Fission Product Yield Data for the Transmutation of Minor Actinide ...

fragment mass distributions are described by two
asymmetric modes only, standard I and standard II
[4.4.3, 4.4.4]. Our studies involved the analysis of
experimental data published in Ref. [4.4.26], and
Figs 4.4.8 and 4.4.9 compare the experimental data
(points) for the photofission of 232 Th, 235 U, 238 U and
239 Pu nuclei at Bremsstrahlung endpoint energies up
to 50 MeV with our calculations (continuous lines).
These figures show the good agreement between
the experimental data and calculations for all of the
nuclei and excitation energy ranges studied. The
asymmetric fragment mass distribution is observed
in photofission even at a Bremsstrahlung endpoint
energy of 50 MeV, which confirms the assumptions
made about the absence of the symmetric fission
mode for very small angular momenta of the
fissioning nucleus.
Referring to the parameters contained in
Eq. (4.4.5) the following equations were obtained
from an analysis of the experimental data:
W II = 96.44 – 0.38 E BS
W I = 100 – W II
s A
s A
where
90 .
= 907 . +
2
1+ ( 92- )
I Z
II
I
H
N fZf = 112 . -553
.
A
f
I
f L
A = 323 . ( Z - 50),
A = A - A
II
L
II
f H
f
I
f H
II
f L
A = 284 . ( Z - 58),
A = A - A
(4.4.12)
(4.4.13)
(4.4.14)
(4.4.15)
(4.4.16)
(4.4.17)
A f , Z f and N f are mass, charge and neutron number
of the fissioning nucleus,
E BS is the Bremsstrahlung endpoint energy.
Results of the analysis for the nuclei studied
show that no difference can be observed in the
description of the fragment mass distributions with
or without the inclusion of the symmetric fission
mode. However, for a description of mass distributions
in terms of five Gaussians, more parameters
have to be used, which essentially complicates the
derivation of the dependence of the model
parameters on mass and charge of a fissioning
nucleus and the Bremsstrahlung endpoint energy.
As the variance for the symmetric mode of
fragment mass distributions in photofission is very
large (s SL > 20), the noticeable difference in calculations
between these two approaches will be seen for
fragment masses A < 70 and A > 170. The contribution
of a symmetric mode to the fragment mass
distributions for photofission will also be visible at
higher energies where shell effects in a fissioning
nucleus are decreasing. Thus experimental yields
given for broader intervals of fragment masses need
to be unambiguously resolved if there is a
symmetric contribution for photofission.
4.4.5. Fragment mass distributions
from fission by a particles
An analysis was made of the experimental
data for the fragment mass distributions of 239 Pu
and 240 Pu fission [4.4.13] formed in reactions with
a particles up to 80 MeV. The basic purpose of the
work was to find the dependence of the parameters
in the Brosa model at higher excitation energies and
greater angular momentum of the fissioning nuclei.
Results show that the critical value of the angular
momentum ( cr ,) above which the asymmetric
standard I fission channel is converted into the
symmetric super long channel is defined by the
following equation:
A
HI
ÏÔ
A
= Ì
ÓÔ A /2
(4.4.18)
and is different for 239 Pu (l cr = 7ћ) and 240 Pu (l cr = 9ћ).
As shown in Refs [4.4.10–4.4.13], the influence of
the shell effects on the fission process decreases
with increasing excitation energy, and therefore the
fragment mass distribution should change from
asymmetric to the symmetric shape. This change of
the fragment mass distribution shape is seen in the
parameters of the model used to describe the
energy dependence (Eq. (4.4.5)), for which the
following equations are derived:
W = W ¥ P
W I = 100 – W II
£
>
HI cr
f cr
II
0
II LD
A
0
A A LD
s = s + D s ( 1 -P)
I I I
0
A A A 1 LD
s = s + D s ( -P)
II
II II II
ALH , A A P
= ¥ /2 ∓ D
f II LD
(4.4.19)
(4.4.20)
(4.4.21)
(4.4.22)
(4.4.23)
165