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