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Comment on a frequent error in calculations of
the ?n/?f ratio W.J. Swiatecki, J. Wilczynski
and K. S-W
70 YEARS OF FISSION Kazimierz 2008
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• G. G. Adamian, N. V. Antonenko, and W.
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  (2002).
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  Scheid, Phys. Rev. C 69, 011601 (2004)
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  Scheid, Phys. Rev. C 69, 014607 (2004)
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• Eur. Phys. J. A 22, 75 (2004).

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E Egs E - total energy En (MnMA-1) c2
Egs Bn Ef the saddle-point energy
To calculate the ratio Gn/Gf we
need the level density of the daugther nucleus
(A-1) ?(E-En) and the level density
at the saddle-point of the nucleus A
?(E-Ef) E-En Egs E-Egs-Bn E- Bn E-Ef
EgsE-Ef E- (Ef-Egs)
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(1)
R. Vandenbosch J.R. Huizenga, Nuclear Fission
- formula (VII-3)

• mn, sn, en - 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 EgsE-Ef E- (Ef-Egs)

, and a const
Assuming
(2)
R. Vandenbosch J.R. Huizenga, Nuclear Fission
- formula (VII-7)
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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
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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)
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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)
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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 Z118 Ethr
Bf 8.27 MeV ? Ethr 6.40 MeV (for Ed25
MeV)
Conclusions The scheme of calculating the Gn/Gf
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.
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Figure taken from Nuclear Fission R.
Vandenbosh J.R. Huizenga Academic Press 1973
Excitation energy dependence of Gn/Gf 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.
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