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

Vivès [II.8], Zöller [II.7] and Äystö [II.9], except for
Zöller data at 50 MeV (both post- and pre-neutron
emission). When Zöller data at 50 MeV were
smoothed over 9 data points, the iteration was
convergent and reasonable results were obtained.
The data were adjusted in the following way: first
smoothed over 7 (or 9) data points according to Eq.
(II.3), and then modified according to Eq. (II.4).
A crucial criterion for the success of the
adjustment is the choice of the number of data
points in a group used in the smoothing procedure.
If too few data points are used in Eq. (II.3) to
smooth out the statistical fluctuations, the iterations
do not converge and there would be unreasonable
structures in the adjusted data. If too many data
points are used in Eq. (II.3), the true structures in
the mass distribution may be smoothed out. Best
results were obtained with 7 data points for most of
the measured data, and with 9 data points for data
with larger fluctuations. The adjusted data with
original experimental uncertainties are listed in
Annex 1.
II.5. ADJUSTMENT OF DATA
UNCERTAINTIES
adjusted data
with exp. uncert.
adjusted data
with adjusted uncert.
FIG. II.4. Intercomparison between adjusted uncertainty
and original experimental uncertainty at E n = 13 MeV.
For the fission yield data measured by the
kinetic energy or the double time-of-flight method,
the uncertainty of the mass calibration (by energy
measurement or the time-of-flight method) could
make a contribution to the total uncertainty of a
yield. At the peak, valley and wings (Figs II.1 and
II.2) the uncertainties due to mass calibration are
smaller, but on the slopes of the light and heavy
peak (where the yields vary rapidly with mass A)
they could be larger. In comparison with the data
measured by the radiochemical method (where this
kind of problem does not exist), the uncertainty of
the mass calibration could be ±1 mass unit.
The data were smoothed with the function Y =
a + bA + cA 2 , and the first differential is
dY
= b+2cA dA
and the uncertainty due to the mass calibration is
DY = (b + 2cA) DA (II.5)
Total uncertainty DY composed of the yield
measurement DY 1 (mainly counting statistics) and
the mass calibration uncertainty DY 2 is given by the
expression:
DY = (DY 2 1 + DY 2 2 )1/2
adjusted data
with exp. uncert.
adjusted data
with adjusted uncert.
FIG. II.5. Intercomparison between adjusted uncertainty
and original experimental uncertainty at E n = 50 MeV.
(II.6)
By using Eq. (II.5) and taking DA = 1, the uncertainties
DY 2 from the mass calibration were
calculated, and DY 1 were taken as given by the
authors. The total uncertainties DY were calculated
from Eq. (II.6). Adjusted data with adjusted uncertainties
are given in Annex 2, and the comparison of
the adjusted uncertainty with the original data is
given in Figs II.4 and II.5 as examples.
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