1. Kazimierz 200 9 What is the best way to synthesize the element Z=120 ? K. Siwek-Wilczyńska, J. Wilczyński, T. Cap

2. A model for calculating the evaporation residue cross sections for reactions with x (1,2,….) neutrons evaporated from the compound nucleus. Our approach is based on the assumption:  (synthesis) =  (capture) × P(fusion) × P(survive)  (fusion) =  (capture) × P(fusion)

3.  Capture cross section  (capture) - the „diffused-barrier formula” ( 3 parameters): W. Świątecki, K. Siwek-Wilczyńska, J. Wilczyński Phys. Rev. C 71 (2005) 014602, Acta Phys. Pol. B34(2003) 2049 A  2 fit to 48 experimental near-barrier fusion excitation functions in the range of 40 < Z CN < 98 resulted in the systematics that allow us to predict values of the three parameters B 0, w, R  (K. Siwek-Wilczyńska, J. Wilczyński Phys. Rev. C 69 (2004) 024611) Formula derived assuming: Gaussian shape of the fusion barrier distribution Classical expression for σ fus (E,B)=πR 2 (1-B/E)

4. For very heavy systems, a range of partial waves contributing to CN formation is limited ( critical angular momentum for disappearing macroscopic + microscopic fission barrier). We propose:  cap (subcritical l ) =  ca p for E ≤ B o  cap ( subcritical l ) =  cap (E=B o )*B o /E c.m. for E > B o

5.  systematics of P(fusion) = Hindrance  (synthesis) =  (capture) × P(fusion) × P(survive) hindrance = P(fusion) = σ exp (synthesis)/(σ(capture)  P(survival)) Hindrance deduced from experimental xn data as a function of Coulomb interaction parameter z and the energy excess above the mean barrier B o. K. Siwek-Wilczyńska, A. Borowiec and J. Wilczyński, IJMP E17 (2008) 12

6. Y. Ts. Oganessian et al.

7.  P(survive) – Statistical model (Monte Carlo method) Partial widths for emission of light particles – Weisskopf formula where: The fission width (transition state method), E*< 40 MeV Upper limit of the final-state excitation energy after emission of a particle i Upper limit of the thermal excitation energy at the saddle  i – cross section for the production of the compound nucleus in the inverse process m i, s i, ε i - mass, spin and kinetic energy of the emitted particle ρ, ρ i – level densities of the parent and daughter nuclei The integrals were calculated using very accurate analytic formulas derived by W.J. Świątecki (W.J. Świątecki et al. Phys. Rev. C78 (2008)0 54604)

8. The level density is calculated using the Fermi-gas-model formula included as proposed by Ignatyuk (A.V. Ignatyuk et al., Sov. J. Nucl. Phys. 29 (1975) 255) Shell effects where: U - excitation energy, Ed - damping parameter – shell correction energy: δ shell (g.s.), (P. Möller et al., At. Data Nucl. Data Tables 59 (1995) 185 Muntian et al. Acta. Phys. Pol. B32 (2003) 2141) δ shell (saddle)≈ 0 B s, B k ( W.D. Myers and W.J. Świątecki, Ann. Phys. 84 (1974) 186) (W. Reisdorf, Z. Phys. A. – Atoms and Nuclei 300 (1981) 227)

9. The ratio of  n  f depends very strongly on the value of B f - B n B f = (saddle mass – ground state mass) B n = neutron separation energy Möller et al. – P. Möller et al., At. Data Nucl. Data Tables 59 (1995) 185, Myers & Swiatecki – W.D. Myers and W.J. Swiatecki LBL-36803 Sobiczewski et al. –I. Muntian et al. Acta. Phys. Pol. B32 (2003) 2141 ) A change of B f -B n by 1 MeV results in the change of  n /  f on each step of the deexcitation cascade by one order of magnitude. BnBn BfBf

10. Comparison of the measured (black dots) cross sections for synthesis of super heavy nuclei (Z = 114-118) with our calculations (solid red and black lines) experimen t - Yu. Ts. Oganessian et al., Phys. Rev. C69 (2004) 021601(R), Phys Rev. C70 (2004) 064609, Phys. Rev. C74 (2006) 044602 calculations – K. Siwek-Wilczyńska, A. Borowiec, J. Wilczyński, IJMP E18 (2009) 1073 Conclusion: the ground state masses and fission bariers of Sobiczewski et al. are the most suitable in the range of heaviest nuclei around Z = 115 and heavier.

11. The heaviest produced superheavy nucleus – 48 Ca + 249 Cf 294 118 + 3n There is a possibility to produce 296 118 in 48 Ca + 251 Cf 299 118 * 296 118 +3n Can we go further? no target heavier than Cf !!!! using heavier projectiles means decreasing the formation cross section

12. Several experimental attempts to produce nuclei with Z > 118 Other reactions to produce nucleus with Z = 120 50 Ti + 249 Cf 299 120* 50 Ti + 251 Cf 301 120* 54 Cr + 248 Cm 302 120* 58 Fe + 244 Pu 302 120* 64 Ni + 238 U 302 120* 58 Fe + 244 Pu 302-xn 120 * + xn - no events observed Yu. Ts. Oganessian et al. Phys. Rev. C 79 (2009) 024603 The sensitivity of the experiment corresponded to a cross section of 0.4 pb for the detection of one event.

13. Evaporation residue cross section for Z=120 Conclusion : The most promising reaction is 54 Cr + 248 Cm.

14.  (synthesis) =  (capture) × P(fusion) × P(survive)  (capture) - Does not change significantly from one system to another. Resulting uncertainties are not large unless deeply sub-barrier reactions are studied (e.q. cold fusion) P(fusion) - Depends on the Coulomb parameter and excitation energy. Theoretical (or phenomenological) predictions may results in large uncertainties of several orders of magnitude for unexplored heavy and symmetric systems. P(survival) - Very strong dependence on B f -B n easily resulting in orders of magnitudes differences of the cross sections. It is very important to use well tested theoretical predictions of both, ground state and saddle masses.

15. Capture and fusion cross section

16. E = E gs + E * - total energy E n = (M n +M A-1 ) c 2 = E gs + B n E f – the saddle-point energy To calculate the ratio Γ n /Γ f we need the level density of the daugther nucleus (A-1) ρ(E-E n ) and the level density at the saddle-point of the nucleus A ρ(E-E f ) E-E n = E gs +E * -E gs -B n = E* - B n E-E f = E gs +E*-E f = E*- (E f -E gs )

17. „Experimental” determination of fusion hindrance 86 Kr + 136 Xe 222 Th 16 0 + 204 Pb 40 Ar + 180 Hf 48 Ca + 172 Yb 220 Th 70 Zn + 150 Nd 124 Sn + 96 Zr 40 Ar + 178 Hf 58 Fe + 160 Gd 218 Th 64 Ni + 154 Sm 124 Sn + 94 Zr 40 Ar + 176 Hf 86 Kr + 130 Xe 216 Th 124 Sn + 92 Zr 19 F + 197 Au 30 Si + 186 W 216 Ra 22 Ne + 194 Pt 86 Kr + 134 Ba 220 U 86 Kr + 138 Ba 224 U 48 Ca + 208 Pb  102 48 Ca + 209 Bi  103 50 Ti + 208 Pb  104 50 Ti + 209 Bi  105 54 Cr + 208 Pb  106 54 Cr + 209 Bi  107 58 Fe + 208 Pb  108 58 Fe + 209 Bi  109 64 Ni + 209 Bi  111 70 Zn + 208 Pb  112

18. m n, s n, ε n - mass, spin and kinetic energy of the emitted neutron  f - level density of the fissioning nucleus (at saddle)  n - level density of the daughter nucleus (A-1) E – total energy E f – saddle-point energy E n - energy of the system n + (A -1) nucleus E-E n = E gs +E*-E gs -B n = E*- B n E-E f = E gs +E*-E f = E*- (E f -E gs ) R. Vandenbosch & J.R. Huizenga, „Nuclear Fission” - formula (VII-3) R. Vandenbosch & J.R. Huizenga, „Nuclear Fission” - formula (VII-7) Assuming:, and a =const (1) (2)

20. independent of the excitation energy Shell effects included using: the energy dependent level density parameter ( A.V. Ignatyuk et al., Sov. J. Nucl. Phys. 29 (1975) 255 ) where: E * - excitation energy, E d – damping parameter E shell – shell correction energy, a LDM - the LDM level density parameter or an exponentially dependent fission barrier replacing the saddle-point energy (erroneously postulated by G. G. Adamian, N. V. Antonenko and W. Scheid, Nucl. Phys. A678, 24 (2000), and their followers) E f – E gs = B LDM + B micr exp(-E*/E d ) dependent on the excitation energy for super-heavy nuclei B LDM = 0 B micr = - E shell (gs) a n, a f = const no shell effects in (A-1) nucleus shell effects in fission channel, only via E shell (gs )