between relativistic electrons and laser photons, the energy of scattered photons is
given by
E γ ¼
4γ
2 E L
1 þ γθ
ð Þ
2 þ 4E L γ=m e
,
ð1:4Þ
where γ ¼ E e /m e is the Lorentz factor of the electron beam with energy E e , m e is the
rest mass of the electron, E L is the energy of the laser photon, and θ is the scattering
angle. From Eq. (1.4), the energy of the scattered photon is maximum at θ ¼ 0, and
it depends on the energy of incident electrons and photons. The minimum energy of
the scattered photon can be fixed by controlling θ with collimators.
The scattering cross section of laser Compton scattering is given by the Klein–
Nishina formula:
dσ
dE γ
¼
πr
2
0
2
m
2
e E L E
2
e
m
4
e
4E
2
L E
2
e
E e
E γ À E e
2
À
m
2
e
4E L E e
E e
E γ À E e
þ
E e
E γ À E e
þ
E γ À E e
E e
(
)
,
r 0 ¼ e
2
=4πm e ,
N γ ¼
Z
dE γ
dN γ
dE γ
¼
Z
dE γ
dσ
dE γ
Á const:
ð1:5Þ
0
50
100
150
200
250
300
350
0
5
10
15
20
Cross Section :s (mb)
Incident Photon Energy : E g (MeV)
B(n)
B(2n)
137 Cs(g,g) 137 Cs
137 Cs(g,n)
136 Cs
137 Cs(g,2n)
135 Cs
Fig. 1.2 Cross sections for
137
Cs (γ, γ),
137
Cs (dashed line),
137
Cs (γ, n),
136
Cs (solid line), and
137
Cs (γ, 2n).
135
Cs (dash-dot line) reactions versus incident photon energy: dotted lines represent
B(n) and B(2n) of
137
Cs
6
S. Takai and K. Hagino