Biomedical Engineering Reference
In-Depth Information
not the sums of separate electronic cross sections, like
e
σ
.) The linear attenuation
coefficient
µ
, given by Eq. (8.44), is also equal to the product of the atomic density
N
A
and the total atomic cross section
σ
A
for all processes:
µ
=
N
A
σ
A
.
(8.49)
The number of atoms cm
-3
of an element is given by
N
A
=
/
A
)
N
0
, where
ρ
is the
density of the material in g cm
-3
,
A
is the gram atomic weight, and
N
0
is Avogadro's
number. Thus, we can write
µ
=
ρN
0
σ
A
/
A
,or
µ
ρ
(
ρ
N
0
σ
A
A
(8.50)
=
,
giving the relationship between the mass attenuation coefficient and the atomic
cross section for photon interaction with any element. For a compound or mixture,
one can add the separate contributions from each element to obtain
µ
.
Cross sections are often expressed in the unit, barn, where
1
barn
=
10
-24
cm
2
.
Example
What is the atomic cross section of lead for 500-keV photons?
Solution
From Fig. 8.8, the mass attenuation coefficient is
0.16 cm
2
g
-1
.Thegram
µ
/
ρ
=
atomic weight of lead is 207 g. We find from Eq. (8.50) that
µ
ρ
A
N
0
= (0.16 cm
2
g
-1
)
10
23
207 g
6.02
= 5.50 × 10
-23
cm
2
.
σ
A
=
(8.51)
×
Alternatively,
σ
A
=
55.0 barn.
8.8
Energy-Transfer and Energy-Absorption Coefficients
In dosimetry we are interested in the energy absorbed in matter exposed to pho-
tons. This energy is related to the linear attenuation coefficients given in Eq. (8.44).
However, some care is needed in making the connections.
Figure 8.10 shows a uniform, broad, parallel beam of monoenergetic photons
normally incident on an absorber of thickness
x
. The incident fluence
0
is the
number of photons per unit area that cross a plane perpendicular to the beam.
2)
The number that cross per unit area per unit time at any instant is called the
fluence
rate
, or flux density:
˙
˙
0
are,
respectively, m
-2
and m
-2
s
-1
. The energy that passes per unit area is called the
energy fluence
0
, having the units J m
-2
. The corresponding instantaneous rate
of energy flow per unit area per unit time is the energy fluence rate, or energy
=
d
0
/d
t
(
=
ϕ
0
)
. Examples of units for
0
and
0
2 Our notation is consistent with that of ICRU
Report 60, listed in Section 8.10.
