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

A code was developed with the following
features: instead of Y C (A), Y U (A) was used as 0
rank approximation in the double differential,
because Y C (A) was unknown. Y U (A) was smoothed
and a 0 , b 0 , c 0 were obtained from group Eq. (II.3).
By using coefficient c 0, Y C1(A) was calculated from
Eq. (II.4¢)
Y C1(A) = Y U(A) – c 0 s 2
306
(II.4¢)
Smoothing Y C1 (A), coefficients a 1 , b 1 , c 1 were
obtained from Eq. (II.3); and using c 1, Y C2(A) was
calculated from Eq. (II.4¢), and so on. Iteration was
continued until convergence. The following
convergence criterion was used in the code: e =
(Y Cn+1 (A) – Y Cn (A))/ Y Cn (A) < 0.000001 for all mass
numbers A, which means that Y Cn+1 (A) and Y Cn (A)
agree within 5 significant figures.
II.3. TESTING THE CODE
Measured
Smoothed
Adjusted
Chapman (1978) 8.1 MeV [II.5]
Li Ze et al. (1985) 8.3 MeV [II.2]
FIG. II.1. Comparison of adjusted Zöller data at 7 MeV
[II.7] with data measured by the radiochemical method.
The method and code were tested. Figures II.1
and II.2 show Zöller data [II.7] in original,
smoothed and adjusted form at 7 and 13 MeV
respectively, compared with the data of Li Ze [II.2,
II.3], Liu Conggui [II.4] and Chapman [II.5]
measured at similar energies by the radiochemical
method. The s values used in the adjustments are
3.3 and 3.675 for 7 and 13 MeV, respectively, as
given by the author. The adjusted data are basically
in agreement within the uncertainty limits with the
data measured by the radiochemical method, in
which the mass resolution problem does not exist.
Using the INTERP code [II.6], the adjusted
data (smoothed over 7 points) at 13 MeV were
folded on the basis of a Gaussian resolution
function with s = 3.675, which is the value given in
Ref. [II.7] for the mass resolution in the
measurement. The results should reproduce the
originally measured data. As shown in Fig. II.3, the
folded data agree well with the original data, which
proves the reliability of the method and code.
II.4. PRACTICAL ADJUSTMENTS
Measured
Smoothed
Adjusted
Liu Conggui et al. (1985) 14.9 MeV [II.4]
Li Ze et al. (1994)11.4 MeV [II.3]
FIG. II.2. Comparison of adjusted Zöller data at 13 MeV
[II.7] with data measured by the radiochemical method.
Measured
Smoothed
Adjusted, sigma = 3.675
Folded, sigma = 3.675
FIG. II.3. Comparison of folded adjusted data with
measured data at 13 MeV.
When smoothing the measured data, the
adoption of 5 adjacent points (as shown in the
equations) was not enough to obtain good results:
the iterations did not converge, there were some
unreasonable fluctuations in the adjusted data, and
incorrect results appeared with increasing iteration
times. An attempt was made to solve the problem
by smoothing the data twice, but this approach did
not always work. It turned out to be more efficient
to smooth the data over 7 points, so that N = n + 7,
and n = 1, 2,……(M – 6) in Eq. (II.3); investigations
showed that the iterations were convergent and
gave more reasonable results for the adjustments
(see Figs II.1 and II.2) of the data measured by