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

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predicted effects <strong>of</strong> multi-chance fission have been<br />

described in Section 1.3.4.2, <strong>the</strong> impact <strong>of</strong> this<br />

phenomenon on <strong>the</strong> observed shape <strong>of</strong> <strong>the</strong><br />

composite mass distribution is briefly outlined<br />

below.<br />

(a) Superposition <strong>of</strong> preferred fission modes<br />

At 100 MeV, <strong>the</strong> asymmetric and symmetric<br />

fission modes are about equal in <strong>the</strong> observed mass<br />

distribution. Asymmetric fission is likely to<br />

dominate below 100 MeV, and expected contributions<br />

from multi-chance fission are probably not<br />

sufficient to change <strong>the</strong> shape <strong>of</strong> <strong>the</strong> mass distribution<br />

significantly. Above 100 MeV, symmetric<br />

fission starts to dominate, contributions from<br />

higher-chance fission are more significant, and<br />

<strong>the</strong>re<strong>for</strong>e <strong>the</strong> composite mass distribution is no<br />

longer symmetric in shape.<br />

(b) Change in peak positions and mass symmetry<br />

point in asymmetric fission<br />

The expected effect <strong>of</strong> <strong>the</strong> contributions from<br />

lower mass fissioning nuclides — a stable position<br />

<strong>for</strong> heavy mass peak, and a broadened and lower<br />

light mass peak — are only observed in <strong>the</strong><br />

predictions <strong>of</strong> Duijvestijn with ALICE-91. There<br />

are several possible reasons:<br />

(1) This possible effect is not included in most<br />

systematics, and reflection symmetry is<br />

assumed in <strong>the</strong> modelling <strong>of</strong> <strong>the</strong> mass<br />

distributions;<br />

(2) As above, <strong>the</strong> predicted effect is too small<br />

below 100 MeV to cause a noticeable change<br />

in <strong>the</strong> mass distribution;<br />

(3) When <strong>the</strong> chosen peak functions are too<br />

broad, any such visible effect at 100 MeV and<br />

above would be washed out, resulting in a flat<br />

plateau (even if reflection symmetry in <strong>the</strong><br />

peak functions is not assumed).<br />

At higher excitation energies, when symmetric<br />

fission becomes significant, <strong>the</strong> composite<br />

symmetric mass peak is expected to broaden<br />

towards lower masses. Similarly, <strong>the</strong> point <strong>of</strong><br />

symmetry in <strong>the</strong> mass distribution, defined<br />

originally as <strong>the</strong> point where both fragments have<br />

equal mass (symmetric fission), changes from <strong>the</strong><br />

position <strong>of</strong> first chance fission towards lower masses<br />

(broader valleys or symmetric peaks) with<br />

decreasing mass <strong>of</strong> <strong>the</strong> fissioning nucleus. When <strong>the</strong><br />

248<br />

composite mass distribution is considered, <strong>the</strong><br />

symmetry point becomes <strong>the</strong> point above and below<br />

which <strong>the</strong> sums <strong>of</strong> <strong>the</strong> mass yields are equal and<br />

total 100%. However, this new point <strong>of</strong> mass<br />

symmetry is not defined solely by <strong>the</strong> mass <strong>of</strong> <strong>the</strong><br />

target, plus projectile, and minus <strong>the</strong> total number<br />

<strong>of</strong> neutrons emitted, as assumed in some<br />

systematics.<br />

(c) Multiplicity distribution <strong>of</strong> neutrons emitted<br />

from fission fragments<br />

The observed multiplicity distribution <strong>of</strong><br />

neutrons emitted from fission fragments is <strong>the</strong> sum<br />

<strong>of</strong> <strong>the</strong> contributions from different fissioning<br />

nuclides. Systematics and models have to include<br />

this effect when calculating <strong>the</strong> unmeasured<br />

neutron distributions derived <strong>for</strong> target nuclei only.<br />

Since <strong>the</strong>re are hardly any measurements at intermediate<br />

energies, <strong>the</strong> neutron multiplicity distributions<br />

used in <strong>the</strong>se models to calculate fission yields<br />

are based on crude assumptions.<br />

5.2.3.4. Consequences <strong>for</strong> model predictions<br />

at higher energies<br />

The following considerations have to be taken<br />

into account in systematics when modelling fission<br />

product mass distributions at higher energies:<br />

(a) Mass distributions are not symmetric in shape;<br />

(b) Light and heavy mass peaks cannot be<br />

described by peak functions that are identical<br />

in shape;<br />

(c) Peak heights and widths are not equal — <strong>the</strong><br />

shapes, particularly that <strong>of</strong> <strong>the</strong> light mass peak,<br />

cannot be described by symmetric functions<br />

like single Gaussians;<br />

(d) When <strong>the</strong> asymmetric and symmetric fission<br />

contributions are both significant, <strong>the</strong> distribution<br />

could be broad and flat;<br />

(e) At still higher energies, symmetric fission<br />

dominates, and <strong>the</strong> mass distribution should<br />

broaden and not have <strong>the</strong> shape <strong>of</strong> a single<br />

Gaussian;<br />

(f) Mass distributions cannot be described by<br />

single Gaussians with identical parameters <strong>for</strong><br />

each fission mode, but ei<strong>the</strong>r by a superposition<br />

<strong>of</strong> Gaussians accounting <strong>for</strong> multi-chance<br />

fission or by using ‘effective’ peak functions<br />

that describe <strong>the</strong> actual peak shapes;<br />

(g) If necessary, an effective point <strong>of</strong> symmetry<br />

has to be calculated from an effective mass <strong>of</strong>

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