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

Appendix II
DATA ADJUSTMENT FOR MASS RESOLUTION
A method and code have been developed for
mass resolution adjustment of mass distribution
data measured by means of the kinetic energy
method. Data were smoothed before adjustment
with a second order function for 7 or 9 adjacent
points, and the investigation shows that taking too
few or too many data points in the smoothing
procedure could lead to unreasonable results. The
code was tested by folding the adjusted data with a
Gaussian distribution and a resolution width the
same as the one used in the adjustment procedure.
Results were practically identical to the original
unadjusted input data. The data uncertainties were
also adjusted by the code. This code has subsequently
been applied to re-define the mass distribution
data measurements of Zöller, Vivès and
Äystö by the kinetic energy method.
II.1. INTRODUCTION
The fission yield for each product nuclide
measured by the kinetic energy or double time-offlight
method is not a true mass yield but, due to
incomplete mass resolution, the sum of contributions
from several adjacent masses, the yields of
which are each folded by a Gaussian distribution
function. They must be adjusted for mass resolution
in order to obtain the true yield.
II.2. ADJUSTMENT METHOD AND CODE
According to Schmitt [II.1], the adjustment
can be done using the following formula:
Y ( A) = Y ( A)
-
C U
s 2 2
2
dYC( A)
2
dA
Liu Tingjin
China Institute of Atomic Energy, China
(II.1)
where Y C , Y U are the corrected/adjusted and
uncorrected/unadjusted yields respectively, and s is
the mass resolution, defined as half-width at halfmaximum
(s is erroneously called the full width in
Ref. [II.1]).
To avoid the effect of statistical fluctuation,
the data were smoothed before adjustment by
fitting with a second order function for every 5
adjacent data points,
Y(A) = a + bA + cA 2
(II.2)
and the yield of the central mass was taken as the
new yield at that mass. For the first and last two data
points at the ends of the measured mass distributions,
the results of the respective complete 5 point
fits for the corresponding third points from the ends
were used as the adjusted yields.
The coefficients a, b, c were obtained from the
following group of equations, which were deduced
by the least squares method for each group of 5 data
points:
Ê
Á
Ë
Ê
Á
Ë
Ê
Á
Ë
N
N
N
N
ˆ Ê ˆ Ê ˆ
2
w a w A b w A c w Y
i ˜ + Á i i˜
+ Á i i ˜ = Â i i
¯ Ë ¯ Ë ¯
  Â
i= n
i= n
Ii= n
i= n
N
N
N
N
ˆ Ê ˆ Ê ˆ
2 3
wA a wA b wA c wY
i i˜
+ Á i i ˜ + Á i i ˜ = Â i i
¯ Ë ¯ Ë ¯
  Â
i= n
i= n
Ii= n
N
(II.3)
where N = n + 5, n = 1, 2,……(M – 4), and M is the
total number of data points to be fitted.
The double differential of Eq. (II.2) with
respect to A is 2c, so Eq. (II.1) becomes
Y C (A) = Y U (A) – c s 2
i= n
N
N
N
ˆ Ê ˆ Ê ˆ
2 3 4
wA a wA b wA c wY
i i ˜ + Á i i ˜ + Á i i ˜ = Â
i i i
¯ Ë ¯ Ë ¯
  Â
i= n
i= n
Ii= n
i= n
(II.4)
The data were adjusted using Eq. (II.4). s
reflects the uncertainty due to the experimental
conditions and is usually given by the author in the
publication.
A i
A 2
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