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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compound nucleus) was analysed recently within<br />
<strong>the</strong> Hauser–Feshbach statistical model [3.1.9].<br />
Individual contributions <strong>of</strong> <strong>the</strong> super long fission<br />
mode to <strong>the</strong> observed fission cross-sections were<br />
reproduced up to <strong>the</strong> emissive fission threshold<br />
[3.1.10, 3.1.11]. A separate outer fission barrier was<br />
assumed <strong>for</strong> <strong>the</strong> super long mode, while a common<br />
inner barrier was assumed <strong>for</strong> <strong>the</strong> symmetric super<br />
long and asymmetric S1 and S2 modes. This<br />
assumption is supported by fission mode calculations<br />
[3.1.12, 3.1.13] that use <strong>the</strong> multimodal<br />
random neck rupture model [3.1.2–3.1.5], and<br />
reveal that <strong>the</strong> final bifurcation point is close to <strong>the</strong><br />
second minimum <strong>of</strong> <strong>the</strong> actinide double humped<br />
fission barrier. The super long mode 235 U(n,f) and<br />
238 U(n,f) fission cross-sections were shown to be<br />
controlled by a ra<strong>the</strong>r high outer fission barrier with<br />
significant transparency. A steeply rising shape <strong>of</strong><br />
<strong>the</strong> super long mode contribution was found to be<br />
compatible with outer saddle point axial asymmetry<br />
that accompanied mass symmetry. Outer saddle<br />
shapes <strong>for</strong> S1 and S2 modes were assumed to be<br />
axially symmetric and mass asymmetric.<br />
Above <strong>the</strong> emissive fission threshold, a<br />
number <strong>of</strong> nuclei contribute to <strong>the</strong> fission observables:<br />
<strong>the</strong> 238 U(n,f) reaction at E n ~ 200 MeV may<br />
involve an appreciable contribution from about<br />
20 nuclides. The ratio <strong>of</strong> symmetric to <strong>the</strong> sum <strong>of</strong><br />
symmetric and asymmetric fission events was<br />
obtained in <strong>the</strong> reaction 238 U(n,f) by Zöller et al.<br />
[3.1.14] <strong>for</strong> incident neutron energies <strong>of</strong> up to E n ~<br />
500 MeV. They deduced <strong>the</strong> ratio <strong>of</strong> symmetric to<br />
all fission events from <strong>the</strong> fission fragment total<br />
kinetic energy distribution as well as from <strong>the</strong> mass<br />
total kinetic energy distributions. A simultaneous<br />
analysis <strong>of</strong> this ratio and <strong>the</strong> observed neutron<br />
induced fission cross-section <strong>for</strong> a 238 U target<br />
[3.1.15, 3.1.16] up to E n ~ 200 MeV might be<br />
attempted within statistical <strong>the</strong>ory. The observed<br />
238 U neutron induced fission cross-section data<br />
[3.1.15, 3.1.16] were analysed recently in a fission/<br />
neutron evaporation approximation up to E n ~<br />
200 MeV, in which first chance pre-equilibrium<br />
neutron emission was taken into account [3.1.17].<br />
<strong>Fission</strong> probabilities <strong>of</strong> U nuclei in <strong>the</strong> domain <strong>of</strong><br />
<strong>the</strong> emissive fission reaction 238 U(n,xnf) were<br />
estimated without making any distinction regarding<br />
symmetric or asymmetric fission (i.e. super long, S1<br />
or S2 modes). These fission probabilities provide<br />
correct estimates <strong>of</strong> lumped fission competition<br />
against neutron emission. Damping <strong>of</strong> <strong>the</strong> collective<br />
26<br />
modes’ contribution to <strong>the</strong> level density at<br />
excitation energies higher than ~20 MeV <strong>for</strong> axial<br />
symmetric saddle and equilibrium de<strong>for</strong>mations was<br />
shown to be essential <strong>for</strong> <strong>the</strong> description <strong>of</strong> <strong>the</strong><br />
observed fission cross-section. Effective estimates<br />
<strong>of</strong> intrinsic level densities were obtained, which<br />
define <strong>the</strong> competition between fission and neutron<br />
emission at high excitation energies when rotational<br />
collective modes are completely damped.<br />
Competition <strong>of</strong> <strong>the</strong> symmetric and asymmetric<br />
fission <strong>of</strong> U nuclei would depend essentially on <strong>the</strong><br />
excitation energies <strong>of</strong> <strong>the</strong> U nuclei emerging after<br />
<strong>the</strong> emission <strong>of</strong> pre-fission (n,xnf) neutrons. Level<br />
densities can be anticipated to play a key role in <strong>the</strong><br />
relevant saddle de<strong>for</strong>mation. We can probe <strong>the</strong><br />
sensitivity <strong>of</strong> <strong>the</strong> calculated super long mode and<br />
lumped asymmetric (S1 + S2) mode yields to <strong>the</strong><br />
damping <strong>of</strong> triaxial de<strong>for</strong>mations at <strong>the</strong> outer<br />
saddles <strong>of</strong> U nuclei. The range <strong>of</strong> mass numbers <strong>of</strong><br />
U nuclei that make an appreciable contribution to<br />
<strong>the</strong> fission observables depends on fission barriers<br />
and intrinsic level densities at saddle and<br />
equilibrium de<strong>for</strong>mation. We anticipate that <strong>the</strong><br />
ratio <strong>of</strong> symmetric to all fission events will strongly<br />
depend on <strong>the</strong> relative contributions to <strong>the</strong><br />
observed cross-section <strong>of</strong> fission chances with<br />
different numbers <strong>of</strong> pre-fission neutrons. The<br />
analysis <strong>of</strong> <strong>the</strong> ratio <strong>of</strong> symmetric to all fission<br />
events might be a sensitive tool <strong>for</strong> <strong>the</strong> partitioning<br />
<strong>of</strong> <strong>the</strong> fission (n,xnf) chance contribution to <strong>the</strong><br />
fission observables.<br />
With an increase <strong>of</strong> <strong>the</strong> target nuclide fissility,<br />
<strong>the</strong> number <strong>of</strong> nuclei that make an appreciable<br />
contribution to <strong>the</strong> fission observables will tend to be<br />
lower. We have developed an approach to describe<br />
<strong>the</strong> 238 U(n,f) cross-section and branching ratio <strong>of</strong><br />
symmetric/asymmetric fission up to 200 MeV<br />
incident neutron energy. This model will be applied<br />
to <strong>the</strong> observed 235 U(n,f), 233 U(n,f), 232 Th(n,f),<br />
237 238 Np(n,f) and U(p,f) fission cross-section data.<br />
235 sym 233 sym<br />
We will predict U(n,f) , U(n,f) ,<br />
232 sym 237 sym 235 asym<br />
Th(n,f) , Np(n,f) and U(n,f) ,<br />
233 asym 232 asym 237 asym U(n,f) , Th(n,f) and Np(n,f) fission<br />
cross-sections, which represent a wide range <strong>of</strong><br />
target nuclide fissilities. Analyses <strong>of</strong> observed<br />
neutron and proton induced fission cross-sections<br />
would provide valuable in<strong>for</strong>mation about <strong>the</strong><br />
relative contributions <strong>of</strong> emissive fission. The<br />
possibility <strong>of</strong> using proton induced fission yields can<br />
<strong>the</strong>n be defined to estimate <strong>the</strong> neutron induced<br />
fission yields at high excitation energies.