70 YEARS OF FISSION Kazimierz 2008

1. Comment on a frequent error in calculations of then/fratio W.J. Świątecki, J. Wilczyński and K. S-W 70 YEARS OF FISSION Kazimierz 2008

2. G. G. Adamian, N. V. Antonenko, and W. Scheid, Nucl. Phys. A678, 24 (2000) • A. S. Zubov, G. G. Adamian, N. V. Antonenko, S. Ivanova, and W.Scheid, Phys. Rev. C 68, 014616(2003). • G. G. Adamian, N. V. Antonenko, S.P. Ivanova, and W. Scheid, Phys.Rev. C 62, 064303 (2000). • A. S. Zubov, G. G. Adamian, N. Antonenko, S. Ivanova, and W.Scheid, Phys. Rev. C 65, 024308(2002). • G. G. Adamian, N. V. Antonenko, and W. Scheid, Phys. Rev. C 69, 011601 (2004) • G. G. Adamian, N. V. Antonenko, and W. Scheid, Phys. Rev. C 69, 014607 (2004) • G. G. Adamian, N. V. Antonenko, and W. Scheid, Phys. Rev. C 69, 044601 (2004). • Z.-Q. Feng, G.-M. Jin, J.-Q. Li, and W. Scheid, Phys. Rev. C 76, 044606 (2007). • Z.-Q. Feng, G.-M. Jin, F. Fu, and J.-Q. Li, Nucl. Phys. A771, 50 (2006). • Z. H. Liu and Jing-Dong Bao, Phys. Rev. C 76, 034604 (2007). • V. I. Zagrebaev, Phys. Rev. C 64, 034606 (2001). • Yu. Ts. Oganessian et al., Phys. Rev. C 64, 054606 (2001). • V. I. Zagrebaev, Y. Aritomo, M. G. Itkis, Yu. Ts. Oganessian, M. Ohta, Phys. Rev. C 65, 014607 (2002). • M. G. Itkis, Yu. Ts. Oganessian, and V. I. Zagrebaev, Phys. Rev. C65, 044602 (2002). • V. I. Zagrebaev, Nucl. Phys. A734, 164 (2004) • R. N. Sagaidak, V. I. Chepigin, A. Kabachenko, J. Rohac, Yu.Ts. Oganessian, A. G. Popeko, A. V. Yeromin, • A. D'Arrigo, G.Fazzio, G. Giardina, M. Herman, R. Ruggieri, and R. Sturiale, J.Phys. G 24, 611 (1998). • G. Fazio, G. Giardina, A. Lamberto, A. I. Muminov, A. K. Nasirov,F. Hanappe, and L. Stuttge, • Eur. Phys. J. A 22, 75 (2004). • G. Fazio, G. Giardina, G. Mandaglio, R. Ruggieri, A. I. Muminov,A. K. Nasirov, Yu. Ts. Oganessian, A. G. • Popeko, R. Sagaidak,A. Yeromin, S. Hofmann, F. Hanappe, C. Stodel, Phys. Rev. C72, 064614 (2005). • W. Loveland, D. Peterson, A. M. Vinodkumar, P. H. Sprunger, D.Shapira, J. F. Liang, G. A. Souliotis, D. J. • Morrissey, and P.Lofy, Phys. Rev. C 74, 044607 (2006). • W. Loveland, Phys. Rev. C 76, 014612 (2007). • R. S. Naik, W. Loveland, P. H. Sprunger, A. M. Vinodkumar, D.Peterson, C. L. Jiang, S. Zhu, X. Tang, E. F. • Moore, and P.Chowdhury, Phys. Rev. C 76, 054604 (2007).

3. E = Egs+E* - total energy En= (Mn+MA-1) c2 = Egs + Bn Ef–the saddle-point energy To calculate the ratio Γn/Γf we need the level density of the daugther nucleus (A-1) ρ(E-En) and the level density at the saddle-point of the nucleus A ρ(E-Ef) E-En= Egs +E*-Egs-Bn= E*- Bn E-Ef= Egs+E*-Ef = E*- (Ef-Egs)

4. (1) R. Vandenbosch & J.R. Huizenga, „Nuclear Fission”- formula (VII-3) • mn,sn, εn - 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 Ef– saddle-point energy En- energy of the system n +(A-1) nucleus • E-En= Egs +E*-Egs-Bn= E*- Bn • E-Ef= Egs+E*-Ef = E*- (Ef-Egs) , and a =const Assuming: (2) R. Vandenbosch & J.R. Huizenga, „Nuclear Fission” - formula (VII-7)

6. 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, Ed – damping parameter Eshell – shell correction energy, aLDM- 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) Ef – Egs = BLDM + Bmicr exp(-E*/Ed) for super-heavy nuclei BLDM= 0 Bmicr= - Eshell(gs) independent of the excitation energy dependent on the excitation energy no shell effects in (A-1) nucleus shell effects in fission channel, only via Eshell(gs) an, af = const

7. ACN= 266 Bn = 8.22 MeV BLDM = 0 Bmicro= -Eshell = 5.27 MeV Bf = Bmicroexp(-E*/Ed) an, af= const numerical integration, with energy dependent level density parameter, Bf = 5.27 MeV G.G. Adamian et al. PRC 69, 014607 (2004) PRC 62, 064303 (2000) PRC 69, 011601 (2004) PRC 69, 014607 (2004) PRC 69, 044601 (2004) W. Loveland PRC 76, 014612 (2007) W. Loveland et al. PRC 74, 044607 (2006) R.S. Naik et al. PRC 76, 054604 (2007)

8. ACN= 297 Bn = 6.21 MeV BLDM = 0 Bmicro= -Eshell = 8.27 MeV Bf = Bmicroexp(-E*/Ed) an, af = const numerical integration, with energy dependent level density parameter, Bf = 8.27 MeV G.G. Adamian et al. PRC 69, 014607 (2004) PRC 62, 064303 (2000) PRC 69, 011601 (2004) PRC 69, 014607 (2004) PRC 69, 044601 (2004) W. Loveland PRC 76, 014612 (2007) W. Loveland et al. PRC 74, 044607 (2006) R.S. Naik et al. PRC 76, 054604 (2007)

9. In case of the saddle-point energy (erroneously) replaced by the energy dependent fission barrier Bf(E*)= - Eshell(gs) exp(-E*/Ed), the classical fission threshold shifts from Ethr = Bf = - Eshell(gs) to a value satisfying Ethr - Eshell(gs)exp(-Ethr/Ed) = 0 For Z=118 Ethr = Bf= 8.27MeV→Ethr= 6.40 MeV (for Ed=25 MeV) Conclusions: The scheme of calculating the Γn/Γf ratios using the concept of energy dependent fission barrier of Adamian et al. is erroneous and leads to predictions which at low excitation energies may deviate from correctly evaluated values by a factor of 1000 or more. Moreover, it leads to unphysical predictions for the existence of fission at energetically forbidden subthreshold excitation energies.

12. Figure taken from „Nuclear Fission” R. Vandenbosh & J.R. Huizenga Academic Press 1973 Excitation energy dependence of Γn/Γf for different values of(Ef-Bn). The level density parameters af and an were assumed to be equal (25 MeV-1) and Bn= 6 MeV.

13. Edef (ε) ε δshellsd δshellg.s. Bf EdefLDM EdefTOT