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

cross-section also has to be incorporated. The calculations
are performed with the level density
parameters stemming from a fit to experimental
neutron and proton induced fission cross-sections
for 209 Bi and 197 Au.
The basic assumption made is that the saddle
point to ground state ratios a f /a n vary smoothly over
the isotopes and hence that the ratios for 208 Pb and
203,205 Tl lie in between those of 209 Bi and 197 Au. The
fission cross-sections in this region of the chart of
nuclides can be predicted with an accuracy of 10%.
This has to be added to the uncertainty in the
prediction of the normalized yields.
The predictions in Fig. 4.6.13 for the production
cross-sections of fission product masses in 190 MeV
proton induced fission of nat W, 197 Au, nat Pb and 208 Pb
are less satisfactory. The experimental data have
been obtained from Ref. [4.6.2]. Figure 4.6.13 also
contains, apart from the experimental data and the
calculation (solid line), a Gaussian (dashed line)
that originates from a fit to the data and is given by
the original authors. The calculation does a fairly
good job in the description of the left wings and of
the top, but the experimental yields are underestimated
by one order of magnitude in the right wings.
The huge discrepancy for heavier masses is mainly
due to the prediction of a too small width. In
addition, the predicted mean mass is shifted to lighter
masses compared to the measured value. A lighter
mean mass is related to an overestimation of the total
number of evaporated mass units. This may indicate
an underprediction of the energy carried away by
the emitted particles prior to or after scission. A
possible explanation of the first effect lies in the
calculation of the post-scission neutron multiplicities.
With the temperature dependent Brosa model
as described in Section 4.6.4.1, the neutron
evaporation between the saddle and scission points
is neglected. This results in an excitation energy of
the fragments that is too high. Since the division of
the excitation energy available at scission between
the two fragments is proportional to the fragment
mass, the heavy fragment will have a relatively
higher post-scission neutron multiplicity. Therefore
it will shift more towards lower masses than the
light fragment, thereby reducing the width of the
mass distribution. A similar situation of a higher
scission temperature occurs if the energy carried
away by the pre-scission neutrons is too small. An
overestimation of the post-scission neutron multiplicity
can also be caused by an under-prediction of
the energy required for the emission of neutrons by
the fragments. The last two assumptions would
Normalized Yield
FIG. 4.6.14. Pre-neutron emission and post-neutron
emission mass yield curves for the super long mode in a
238U nucleus with excitation energies at scission of 50 and
200 MeV.
simultaneously explain the smaller predicted mean
mass, as already mentioned above.
A higher excitation energy at scission is linked
to a higher scission temperature, and this also
influences the width. The pre-scission shape halflength
is smaller at higher temperatures (see
Fig. 4.6.8). A more compact shape results in a
narrower mass distribution. On the other hand, an
increase of the temperature enlarges the width (see
Eq. (4.6.12)). A comparison of the two effects shows
that the latter is stronger. Figure 4.6.14 contains the
pre-neutron emission and post-neutron emission
mass yield curves of the super long mode for a 238 U
nucleus with an excitation energy of 50 and
200 MeV at scission. The pre-neutron emission
yield curve at 200 MeV is broader than the preneutron
emission yield curve at 50 MeV, although
the pre-scission shape is shorter around 200 MeV.
The post-neutron emission yield distribution at
200 MeV becomes slightly narrower than the one
around 50 MeV. This observation supports the
explanation given above that the inclusion of postscission
neutron emission in its present form
reduces the width of the mass distribution. Whether
the overprediction of the post-scission neutron
multiplicity is connected to an overestimation of the
temperature at scission or to an underestimation of
the energy required for the emission of a neutron by
the fragments cannot be concluded from these data.
The next section will shed more light on this
question.
Table 4.6.4 shows the fission cross-sections
resulting from the experiment, the calculations and
the Eismont et al. data compilation [4.6.25].
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