r X!X
0 t
ð Þ ¼
Z
B 2n
ð Þ
B n
ð Þ
dE γ
dN γ
dE γ
σ X!X 0 E γ
À Á
n X t
ð Þa,
ð1:6Þ
where σ X ! X
0 (E γ ) is the reaction cross section of X(γ, n)X
0 , n X (t) is the number of
target nucleus per unit area at time t, and a is the attenuation factor of incident
photons through a thick target. dN γ /dE γ is expressed with Eq. (1.5) and σ X ! X
0 (E γ )
is calculated from Eq. (1.2) using the TALYS code.
Figure 1.4 shows a calculation in which the photon beam is generated by the
laser Compton scattering of 1.2 GeV electrons and 0.7 eV laser beams. We assume
that the cylindrical target of
137 Cs of 1 g is irradiated with a photon beam with
energy B(n) E γ < B(2n) within a radius r % 0.8 mm at 2 m from the interaction
point. When a target of
137 Cs is irradiated with photons and is excited to GDR, the
(γ, γ), (γ, n) and (γ, 2n) reactions mainly occur. We consider
137
Cs,
136 Cs,
135 Cs,
and
134 Cs as the isotopes generated by the transmutation. The numbers of these
isotopes are expressed as
n 137 t þ Δt
ð
Þ¼n 137 t
ð Þe
Àλ 137 Δt
À r 137!136 t
ð Þ À r 137!135 t
ð Þ,
ð1:7Þ
n 136 t þ Δt
ð
Þ¼n 136 t
ð Þe
Àλ 136 Δt
þ r 137!136 t
ð Þ À r 136!135 t
ð Þ À r 136!134 t
ð Þ, ð1:8Þ
n 135 t þ Δt
ð
Þ¼n 135 t
ð Þe
Àλ 135 Δt
þ r 137!135 t
ð Þ þ r 136!135 t
ð Þ À r 135!134 t
ð Þ, ð1:9Þ
n 134 t þ Δt
ð
Þ¼n 134 t
ð Þe
Àλ 134 Δt
þ r 136!134 t
ð Þ þ r 135!134 t
ð Þ:
ð1:10Þ
One can calculate the number of each isotopes by solving these equations with
the Runge–Kutta method.
1.3 Results and Discussion
1.3.1 Nuclear Transmutation of
137
Cs with Laser Compton
Scattering
Figure 1.5 shows the dependence of the reduction of 1 g
137 Cs on the photon flux
N γ ¼ 10
12 , 10
18 , 10
19 , 10
20 /s, which is calculated with this setup (Fig. 1.4). The
number of
137 Cs is effectively reduced with photon flux over 10
18 /s, that is, the
number of
137 Cs is reduced by 10 % for 24 h irradiation. Figure 1.6 shows the
number of Cs isotopes when 1 g
137 Cs is irradiated with photon flux 2 Â 10
12 /s with
the same setup. From this figure, we can see that the reduction rate of
137 Cs by the
transmutation, which is nearly equal to the generation rate of
136 Cs, is two orders of
magnitude smaller than the natural decay rate of 1 g
137 Cs. Thus, the transmutation
of
137 Cs is not effective with photon flux 2 Â 10
12 /s, which is maximum with
present accelerator systems.
8
S. Takai and K. Hagino
0 t
ð Þ ¼
Z
B 2n
ð Þ
B n
ð Þ
dE γ
dN γ
dE γ
σ X!X 0 E γ
À Á
n X t
ð Þa,
ð1:6Þ
where σ X ! X
0 (E γ ) is the reaction cross section of X(γ, n)X
0 , n X (t) is the number of
target nucleus per unit area at time t, and a is the attenuation factor of incident
photons through a thick target. dN γ /dE γ is expressed with Eq. (1.5) and σ X ! X
0 (E γ )
is calculated from Eq. (1.2) using the TALYS code.
Figure 1.4 shows a calculation in which the photon beam is generated by the
laser Compton scattering of 1.2 GeV electrons and 0.7 eV laser beams. We assume
that the cylindrical target of
137 Cs of 1 g is irradiated with a photon beam with
energy B(n) E γ < B(2n) within a radius r % 0.8 mm at 2 m from the interaction
point. When a target of
137 Cs is irradiated with photons and is excited to GDR, the
(γ, γ), (γ, n) and (γ, 2n) reactions mainly occur. We consider
137
Cs,
136 Cs,
135 Cs,
and
134 Cs as the isotopes generated by the transmutation. The numbers of these
isotopes are expressed as
n 137 t þ Δt
ð
Þ¼n 137 t
ð Þe
Àλ 137 Δt
À r 137!136 t
ð Þ À r 137!135 t
ð Þ,
ð1:7Þ
n 136 t þ Δt
ð
Þ¼n 136 t
ð Þe
Àλ 136 Δt
þ r 137!136 t
ð Þ À r 136!135 t
ð Þ À r 136!134 t
ð Þ, ð1:8Þ
n 135 t þ Δt
ð
Þ¼n 135 t
ð Þe
Àλ 135 Δt
þ r 137!135 t
ð Þ þ r 136!135 t
ð Þ À r 135!134 t
ð Þ, ð1:9Þ
n 134 t þ Δt
ð
Þ¼n 134 t
ð Þe
Àλ 134 Δt
þ r 136!134 t
ð Þ þ r 135!134 t
ð Þ:
ð1:10Þ
One can calculate the number of each isotopes by solving these equations with
the Runge–Kutta method.
1.3 Results and Discussion
1.3.1 Nuclear Transmutation of
137
Cs with Laser Compton
Scattering
Figure 1.5 shows the dependence of the reduction of 1 g
137 Cs on the photon flux
N γ ¼ 10
12 , 10
18 , 10
19 , 10
20 /s, which is calculated with this setup (Fig. 1.4). The
number of
137 Cs is effectively reduced with photon flux over 10
18 /s, that is, the
number of
137 Cs is reduced by 10 % for 24 h irradiation. Figure 1.6 shows the
number of Cs isotopes when 1 g
137 Cs is irradiated with photon flux 2 Â 10
12 /s with
the same setup. From this figure, we can see that the reduction rate of
137 Cs by the
transmutation, which is nearly equal to the generation rate of
136 Cs, is two orders of
magnitude smaller than the natural decay rate of 1 g
137 Cs. Thus, the transmutation
of
137 Cs is not effective with photon flux 2 Â 10
12 /s, which is maximum with
present accelerator systems.
8
S. Takai and K. Hagino