1. 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)

2. 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

3. 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

4. LvFl May 2012 IUPAC 104 105 106 107 108 109 110 111 112 f lerovium livermorium Periodic Table Менделеев(1834-1907) 1869 Super Heavy Elements  less stable Jan. 2016 IUPAC

6. 1. Introduction Nuclear Chart and Stability of Nuclei

7. 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

8. 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

9. 268 106 162 298 114 184 Quadrupole deformation β 2 LD Potential energy / MeV LD + shell 250 98 152 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

10. 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) 10 20 Z=107 104 102 LDM 10

11. 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

12. G.N. Flerov (1913 -1990) Yu.Ts. Oganessian (1933-) P. Armbruster (1931-) S. Hofmann (1943-) G. Muenzenberg (1940-) K. Morita (1957-)

13. Fusion process in Superheavy mass region FUSION TRANSFER, QUASI-FISSION Nuclear Molecule Compound Nucleus (CN) Evaporation Residue (ER) FUSION-FISSION Fission Fragments 90~99%

14. „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

15. Y. Aritomo et al. PRC 59, 796 (1999) Cold fusion Hot fusion formation survival formation survival

16. Cold fusion reaction Hot fusion reaction 1994 110 Ds 62 Ni + 208 Pb  269 110 + n (GSI) 111 Rg 64 Ni + 209 Bi  272 111 + n (GSI) 1996 112 Cn 70 Zn + 208 Pb  277 112 + n (GSI)  named in Feb. 2010 1999 114 Fl 48 Ca + 244 Pu  292 114 + 3n (FLNR)  named in May. 2012 2000 116 Lv 48 Ca + 248 Cm  292 116 + 4n (FLNR)  named in May. 2012 2002 118 48 Ca + 249 Cf  294 118 + 3n (FLNR) 2003 115 48 Ca + 243 Am  288 115 + 3n  284 113 + α (FLNR) 2004 113 70 Zn + 209 Bi  278 113 + n (RIKEN) 2010 117 48 Ca + 249 Bk  294,293 117 + 3-4n (FLNR) Synthesis of New Elements Reports of new elements 2012 119 50 Ti + 249 Bk  296,295 119 + 3-4n (GSI- TASCA) 20

17. Cold fusion reaction Hot fusion reaction RIKEN 20

18. Experimental data Evaporation Residue Cross Section

19. Yu. Ts. Oganessian

20. Way to synthesize new SHE 1) Ti, Cr, Fe etc. beams  48 Ca beams 2) Secondary beams 3) Transfer reaction U+Th, U+Cm

21. Cold fusion reaction Hot fusion reaction RIKEN 20

22. G.N. Flerov (1913 -1990) “ On the way to Super-elements” 1986 Mir publishers Moscow 48 Ca + 244 Pu  290 114 + 2n 48 Ca + 248 Cm  294 116 + 2n 60 Ni + 238 U  298 120 84 Kr + 232 Th  316 126 84 Kr + 208 Pb  292 118 238 U + 238 U  476 184  166 Yb + 298 114 + 12n 136 Xe + 238 U  374 146  298 114 + 72 Ge + 4n Yu. Ts. Oganessian (1933 -)

23. Experimental data 蒸発残留核断面積

24. 合成のしやすさ（し難さ） 208 Pb, 209 Bi 標的＋重イオン 反応 100 102104106108110112114 原子番号 1b1b 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

25. Cold fusion reaction Hot fusion reaction RIKEN 20

27. Formation probability Survival probability Reaction time t < 10 -22 s 10 -22 < t < 10 -18 s ~10 -18 < t s Quasi-fission 90~99 % Fusion-fission TℓTℓ 1 st stage 2 nd stage 3 rd stage Touching probability

29. V.I. Zagrebaev, et al. Phy. Rev. C. 65. (2001) 014607

30. Fission width Bohr and Wheeler (1939) Statistical model (transition state method) initial state and final state Fission width ～

32. Nuclear shape is described by Two center parametrozation

33. 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

34. 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

35. Overview of Dynamical Process in reaction 36 S+ 238 U 10

36. two-center parametrization (Maruhn and Greiner, Z. Phys. 251(1972) 431) Nuclear shape (δ1=δ2)

37. Potential Energy mass asymmetry c.m. distance z δ=0

38. 298 114 Fission barrier recovers at low excitation energy

39. 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

40. 236U E*=20 MeV Process Without fluctuation : Newton EqWith fluctuation : Langevin Eq. 6

42. Itkis et al. Cal. Calculation results 48 Ca + 244 Pu Calculation

43. Way to synthesize new SHE 1) Ti, Cr, Fe etc. beams  48 Ca beams 2) Secondary beams 3) Transfer reaction U+Th, U+Cm

44. Yu. Ts. Oganessian and K. Morita 190 A=304 Possibility of synthesizing 298 114 Model Calculation Introduction 118 117 293 11 7 294 11 7 116 115 287 11 5 288 11 5 289 11 5 290 11 5 114 113 282 11 3 283 11 3 284 11 3 285 11 3 286 11 3 283 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 294 11 8 290 Lv 291 Lv 286 Fl 287 Fl 282 Cn 275 Hs 267 Rf CN 278 1 13 274 R g 270 Mt 266 B h 262 D b     278 113 274 Rg 270 Mt 266 Bh 262 Db 258 Lr  254 Md  254 Fm  250 Cf Z=114 N=184

45. Y. Aritomo et al. PRC 59, 796 (1999) Langevin eq. Statistical model

46. Trajectory calculation Two-center parametrization Capture Fusion Survival 3-dim Langevin Statistical model To estimate survival probability Dynamical model

47. 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

48. 298 114 Fission barrier recovers at low excitation energy

49. Smoluchowski equation

50. Time dependence of fission barrier height A=298

51. Yu. Ts. Oganessian and K. Morita 190 A=304 Possibility of synthesizing 298 114 Model Calculation Introduction 118 117 293 11 7 294 11 7 116 115 287 11 5 288 11 5 289 11 5 290 11 5 114 113 282 11 3 283 11 3 284 11 3 285 11 3 286 11 3 283 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 294 11 8 290 Lv 291 Lv 286 Fl 287 Fl 282 Cn 275 Hs 267 Rf CN 278 1 13 274 R g 270 Mt 266 B h 262 D b     278 113 274 Rg 270 Mt 266 Bh 262 Db 258 Lr  254 Md  254 Fm  250 Cf Z=114 N=184

52. Neutron Separation energy 3. Survival process Neutrons Easily evaporate

53. Neutron Separation energy 3. Survival process Rapid cooling n

54. 3. Survival process Approaching to the closed shell n

55. Neutron Separation energy 3. Survival process Rapid cooling Approaching to the closed shell

56. A=304 B f (MeV) Time dependence of fission barrier height

57. Smoluchowski equation

59. 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

60. Summary 1. The possibility of synthesizing a doubly magic superheavy nucleus, 298 114 184, 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. 4. 304 114 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.