Biomedical Engineering Reference
In-Depth Information
level. This and subsequent electronic transitions are accompanied by the simulta-
neous emission of photons or Auger electrons (Sections 2.10 and 2.11). The frac-
tion of the incident intensity transferred to electrons (i.e., the photoelectron and the
Auger electrons) can be expressed as
1-
δ
/
h
ν
, where
δ
is the average energy emitted
as fluorescence radiation following photoelectric absorption in the material. Just as
the mass attenuation coefficient
τ
/
ρ
, defined after Eq. (8.44), describes the fraction
of photons that interact by photoelectric absorption per g cm
-2
of matter traversed,
the mass energy-transfer coefficient,
1-
h
ν
,
τ
tr
ρ
=
τ
ρ
(8.53)
gives the fraction of the intensity that is transferred to electrons per g cm
-2
.To
the extent that the photoelectron and Auger electrons subsequently emit photons
(as bremsstrahlung), the energy-
transfer
coefficient does not adequately describe
energy
absorption
in the slab. We return to this point after defining the mass energy-
transfer coefficients for Compton scattering and pair production.
For Compton scattering of monoenergetic photons (Fig. 8.4), the mass energy-
transfer coefficient follows directly from Eq. (8.38):
T
avg
h
ν
σ
tr
ρ
=
σ
ρ
.
(8.54)
The factor
T
avg
/
h
ν
gives the average fraction of the incident photon energy that
is converted into the initial kinetic energy of the Compton electrons. As with the
photoelectric effect, the energy-transfer coefficient (8.54) takes no account of sub-
sequent bremsstrahlung by the Compton electrons.
A photon of energy
h
ν produces an electron-positron pair with a total initial
kinetic energy
h
-2
mc
2
, where 2
mc
2
is the rest energy of the pair [Eq. (8.41)].
Therefore, the mass energy-transfer coefficient for pair production is related to the
mass attenuation coefficient, defined after Eq. (8.44), as follows:
ν
1-
2
mc
2
h
ν
.
κ
tr
ρ
=
κ
ρ
(8.55)
This relationship applies to pair production in the field of an atomic nucleus; we
neglect the small contribution from triplet production (Section 8.5).
The total mass energy-transfer coefficient
µ
tr
/
ρ
for photons of energy
h
ν
in a
given material is found by combining the last three equations:
µ
tr
ρ
=
τ
tr
ρ
+
σ
tr
ρ
+
κ
tr
ρ
(8.56)
1-
h
ν
+
σ
ρ
T
avg
h
ν
+
κ
ρ
1-
2
mc
2
h
ν
.
τ
ρ
=
(8.57)
This coefficient determines the total initial kinetic energy of all electrons produced
by the photons, both directly (as in photoelectric absorption, Compton scattering,
