Kazimierz 2011

1. Predictions of the FBD model for the synthesis cross sections of Z=114-120 elements based on macroscopic-microscopic fission barriers T. Cap, M. Kowal, K. Siwek-Wilczyńska, A. Sobiczewski, J. Wilczyński Kazimierz 2011

3. Existence of super–heavy nuclei due to shell effects Nuclear Elongation

4. 249Bk(48Ca,xn) 297-xn117; x = 3, 4 X + 208Pb, 209Bi 48Ca + X Yu. Ts. Oganessian et al. PRL 104, 142502 (2010)

5. Confirmation of Dubna results at GSI 283Cn CN 9.54±0.06 MeV T½ = 3.8 s bsf= 0.10 279Ds CN 283Cn 3 chains 9.70 / 228 MeV T½ = 0.20 s b= 0.10 275Hs 9.5200.015 /23215 MeV T½ = 6.9 s bsf = 0.5 9.29±0.08 MeV T½ = 0.19 s b= 1.0 279Ds 271Sg 6.9 –2.3 8.54 / 248 MeV T½ = 1.9 min b= 0.70 4 chains 267Rf 30 –15 210 MeV T½ = 0.18 s FLNR GSI 0.32 –0.07  = 2.5 (+1.8,-1.1) pb  = 0.72 (+0.58,–0.35) pb 260 MeV TKE T½ = 1.3 h bsf= 1.0 S. Hofmann et al. , Eur. Phys. J. A32,251 (2007) 48Ca+238U 286Cn + 3n

6. 48Ca+244Pu288114+4n CN 288114 CN 288114 9.940.06 T½ = 0.8 s 284Cn 9.940.04 T½ = 0.47 s 0.27 –0.16 284Cn 0.24 –0.12 30 –15 216 MeV T½ = 97 ms 50 –25 T½ = 101 ms 31 –19 FLNR GSI 8 events, = 12 events, = Ch. Düllmann et al., PRL 104, 252701(2010) J.M. Gates et al. PRC 83, 054618 (2010) Yu.Ts. Oganessian, Phys. Rev. C 70, 064609 (2004) Yu.Ts. Oganessian, J. Phys. G 34 (2007) R165

7. 48Ca+244Pu289114+3n CN 289114 9.850.04 T½ = 0.97 s 285Cn 0.97 –0.32 9.190.04 T½ = 30 s 281Ds GSI 30 –10 (8.67 MeV) (T = 5.7 s) 20 –7 T½ = 20 s 277Hs 18 –2 Tsf = 3 s s= 5 chains, CN 289114 FLNR 9.820.05 T½ = 2.6 s 285Cn 1.2 –0.7 9.150.05 T½ = 29 s 281Ds 13 –7 212 MeV T½ = 11.1 s s = 2 chains, 5.0 –2.7 Yu.Ts. Oganessian, Phys. Rev. C 70, 064609 (2004) Yu.Ts. Oganessian, J. Phys. G 34 (2007) R165 Ch. Düllmann et al. PRL 104, 252701 (2010)J.M. Gates et al. PRC 83, 054618 (2011)

8. 48Ca+248Cm 296-xn116 248Cm 296116 6 chains 4 chains 4 chains1 chains 3.4 pb0.9 pb E* = 41.0 MeV GSI-SHIP 6 chains2 chains 3.3 pb1.2 pb E* = 39.0 MeV FLNR S. Hofmann et al., GSI Scientific Report 2010, 197

9. Confirmation of Dubna results in LBNL 48Ca + 242Pu290-xn114+xn x = 3, 4, 5 242 LBNL, Berkeley FLNR,DUBNA 2n - 1 event,=0.5 (+1.0, -0.5)pb 3n - 15 events, =3.6 (+2.4, -1.6) pb 4n - 9 events, =4.5 (+2.5, -1.5) pb 3n - 1 event, =3.1 (+4.9, -2.6) pb 4n - 1 event, =3.1 (+4.9, -2.6) pb 5n - 1 event, =0.6 (+0.9, -0.5) pb Yu.Ts. Oganessian, Phys. Rev. C 70, 064609 (2004) Yu.Ts. Oganessian, J. Phys. G 34 (2007) R165 L. Stavstera et al., Phys. Rev. Lett. 103, 132502 (2009) P. A. Ellison et al.,Phys. Rev. Lett. 105, 182701 (2010)

10. How to produce elements with Z > 118? Essential experimental difficulties: The use of48Ca beams will require heavier targets of Z > 98. Possibilities:Z=99, 252Es, 254Es T1/2 = 472 d, 275.7 d Z=100 257Fm T1/2 =100.5 d Alternative: Heavier beams → much smaller cross section Multi-nucleon transfer reactions.

11. First experiments to produce element of Z = 120 GSI Dubna 58Fe 244Pu Experiments 2007/2008 GSIDubna Number of irradiation days : 120 days --- Excitation energy of the CN : 36.0 MeV 45.5 MeV Total number of beam particles : ≈ 2 x 1019 7.1 x 1018 Number of detected events : 0 0 Cross section limits: <0.1 pb< 0.4 pb Yu. Ts. Oganessian et al. Phys. Rev. C 79, 024603 (2009)

12. Nucleus-nucleus collision which may lead to the formation of super-heavy nuclei survive evaporation residue fusion capture symetric fission fast fission (synthesis) =(capture)×P(fusion)× P(survive) T. Cap, K. Siwek-Wilczyńska, J. Wilczyński, IJMP E 20, 308 (2011) T. Cap, K. Siwek-Wilczyńska, J. Wilczyński, PR C 83, 054602 (2011)

13. FBD lmax– calculated from the capture cross section. semiempirical formula Gaussian error function • This formula derived assuming: • Gaussian shape of the fusion barrier distribution • Classical expression forσfus(E,B)=πR2(1-B/E) W. Świątecki, K. Siwek-Wilczyńska, J. Wilczyński Phys. Rev. C 71 (2005) 014602, Acta Phys. Pol. B34(2003) 2049 3 parameters:B0, w, R obtained from2 fit to 48 experimental near-barrier fusion excitation functions for 40 < ZCN< 98 (K. Siwek-Wilczyńska, J. Wilczyński Phys. Rev. C 69 (2004) 024611)

14. d2 d1 R1 R2 r Pl(fusion) J. Błocki, W. J. Świątecki, Nuclear Deformation Energies, Report LBL 12811 (1982) CN Smoluchowski Diffusion equation for the parabolic potential Pl(fusion) = ½(1-erf√H(l)/T) H - the barrier opposing fusion T - the temperature of the fusing system λ= (d1+ d2)/(R1 + R2) - neck parameter ρ = r/(R1+ R2) – relative distance Δ = (R1- R2)/(R1+ R2) – asymmetry parameter

15. Pxnl (survive)for xn reaction Partial widths forneutron emission – Weisskopf formula Upper limit of the final-state excitation energy after emission of a particle i where: i– crosssection for the production of the compound nucleus in the inverse process mi, si, εi- mass, spin and kinetic energy of the emitted particle ρ, ρi –level densities of the parent and daughter nuclei The fissionwidth (transition state method), E*< 40 MeV Upper limit of the thermal excitation energy at the saddle

16. – shell correction energy, δshell(g.s.),δshell(saddle) The level density is calculated using the Fermi-gas-model formula • Shell effects included as proposed by Ignatyuk (A.V. Ignatyuk et al., Sov. J. Nucl. Phys. 29 (1975) 255) where: U - excitation energy, Ed - damping parameter , (W. Reisdorf, Z. Phys. A. – Atoms and Nuclei 300 (1981) 227) Bs , Bk ( W.D. Myers and W.J. Świątecki, Ann. Phys. 84 (1974) 186)

17. 1n reaction channel Neutron energy spectrum P<1n-probability that after emission of the first neutronthe excitation energy is smaller than the threshold for second chance fission or 2n emission. threshold 2n reaction channel (1 - P<) P<  xn reaction channel

18. To calculate the survival probability we need to know (for all nuclei in the xn deexcitation cascade): • ground state masses, • fission barriers, • shell correction energies and deformations (in the ground state and saddle). • Those values were calculated using the Warsaw macroscopic-microscopic model including thenonaxial shapes. • M. Kowal, Jachimowicz, A. Sobiczewski, Phys. Rev. C82 (2010) 014303 • M. Kowal (unpublished) • A. Sobiczewski (unpublished).

19. d2 d1 R1 R2 r Systematics of the sinj parameter from the fit to the maximum values of the experimental cross sections for 2n, 3n, 4n and 5n channels in 48Ca + X reactions (complete set of existing data) sinj

21. The systematics of the sinj used to predict cross sections for Z = 119 The reaction 48Ca +252Es predicted to have measurable cross section

22. Z = 120 These values of the evaporation residue cross sections are much smaller (at least one order of magnitude) than previouslypublished predictions. V.Zagrebaev and W. Greiner, Phys. Rev. C78 (2008) 034610 K. Siwek-Wilczynska, T. Cap, J. Wilczynski, IJMP E19 (2010) 500

23. The largest cross section for producing the element 120 is expected for the reaction Ti + Cf. Maximum value, of several femtobarns, is however below possibilities of present experiments. V.Zagrebaev and W. Greiner, Phys. Rev. C78 (2008) 034610 Z. H. Liu, Jing-Dong Bao, Phys. Rev C80 (2009) 054608 K. Siwek-Wilczynska, T. Cap, J. Wilczynski, IJMP E19 (2010) 500 A. Nasirov et al. IJMP E20 (2011) 406

24. SUMMARY A modified, l-dependent version of the Fusion by Diffusion model was applied to calculate synthesis cross sections of superheavy nuclei of Z =114 – 120 in hot fusion reactions. Fission barriers and ground state masses calculated with the Warsaw macroscopic-microscopic model (including nonaxial shapes) were applied. Good agreement with experimental cross sections was obtained. This allowed us to use the same theoretical input to predict cross sections for synthesis of elements Z = 119 and 120.

28. P. Möller et al., PRC 79, 064304 (2009) M. Kowal, P. Jachimowicz, A. Sobiczewski, PRC 82,014303 (2010)