7 Neutronics of Lead and Bismuth
203
Fig. 7.15 Sensitivity
coefficients of inelastic
scattering reactions of 209 Bi
and 27 Al in JENDL-4.0 (Ref.
[3])
(a)
209
Bi
(b)
27
Al
10
-5 10
-4 10
-3 10
-2 10
-1 10
0 10
1 10
2 10
3 10
4 10
5 10
6 10
7
0
0.01
0.02
0.03
0.04
0.05
Neutron energy [eV]
Sensitivity coefficient per lethargy
27 Al
10
-5 10
-4 10
-3 10
-2 10
-1 10
0 10
1 10
2 10
3 10
4 10
5 10
6 10
7
0
0.001
0.002
Neutron energy [eV]
Sensitivity coefficient per lethargy
209 Bi
ν = G tar M (G tar )
t
=
i
j
s i c i, j s j ≡
i
j
υ i, j (1 ≤ i, j ≤ p),
(7.21)
where G tar (1 × p) indicates the sensitivity vector of reactor physics parameters,
M (p × p) the covariance matrix of nuclear reaction parameters, s i the sensitivity
coefficient, c i, j the covariance, υ i, j the factor of uncertainty and p the number of
nuclear reactions including the nuclides. Thus, the contribution of uncertainty u i in
each nuclear reaction can be defined as follows:
u i ≡
i
υ i, j .
(7.22)
Generally, since sensitivity coefficient s i and covariance c i, j are dominant in
the energy group, the factor of uncertainty is finally expressed with the use of the
maximum number of energy group G as follows: