Biomedical Engineering Reference
In-Depth Information
Scatter photon
E
s
=
h
ν
s
Incident photon
α
E
i
=
h
ν
i
β
Recoil electron
Fig. 1
Schematic representation of the Compton effect. The incident photon with energy
E
i
interacts with an electron: the photon is deflected (represented by angle
'
) and the electron recoils
(at an angle
“
) because of the energy given by the incident photon. Consequently the scattered
photon has less energy (longer wavelength) than the incident photon
differential cross section for the Compton effect suffered by X and gamma radiation
was introduced by Klein and Nishina [
2
] in 1928 and is generally known as Klein-
Nishina formula:
r
0
2
P
E
i
;˛
P
E
i
;˛
sen
2
.˛/ C P
E
i
;˛
;
d
d
D
(2)
where
r
0
De
2
ı
4 "
0
m
0
c
2
D 2; 817 10
15
m
represents the classical elec-
tron radius and
P
E
i
;˛
is the ratio between the energies before and after the Compton
effect, which is given by:
E
d
E
i
D
1
P
E
i
;˛
D
cos
˛/
:
(3)
E
i
1 C
m
0
c
2
.1
While in the Compton effect the incident photon transfers only part of his energy,
in the photoelectric effect the photon gives all its energy to an electron of an atom,
causing the ejection of the electron with an energy equal to the difference of photon
energy and the binding energy.
E
c
:
electron
D h
incident photon
E
binding
(4)
The ionization created by the electron ejection has short duration and the gap is
filled by another electron. This process is accompanied by the emission of a photon
(fluorescence) or an Auger electron.
In Rayleight scattering, the photon is deflected without loosing energy to the
electron. Therefore, the conservation of the kinetic energy holds and the scattering
is elastic. The differential cross section per electron for a photon that is scattered
into the solid angle
'
is given by:
1 C
cos
2
˛
;
r
0
2
d
e
d
D
(5)
where
r
0
is, as before, the “classical radius” of the electron.
