R self ¼
Z E max
E min
1 À exp Ànσ tot E
ð Þ
ð
Þ
f
g n ind σ cap E
ð ÞdE=
Z E max
E min
n ind σ cap E
ð ÞdE, ð3:3Þ
where n and n ind denote the thickness (the number of target nuclide per unit area) of
the sample and indicator, respectively. The quantities σ tot and σ cap represent the
energy-dependent neutron total and capture cross sections of the target nuclide,
respectively. The integration is performed over the resonance peak region. By
applying Eqs. (3.2) and (3.3), the relationships between the net area ratio and the
thickness were obtained using point-wise cross-section data of JENDL-4.0 [7], as
shown in Fig. 3.3. If nσ tot is not large, the net area ratio is proportional to the sample
thickness. However, it converges to unity and loses information about thickness as
nσ tot becomes larger. The thickness of each gold foil sample was derived from the
relationship of Fig. 3.3 and the value of R was determined by experiment. Figure 3.4
shows the results of quantitative examination. It was confirmed that the thickness of
the target nuclide can be determined by both methods within 3 % accuracy. The
accuracy can be improved further by using a smaller resonance (nσ tot is not large).
The TOF spectra with silver and gold samples are shown with the NRTA method
in Fig. 3.5 and with the self-indication method in Fig. 3.6. In NRTA, the dips of the
4.9 eV resonance of
197
Au and the 5.2 eV resonance of
109 Ag overlapped around
400 ch. in Fig. 3.5. In the self-indication method, the contribution from impurity
was suppressed and a weak 58 eV resonance of
197 Au was emphasized around
120 ch. (Fig. 3.6). The TOF spectra for the mixture composed of
nat U,
237 Np, and
243 Am are shown in Figs. 3.7 and 3.8. Although many resonance dips caused by
impurities of
237 Np and
243 Am were observed (Fig. 3.7), there are no differences
Net area ratio R
Thickness [atoms/b]
Net area ratio R can be obtained
from the TOF measurement easily.
Estimated value
Fig. 3.3 Relationship between net area ratio and sample thickness
3 Development of Nondestructive Assay to Fuel Debris of Fukushima Daiichi. . .
25
Z E max
E min
1 À exp Ànσ tot E
ð Þ
ð
Þ
f
g n ind σ cap E
ð ÞdE=
Z E max
E min
n ind σ cap E
ð ÞdE, ð3:3Þ
where n and n ind denote the thickness (the number of target nuclide per unit area) of
the sample and indicator, respectively. The quantities σ tot and σ cap represent the
energy-dependent neutron total and capture cross sections of the target nuclide,
respectively. The integration is performed over the resonance peak region. By
applying Eqs. (3.2) and (3.3), the relationships between the net area ratio and the
thickness were obtained using point-wise cross-section data of JENDL-4.0 [7], as
shown in Fig. 3.3. If nσ tot is not large, the net area ratio is proportional to the sample
thickness. However, it converges to unity and loses information about thickness as
nσ tot becomes larger. The thickness of each gold foil sample was derived from the
relationship of Fig. 3.3 and the value of R was determined by experiment. Figure 3.4
shows the results of quantitative examination. It was confirmed that the thickness of
the target nuclide can be determined by both methods within 3 % accuracy. The
accuracy can be improved further by using a smaller resonance (nσ tot is not large).
The TOF spectra with silver and gold samples are shown with the NRTA method
in Fig. 3.5 and with the self-indication method in Fig. 3.6. In NRTA, the dips of the
4.9 eV resonance of
197
Au and the 5.2 eV resonance of
109 Ag overlapped around
400 ch. in Fig. 3.5. In the self-indication method, the contribution from impurity
was suppressed and a weak 58 eV resonance of
197 Au was emphasized around
120 ch. (Fig. 3.6). The TOF spectra for the mixture composed of
nat U,
237 Np, and
243 Am are shown in Figs. 3.7 and 3.8. Although many resonance dips caused by
impurities of
237 Np and
243 Am were observed (Fig. 3.7), there are no differences
Net area ratio R
Thickness [atoms/b]
Net area ratio R can be obtained
from the TOF measurement easily.
Estimated value
Fig. 3.3 Relationship between net area ratio and sample thickness
3 Development of Nondestructive Assay to Fuel Debris of Fukushima Daiichi. . .
25