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

hand, the on average longer half-lives of the less
neutron rich fission products also give rise to an
advantage. Part of the primary fission products,
which remain after post-scission neutron
evaporation by the fragments, occur with longer
half-lives and hence are easier to observe. They can
now be measured directly, instead of only through
their beta decay products.
4.6.3.2. Sub-actinide fission
4.6.3.2.1. Mass distributions
For each sub-actinide target, the mass distribution
is extracted from the measured cumulative
and independent isotope yields by fitting simultaneously
the mass and charge distribution. The fission
process is assumed to be symmetric for the subactinide
targets. Therefore, the mass and the charge
distribution for a given mass are each described by a
single Gaussian in the fit. Moreover, the assumption
is made that the most probable charge, as well as the
width of the charge distribution, vary linearly with
the mass of the fission fragment. The following
parameterization of the production cross-section as
a function of the mass and charge of the fission
fragment is adopted:
-
2 1
s prod ( AZ , ) = lAe
A Âe
p G
212
2 ( A-M ) ( Z-- i Z )
A
p
2
G G
(4.6.1)
with Z p = m 1 + m 2 A and G Z = g 1 + g 2 A. The first
Gaussian represents the symmetric mass distribution
defined by the height l A , mean M A and
width G A . The rest of the formula reflects the charge
distribution. In the case of an independent yield,
only one term in the sum of the normalized
Gaussian charge distribution (i.e., i = 0) contributes.
A cumulative yield is described by summing the
contributions of neighbouring isobars. The index i is
equal to 0, 1,…5 for neutron rich cumulative yields,
and equal to 0, –1,…–5 for neutron deficient
cumulative yields. The number of terms (six) in the
summation for cumulative yields is rather arbitrary,
but in these investigations has turned out to be
sufficient. A more elaborate description of the
functional form can be found in the work by
Hagebø and Lund [4.6.24].
The values of the fit parameters obtained for
all sub-actinide targets are tabulated in Table 4.6.2.
Z
i
Z
2
The mean value as well as the height of the mass
distribution clearly increases with increasing target
mass, as expected. From the mean of the mass distributions
it can be concluded that, on average, nine
mass units are emitted before and after fission. With
the charge distribution known from the fit of
Eq. (4.6.1), it is straightforward to determine the
fractional independent or cumulative yields
represented by each of the observed independent or
cumulative isotope yields in their mass chains.
Subsequently, the measured yields are divided by
their corresponding fractional yields to derive the
experimental mass yields. In the case of nat Pb, the
spread in the adjusted yields is rather large.
Therefore, the final mass distribution has been
obtained after fitting to the measured yields, which
represent at least 50% of the complete mass distribution.
The total mass yields are plotted in
Fig. 4.6.1, together with the mass distribution
obtained in the fit for nat W, 197 Au, nat Pb and 208 Pb.
The results agree with the assumption of a
symmetric mass and charge distribution.
4.6.3.2.2. Charge distributions
Integrating over the Gaussian and multiplying
by a factor 1/2, because of the two fission fragments
in each fission event, gives an estimate for the
fission cross-section. The values for the fission
cross-sections determined in this way are also given
in Table 4.6.2. The assumption is made that the
uncertainties in the independent and cumulative
yields that have been used in the fit are uncorrelated,
since they stem from many different spectra.
Therefore the only uncertainty remaining in the
deduced fission cross-sections is the systematic
uncertainty due to the overall normalization
determined from the proton flux. Eismont et al.
[4.6.25] have made a data compilation for the fission
cross-section as a function of incident proton energy
for some of these target materials. The values from
the Eismont et al. fit are also shown in Table 4.6.2
for comparison and are in fairly good agreement
with the results from this work.
By fitting Eq. (4.6.1) to the available experimental
independent and cumulative yields,
information on the charge distribution is obtained.
The charge distributions in three fission fragment
mass regions of 208 Pb are shown in Fig. 4.6.2 as an
example. The fitted charge distributions are
evaluated for the indicated masses. Since the charge
yield curves vary only slowly as a function of mass,
the fits should give a good representation of the