J ¼ T À T 0
ð
ÞW
À1 T À T 0
ð
Þ
t þ R e À R c T
ð Þ
½
ŠV e þ V m
½
Š
À1 R e À R c T
ð Þ
½
Š
t
ð17:41Þ
where W is the cross-section covariance data, and V e and V m are the variance of
measured data and calculation method, respectively. In Eq. (17.41), we replace R e
and R c (T ) by
R e ! R e À R e0 R eb
R c T
ð Þ ! R c T
ð Þ À R c0 R cb
ð17:42Þ
because the true values are unknown, they are approximated by R e and R c . The
adjusted cross section is given by
T ¼ T 0 þ WG
t GWG
t
þ V e þ V m
½
ŠR e 1 À R eb
ð
ÞÀR
0
c T 0
ð Þ 1 À R cb
ð
Þ
h
i
ð17:43Þ
The covariance of the adjusted cross section is expressed by
W
0 ¼ W À WG GWG
t
þ V e þ V m
½
Š GW
ð17:44Þ
This expression is the same as in [13], but we have to use the adjusted cross section
shown in Eq. (17.43).
Using the adjusted cross section, the MA transmutation rate can be estimated by
R
2
ð Þ
c T
ð Þ ¼ R
2
ð Þ
c T 0
ð Þ þ G
2
ð Þ T À T 0
ð
Þ
ð17:45Þ
where the superscript (2) indicates the MA transmutation rate of the target reactor.
The variance, the uncertainty, of the MA transmutation rate is given by
V R
2
ð Þ
c T
ð Þ
h
i
¼ G
2
ð Þ W
0 G
2
ð Þt
þ V
2
ð Þ
m À NV
12
ð Þ
m À V
12
ð Þt
m N
t
ð17:46Þ
where V
ð2Þ
m is the covariance of the calculation method used for the MA transmutation rate in the target reactor core, V
ð12Þ
m is the correlation between the calculation
method errors for the critical assemblies and the target core, and N is defined by
N ¼ G
2
ð Þ WG
1
ð Þt G
1
ð Þ WG
1
ð Þt
þ V
1
ð Þ
e þ V
1
ð Þ
m
n
o À1
ð17:47Þ
We will estimate the MA transmutation amount and the uncertainties by using these
methods.
194
T. Takeda et al.