSI) 111 Rg 64 Ni Bi n (GSI) Cn 70 Zn Pb n (GSI) named in Feb Fl 48 Ca Pu n (FLNR) named in May Lv 48 Ca Cm n (FLNR) named in May Ca Cf n (FLNR) Ca Am n α (FLNR) Zn Bi n (RIKEN) Ca Bk 294, n (FLNR) Synthesis of New Elements Reports of new elements Ti Bk 296, n (GSI- TASCA) 20
Cold fusion reaction Hot fusion reaction RIKEN 20
Experimental data Evaporation Residue Cross Section
Yu. Ts. Oganessian
Way to synthesize new SHE 1) Ti, Cr, Fe etc. beams 48 Ca beams 2) Secondary beams 3) Transfer reaction U+Th, U+Cm
Cold fusion reaction Hot fusion reaction RIKEN 20
G.N. Flerov ( ) “ On the way to Super-elements” 1986 Mir publishers Moscow 48 Ca Pu n 48 Ca Cm n 60 Ni U Kr Th Kr Pb U U 166 Yb n 136 Xe U Ge + 4n Yu. Ts. Oganessian (1933 -)
Experimental data 蒸発残留核断面積
合成のしやすさ（し難さ） 208 Pb, 209 Bi 標的＋重イオン 反応 原子番号 1b1b 1nb 10nb 100nb 100pb 10pb 1pb 0.1pb 理研 1 週間に 1 個 10 週間に 1 個 1 日に 1 個 1 日に 7 個 1 時間に 3 個 2 年に 1 個 2 分に 1 個 1 分に 5 個 1 秒に 1 個 2012/12/2524 九大 森田浩介氏による
Cold fusion reaction Hot fusion reaction RIKEN 20
Formation probability Survival probability Reaction time t < s < t < s ~ < t s Quasi-fission 90~99 % Fusion-fission TℓTℓ 1 st stage 2 nd stage 3 rd stage Touching probability
V.I. Zagrebaev, et al. Phy. Rev. C. 65. (2001)
Fission width Bohr and Wheeler (1939) Statistical model (transition state method) initial state and final state Fission width ～
Nuclear shape is described by Two center parametrozation
Goal of reaction theory Prediction of evaporation residue cross section of superheavy elements Proposal for optimum combination and incident energy Purpose of the dynamical calculation 1. mass and TKE distribution of fission fragments 2. fusion cross section 3. evaporation residue cross section 4. possibility of synthesis of superheavy elements 5. clarify fusion-fission dynamics Study for nuclear reaction theory
計算処方の概観 Time-evolution of nuclear shape in fusion-fission process 1. Potential energy surface 2. Trajectory described by equations Model Outlook of calculation methods c.m. distance z Mass asymmetry α
Overview of Dynamical Process in reaction 36 S+ 238 U 10
two-center parametrization (Maruhn and Greiner, Z. Phys. 251(1972) 431) Nuclear shape (δ1=δ2)
Potential Energy mass asymmetry c.m. distance z δ=0
Fission barrier recovers at low excitation energy
q i : deformation coordinate （ nuclear shape ） two-center parametrization (Maruhn and Greiner, Z. Phys. 251(1972) 431) p i : momentum m ij : Hydrodynamical mass ( inertia mass ） γ ij : Wall and Window (one-body) dissipation （ friction ） 多次元ランジュバン方程式 Multi-dimensional Langevin Equation Newton equation Friction Random force dissipation fluctuation ordinary differential equation Einstein relation Fluctuation-dissipation theorem
236U E*=20 MeV Process Without fluctuation : Newton EqWith fluctuation : Langevin Eq. 6
Itkis et al. Cal. Calculation results 48 Ca Pu Calculation
Way to synthesize new SHE 1) Ti, Cr, Fe etc. beams 48 Ca beams 2) Secondary beams 3) Transfer reaction U+Th, U+Cm
Yu. Ts. Oganessian and K. Morita 190 A=304 Possibility of synthesizing Model Calculation Introduction Cn 278 Rg 279 Rg 280 Rg 281 Rg 282 Rg 274 Mt 275 Mt 276 Mt 278 Mt 270 Bh 271 Bh 272 Bh 274 Bh 266 Db 267 Db 268 Db 270 Db Lv 291 Lv 286 Fl 287 Fl 282 Cn 275 Hs 267 Rf CN R g 270 Mt 266 B h 262 D b Rg 270 Mt 266 Bh 262 Db 258 Lr 254 Md 254 Fm 250 Cf Z=114 N=184
Y. Aritomo et al. PRC 59, 796 (1999) Langevin eq. Statistical model
Trajectory calculation Two-center parametrization Capture Fusion Survival 3-dim Langevin Statistical model To estimate survival probability Dynamical model
W ; survival probability One-dimensional Smoluchowski equation T(t) : temperature statistical code SIMDEC Cooling curve statistical code q ; separation distance We assume the particle emissions are limited to neutron emission in the neutron-rich heavy nuclei. probability distribution
Fission barrier recovers at low excitation energy
Smoluchowski equation
Time dependence of fission barrier height A=298
Yu. Ts. Oganessian and K. Morita 190 A=304 Possibility of synthesizing Model Calculation Introduction Cn 278 Rg 279 Rg 280 Rg 281 Rg 282 Rg 274 Mt 275 Mt 276 Mt 278 Mt 270 Bh 271 Bh 272 Bh 274 Bh 266 Db 267 Db 268 Db 270 Db Lv 291 Lv 286 Fl 287 Fl 282 Cn 275 Hs 267 Rf CN R g 270 Mt 266 B h 262 D b Rg 270 Mt 266 Bh 262 Db 258 Lr 254 Md 254 Fm 250 Cf Z=114 N=184
Neutron Separation energy 3. Survival process Neutrons Easily evaporate
Neutron Separation energy 3. Survival process Rapid cooling n
3. Survival process Approaching to the closed shell n
Neutron Separation energy 3. Survival process Rapid cooling Approaching to the closed shell
A=304 B f (MeV) Time dependence of fission barrier height
Smoluchowski equation
中性子放出エネルギー 中性子過剰核を使った実験的研究 Neutron rich beam --- J-PARC
Summary 1. The possibility of synthesizing a doubly magic superheavy nucleus, , was investigated on the basis of fluctuation dissipation dynamics. 2. Owing to the neutron emissions, we must generate more neutron-rich compound nuclei. 3. To calculate the survival probability, we employ the dynamical model has two advantages to achieving a high survival probability. 1 ) small neutron separation energy and rapid cooling 2 ) the neutron number of the nucleus approaches that of the double closed shell obtain a large fission barrier 5. The systematical investigation compared with the statistical model and dynamical one is necessary. We must apply the dynamical model for known systems.