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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P<br />
LD<br />
È Ê * E - 44. 7ˆ<br />
˘<br />
= Í1<br />
+ exp<br />
Ë<br />
Á<br />
¯<br />
˜ ˙<br />
ÎÍ<br />
91. 2 ˚˙<br />
(4.4.33)<br />
The data <strong>of</strong> Maslov were used <strong>for</strong> <strong>the</strong> transmission<br />
coefficients (T l ) [4.4.28]. These coefficients<br />
provide a good description <strong>of</strong> <strong>the</strong> cross-sections <strong>for</strong><br />
<strong>the</strong> fission <strong>of</strong> 238 U by neutrons and take into account<br />
pre-fission neutron emission up to incident neutron<br />
energies <strong>of</strong> 200 MeV.<br />
Zöller data [4.4.27] <strong>for</strong> pre-neutron emission<br />
fragment mass distributions from 238 U fission by<br />
neutrons with energies from 2 to 200 MeV are<br />
summarized in Figs 4.4.12–4.4.14. As can be seen<br />
from <strong>the</strong>se figures, <strong>the</strong> assumption made in <strong>the</strong><br />
present work results in satisfactory agreement<br />
between <strong>the</strong> experimental data and calculations<br />
over <strong>the</strong> whole energy range.<br />
The following expressions were obtained from<br />
an analysis <strong>of</strong> Zöller data [4.4.27] to describe <strong>the</strong><br />
post-neutron emission fragment mass distributions<br />
<strong>of</strong> 238 U fission by neutrons in this energy range:<br />
A<br />
ÏÔ<br />
A<br />
= Ì<br />
ÓÔ A<br />
(4.4.34)<br />
(4.4.35)<br />
where v – i L,H are <strong>the</strong> average values <strong>of</strong> <strong>the</strong> neutrons<br />
emitted from fragments <strong>for</strong> <strong>the</strong> corresponding<br />
fission modes:<br />
(4.4.36)<br />
Descriptions <strong>of</strong> <strong>the</strong> post-neutron emission fragment<br />
mass distributions <strong>for</strong> 238 U fission by neutrons in <strong>the</strong><br />
energy range from 2 to 200 MeV are summarized in<br />
Figs 4.4.15–4.4.17 and compared with <strong>the</strong> experimental<br />
data [4.4.27].<br />
4.4.7. Fragment mass distribution<br />
<strong>for</strong> spontaneous fission<br />
We have per<strong>for</strong>med an analysis <strong>of</strong> <strong>the</strong><br />
evaluated data on fragment mass distributions from<br />
spontaneous fission <strong>of</strong> nuclei [4.4.25] in order to<br />
determine <strong>the</strong> dependence <strong>of</strong> <strong>the</strong> model parameters<br />
on <strong>the</strong> mass and charge <strong>of</strong> <strong>the</strong> fissioning nuclei at<br />
zero excitation energy and angular momentum.<br />
-1<br />
I f<br />
I<br />
2∓1718 . - n L, H £ cr<br />
LH ,<br />
f 2 - n S > cr<br />
II<br />
II<br />
LH , f L, H<br />
A = A 2∓20. 56-n<br />
I<br />
I<br />
n L = 326 . , n H = 388 . ,<br />
II n L = 026 . , II n H = 36 . ln( 0039 . En<br />
+ 167 . ),<br />
n = 364 .<br />
S<br />
The following equations were obtained <strong>for</strong> <strong>the</strong><br />
parameters appearing in Eq. (4.4.5):<br />
I<br />
H<br />
I<br />
L<br />
A = 140, A = A -A<br />
II<br />
H<br />
II<br />
L<br />
(4.4.37)<br />
(4.4.38)<br />
(4.4.39)<br />
Af = A0-v, (4.4.40)<br />
v = 5. 355 -0. 644( Z - 96) + 0. 386( A -252)<br />
W II = 100 – W I – W III<br />
I<br />
f H<br />
II<br />
f H<br />
A = 140, A = A -A<br />
III<br />
H<br />
III<br />
L<br />
III<br />
f H<br />
A = 146, A = A -A<br />
s AI<br />
s AII<br />
s AIII<br />
0 0<br />
= 2. 472 + 0. 005( A -252)<br />
0<br />
(4.4.41)<br />
= 4. 140 + 0. 041( Z - 96) + 0. 082( A -252)<br />
(4.4.42)<br />
(4.4.43)<br />
(4.4.44)<br />
(4.4.45)<br />
(4.4.46)<br />
The fragment mass distributions <strong>for</strong> <strong>the</strong><br />
spontaneous fission <strong>of</strong> 252 Cf nuclei are shown in<br />
Fig. 4.4.18, where our calculations are also<br />
compared with <strong>the</strong> evaluated data [4.4.25] and<br />
calculations <strong>of</strong> Wahl [4.4.29]. Figure 4.4.19<br />
compares evaluated data [4.4.25] with our calculations<br />
<strong>of</strong> fragment mass distribution <strong>for</strong> <strong>the</strong><br />
spontaneous fission <strong>of</strong> nuclei from 240 Pu up to 256 Fm.<br />
Results <strong>of</strong> <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> fragment mass<br />
distributions from spontaneous fission show <strong>the</strong><br />
absence <strong>of</strong> <strong>the</strong> symmetric fission contribution, in<br />
agreement with <strong>the</strong> results <strong>of</strong> Wahl [4.4.29].<br />
However, at least three asymmetric modes need to<br />
be taken into account <strong>for</strong> a satisfactory description<br />
<strong>of</strong> fragment mass distributions from <strong>the</strong><br />
spontaneous fission <strong>of</strong> nuclei with Z > 94.<br />
4.4.8. Description <strong>of</strong> fission fragment mass<br />
and charge distributions<br />
0<br />
= 6. 166 + 0. 027( Z - 96) + 0. 150( A -252)<br />
W = 14. 0 -2. 993 Z - 96 + 2. 694 A -252<br />
I<br />
0<br />
0 0<br />
W = 34. 222 -1. 445 Z - 96 + 2. 427 A -252<br />
III<br />
A phenomenological approach has been<br />
developed in <strong>the</strong> present study to describe <strong>the</strong><br />
2<br />
2<br />
0 0<br />
0<br />
0<br />
171