cross section varies by a unit amount. Therefore, a positive value of this coefficient
indicates that the target activation product is generated through the nuclear reaction.
Thus, if a sensitivity coefficient is positive and large, the cross section of the nuclear
reaction is significant for the generation of the target activation products. In the
analyses, the objectives of reaction were six reactions treated in ORLIBJ40 library;
the reaction of (n, γ), (n, 2n), (n, α), and (n, p) yielding to nuclides of ground state
and the reaction of (n, γ) and (n, 2n) yielding to nuclides of meta-stable state. The
summary of the results of sensitivity analyses of cross sections are shown in
Table 20.8, where the sensitivity coefficients that are positive and more than 0.01
are extracted from all the results and listed in descending order. The results clarified
the nuclear reaction dominating the generation of target nuclides. For example, it is
thought that Fe-55 in Zircaloy-2 can be generated from the (n, γ) reaction of Fe-54,
the (n, α) reaction of Ni-58, and the (n, 2n) reaction of Fe-56. Table 20.8a clearly
shows the (n, γ) reaction of Fe-54 is dominant in the generation of Fe-55.
It was remarkable that the dominant generation pathways were clarified even for
the target nuclides generated through complicated pathways. Some of the examples
are shown in Fig. 20.2.
Figure 20.2a shows an example of nuclides generated with some contributing
pathways. Be-10 is generated in Zircaloy-2 mainly through two pathways, the (n, p)
reaction of Be-10 and the (n, α) reaction of C-13. It is not predictable which
pathway is dominant from the initial composition of the material. The sensitivity
Table 20.8 (continued)
Target nuclide
Sensitivity coefficient of cross section
First largest
Second largest
Others
Zn-65
Zn-64
(n, γ)
0.99 Cu-63
(n, γ)
0.99
Sr-90
Zr-93
(n, α)
1.00 Nb-93
(n, p)
0.98
Si-32
Si-31
(n, γ)
1.00 Si-30
(n, γ)
0.71 P-31
(n, p)
0.29
H-3
H-2
(n, γ)
1.00 H-1
(n, γ)
1.00 Ni-58 (n, p)
0.95
He-3
(n, p)
0.01
(n, γ) m means the (n, γ) reaction yielding to meta-stable state
Fig. 20.2 Examples of complicated generation pathways of activation products. The values in
bold font in the figures show the sensitivity coefficients of the cross sections. a Be-10 generation in
Zircaloy-2. b Cl-36 generation in SUS304 stainless steel
20 Sensitivity Analyses of Initial Compositions and Cross Sections. . .
245
indicates that the target activation product is generated through the nuclear reaction.
Thus, if a sensitivity coefficient is positive and large, the cross section of the nuclear
reaction is significant for the generation of the target activation products. In the
analyses, the objectives of reaction were six reactions treated in ORLIBJ40 library;
the reaction of (n, γ), (n, 2n), (n, α), and (n, p) yielding to nuclides of ground state
and the reaction of (n, γ) and (n, 2n) yielding to nuclides of meta-stable state. The
summary of the results of sensitivity analyses of cross sections are shown in
Table 20.8, where the sensitivity coefficients that are positive and more than 0.01
are extracted from all the results and listed in descending order. The results clarified
the nuclear reaction dominating the generation of target nuclides. For example, it is
thought that Fe-55 in Zircaloy-2 can be generated from the (n, γ) reaction of Fe-54,
the (n, α) reaction of Ni-58, and the (n, 2n) reaction of Fe-56. Table 20.8a clearly
shows the (n, γ) reaction of Fe-54 is dominant in the generation of Fe-55.
It was remarkable that the dominant generation pathways were clarified even for
the target nuclides generated through complicated pathways. Some of the examples
are shown in Fig. 20.2.
Figure 20.2a shows an example of nuclides generated with some contributing
pathways. Be-10 is generated in Zircaloy-2 mainly through two pathways, the (n, p)
reaction of Be-10 and the (n, α) reaction of C-13. It is not predictable which
pathway is dominant from the initial composition of the material. The sensitivity
Table 20.8 (continued)
Target nuclide
Sensitivity coefficient of cross section
First largest
Second largest
Others
Zn-65
Zn-64
(n, γ)
0.99 Cu-63
(n, γ)
0.99
Sr-90
Zr-93
(n, α)
1.00 Nb-93
(n, p)
0.98
Si-32
Si-31
(n, γ)
1.00 Si-30
(n, γ)
0.71 P-31
(n, p)
0.29
H-3
H-2
(n, γ)
1.00 H-1
(n, γ)
1.00 Ni-58 (n, p)
0.95
He-3
(n, p)
0.01
(n, γ) m means the (n, γ) reaction yielding to meta-stable state
Fig. 20.2 Examples of complicated generation pathways of activation products. The values in
bold font in the figures show the sensitivity coefficients of the cross sections. a Be-10 generation in
Zircaloy-2. b Cl-36 generation in SUS304 stainless steel
20 Sensitivity Analyses of Initial Compositions and Cross Sections. . .
245