7 Neutronics of Lead and Bismuth
205
Fig. 7.17 Sensitivity
coefficients of capture
reactions of 209 Bi, 27 Al,
235 U and 238 U in JENDL-4.0
(Ref. [3])
(a)
209
Bi
(b)
27
Al,
235
U and
238
U
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
-0.00015
-0.00010
-0.00005
0
Neutron energy [eV]
Sensitivity coefficient per lethargy
209 Bi
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
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
Neutron energy [eV]
Sensitivity coefficient per lethargy
238 U
27 Al
235 U
can be expressed as follows:
P(R 0 ) ∝ exp
−(R e − R e 0 )
t V
−1
e (R e − R e 0 )/2
.
(7.25)
The values R e are distributed around true values R e0 of experiment with covariance
V e of experimental value, giving true values T 0 of a set of nuclear cross sections.
Also, the values R c (T 0 ) of experiment with the true value of the nuclear data crosssection set are distributed around true value R e0 with covariance V e + V m , giving
true value T 0 of a set of nuclear cross sections, as follows:
P(R 0 |T 0 ) ∝ exp
−(R e − R c (T 0 ))
t
(V e + V m )
−1
(R e − R c (T 0 ))/2
,
(7.26)
where V m indicates the covariance of calculation value.
Using Eqs. (7.24) through (7.26), the following equations are obtained with the
consideration of mathematical formulation [24]: