Biomedical Engineering Reference
In-Depth Information
Solution
Note that Eq. (7.3) for LET involves stopping power rather than mass stopping power.
Since
ρ
= 1 for water, the numbers in Table 7.1 also give (-d
E
/d
x
)
in MeV cm
-1
.We
238 MeV cm
-1
given directly in the table. Linear interpolation gives
LET
5keV
= 252 MeV cm
-1
.
find LET
1keV
=
LET is often expressed in units of keV
µ
m
-1
of water. Conversion of units shows
that 1 keV
µ
m
-1
= 10 MeV cm
-1
(Problem 10).
In 1998, the ICRU introduced the following new definition, also called “linear
energy transfer, or restricted linear electronic stopping power,
L
”:
-
d
E
L
=
d
x
.
(7.4)
Here
E
is the total energy lost by the charged particle due to electronic collisions
in traversing a distance
d
x
, minus the sum of the kinetic energies of all electrons
released with energies in excess of
. Compared with the 1980 definition, Eq. (7.3),
there are two important differences. First, the binding energies for all collisions are
included in (7.4). Second, the threshold kinetic energy of the secondary electrons
for a collision is now
, rather than
minus the binding energy. Equation (7.4)
can be written in the alternate form,
L
= -
d
E
d
x
-
d
E
ke,
,
(7.5)
d
x
where
d
E
ke,
is the sum of the kinetic energies greater than
of the secondary
electrons. We shall not deal further with the newer quantity. The reader is referred
to the 1980 and 1998 ICRU Reports 33 and 60 listed in Section 7.8.
7.4
Specific Ionization
The average number of ion pairs that a particle produces per unit distance trav-
eled is called the specific ionization. This quantity, which expresses the density of
ionizations along a track, is often considered in studying the response of materials
to radiation and in interpreting some biological effects. The specific ionization of
a particle at a given energy is equal to the stopping power divided by the average
energy required to produce an ion pair at that particle energy. The stopping power
of air for a 5-MeV alpha particle is 1.23 MeV cm
-1
, and an average of about 36 eV
is needed to produce an ion pair. Thus, the specific ionization of a 5-MeV alpha
particle in air is (
1.23
10
6
eV cm
-1
)/(36 eV)
34
,200 cm
-1
.Fora5-MeValpha
×
=
950
MeV cm
-1
(Fig. 5.6). Since about 22
eV is required to produce an ion pair, the specific ionization is
4.32
particle in water or soft tissue,
-d
E
/d
x
=
10
7
cm
-1
.
×
