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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TABLE 4.6.5. ACCURACIES OBTAINED FROM COMPARING THE PREDICTIONS WITH EXPERI-<br />
MENTAL DATA FOR INCIDENT ENERGIES BETWEEN 15 AND 200 MeV AND SEVERAL<br />
ISOTOPES.<br />
Uncertainties in <strong>the</strong> proton and neutron induced fission cross-sections, as well as in <strong>the</strong> pre-neutron and postneutron<br />
emission mass yields, are given, and are expressed as percentages.<br />
Mass yields can be predicted with a proper<br />
choice <strong>of</strong> both <strong>the</strong> ground state to saddle point level<br />
density parameter ratio and <strong>the</strong> pre-scission shapes.<br />
The pre-scission shapes are fixed by applying <strong>the</strong><br />
same recipe to all nuclei. This leaves a f/a n as <strong>the</strong> only<br />
parameter which is tuned to reproduce at best both<br />
<strong>the</strong> fission cross-section and <strong>the</strong> mass yield curve <strong>for</strong><br />
a given reaction. The obtainable accuracy depends<br />
in general on <strong>the</strong> incident energy, as well as on <strong>the</strong><br />
isotope investigated. Table 4.6.5 contains a<br />
summary <strong>of</strong> <strong>the</strong> uncertainties. They are extracted<br />
from comparing <strong>the</strong> predictions <strong>for</strong> <strong>the</strong> total fission<br />
cross-sections, as well as <strong>for</strong> <strong>the</strong> pre-neutron and<br />
post-neutron emission mass yields with experimental<br />
data. The incident nucleon energies range<br />
from 15 to 200 MeV and <strong>the</strong> isotopes are ei<strong>the</strong>r<br />
sub-actinides or actinides. In Table 4.6.5 <strong>the</strong> actinide<br />
region is subdivided into (a) <strong>the</strong> nuclides on <strong>the</strong><br />
edge marking <strong>the</strong> transition to low energy<br />
symmetric fission, (b) uranium <strong>for</strong> which a large<br />
amount <strong>of</strong> data is available, and (c) <strong>the</strong> heavier<br />
actinides. The predictive power changes drastically<br />
with observable nuclide and excitation energy.<br />
The prediction <strong>of</strong> <strong>the</strong> total fission crosssection<br />
is fairly accurate. Deviations <strong>of</strong> up to 100%<br />
can occur only in <strong>the</strong> case <strong>of</strong> <strong>the</strong> sub-actinides, <strong>for</strong><br />
which <strong>the</strong> probabilities become very small. The<br />
determination <strong>of</strong> pre-neutron emission mass yields<br />
is satisfactory. The good agreement <strong>for</strong> uranium at<br />
energies as high as 200 MeV suggests that <strong>the</strong><br />
temperature dependent liquid droplet model does<br />
not break down above a temperature <strong>of</strong> 2.0 MeV<br />
[4.6.40]. This value has been given as <strong>the</strong> validity<br />
boundary. Only in <strong>the</strong> fission <strong>of</strong> 226 Ra and 232 Th can<br />
<strong>the</strong> model not correctly describe <strong>the</strong> experimentally<br />
observed transition to symmetric fission.<br />
Asymmetric fission persists up to incident energies<br />
Sub-actinide region <strong>Actinide</strong> region<br />
Z < 84 Z < 91 Uranium Z > 93<br />
sF (p,f) 10–100% 10–20% 10% —<br />
sF (n,f) 10–15% 10–20% 10–15% 20%<br />
Ypre (A) 10–15% 10–50% 10% —<br />
Ypost (A) 50–1000% — 10–1000% 30%<br />
that are too high. This leads to deviations between<br />
10% at low energies and 50% at high energies in <strong>the</strong><br />
fission fragment mass yields. Whe<strong>the</strong>r this stems<br />
from asymmetric fission that vanishes too slowly<br />
with increasing excitation energies or from a lack <strong>of</strong><br />
symmetric fission contributions from neutron<br />
deficient nuclides could not be determined from <strong>the</strong><br />
results <strong>of</strong> this work. In general, <strong>the</strong> calculated postneutron<br />
emission mass yields are too narrow: <strong>the</strong><br />
light wing and <strong>the</strong> top are reproduced within 50%<br />
or better, whereas <strong>the</strong> heavy wing is underestimated<br />
by one order <strong>of</strong> magnitude. This is probably related<br />
to an overestimation <strong>of</strong> <strong>the</strong> post-scission neutron<br />
multiplicity. The model neglects <strong>the</strong> neutron<br />
evaporation between <strong>the</strong> saddle point and <strong>the</strong><br />
scission point, leaving too much excitation energy in<br />
<strong>the</strong> fission fragments. Consequently <strong>the</strong> heavier<br />
fragment, which receives a larger portion <strong>of</strong> <strong>the</strong><br />
excitation energy <strong>of</strong> <strong>the</strong> fissioning system,<br />
evaporates more neutrons than <strong>the</strong> lighter fragment<br />
and reduces <strong>the</strong> width <strong>of</strong> <strong>the</strong> final mass distribution.<br />
However, since <strong>the</strong> calculated mean mass <strong>of</strong> <strong>the</strong><br />
pre-neutron emission mass yield curves agrees very<br />
well with <strong>the</strong> experimental values, <strong>the</strong> pre-scission<br />
neutron multiplicity, which momentarily excludes<br />
neutron evaporation between <strong>the</strong> saddle point and<br />
<strong>the</strong> scission point, cannot be completely wrong.<br />
Fur<strong>the</strong>rmore, <strong>the</strong> temperature <strong>of</strong> <strong>the</strong> fissioning<br />
system cannot be far too high because <strong>of</strong> <strong>the</strong><br />
correctly reproduced relative contributions <strong>of</strong> <strong>the</strong><br />
different fission modes in <strong>the</strong> calculated preneutron<br />
emission mass yield distributions.<br />
There<strong>for</strong>e, a more likely explanation is provided by<br />
<strong>the</strong> supposition that <strong>the</strong> fragments evaporate too<br />
many neutrons because <strong>of</strong> an underestimation <strong>of</strong><br />
<strong>the</strong> energy required <strong>for</strong> <strong>the</strong> emission <strong>of</strong> particles.<br />
235