THE EGS5 CODE SYSTEM

X
S
k
e
=
Z
e
0
O
k
0
Y
Figure 2.24: Direction of the polarization vector of the scattered photon. Plane S contains ⃗e 0
and ⃗ k. ⃗e ‖ is in plane S, and is perpendicular to ⃗ k. e⃗
⊥ is perpendicular to plane S.
tic impulse approximation [134]. By modifying Ribberfors’ formula, a doubly differential Compton
scattering cross section for a linearly polarized photon can be derived as:
(
d 2 ) ( ) (
σ
= r2 0 kc k kc
+ k )
0
− 2 + 4 cos 2 Θ × dp z
dΩdk 4 k 0 k c dk J i(p z ), (2.430)
bC,i
k 2 0
where Θ is the angle between the incident polarization vector ⃗e 0 and the scattered polarization vector
⃗e. Note that Equation 2.415 can be obtained by integrating Equation 2.430 over the azimuthal
angle, and that the Compton-scattering cross section of a free electron (i.e., ignoring binding effects)
for linearly polarized photons is obtained by integrating Equation 2.430 over ˘k and putting
I i = 0,
( ) dσ
= 1 ( ) 2 ( ˘kc ˘kc
dΩ fC 4 r2 0
+ ˘k
)
0
− 2 + 4 cos
˘k 0
˘k 0
˘k 2 Θ . (2.431)
c
The Rayleigh scattering cross section for linearly polarized photons The Rayleigh scattering
cross section for linearly polarized photons is the product of the square of the atomic form
factors (as defined earlier in Equation 2.408) and the single electron elastic scattering (Thomson)
cross section for linear polarized photons. The polarized Thomson scattering cross section per
electron is given by [86]
( ) dσ
= r0 2 cos 2 Θ, (2.432)
dΩ T
and so the polarized Rayleigh scattering cross section is thus
( ) dσR
= r0 2 cos 2 Θ[F T (q)] 2 . (2.433)
dΩ
R
134