2.4. Interaction of Heavy Charged Particles with Matter 115
<Z/A>,and<δ>. However these expressions do not give reliable results due
mainly to the increased bonding strength of electrons in compounds as compared to
that in elements. The higher bonding energy of electrons in a compound means that
a simple weighted mean of individual ionization potentials would be an underesti-
mate. For more reliable estimates, one can use tables given in (52) and (51), which
have been generated after including several correction.
Example:
Calculate the stopping power of 5 MeVα-particles in air.Solution:
Let us assume that air is composed of 80% nitrogen and 20% oxygen. Accord-
ing to Bragg-Kleeman rule (equation 2.4.16), the total mass stopping power
of air would be the weighted sum of the mass stopping powers of nitrogen and
oxygen.
For simplicity, let us use the uncorrected Bethe-Bloch formula 2.4.10 (this
assumption is valid since at this energy the correction factorsδandCare
insignificantly small). Forα-particles we haveZ=2andq= 2. The other
factors in equation 2.4.10 can be calculated as follows.β =[
1 −
E 0
E 0 +E/Aα] 1 / 2
=
[
1 −
931. 5
931 .5+5/ 2
] 1 / 2
.
=0. 05174
Wmax =2mec^2β^2
1 −β^2=2(0.511)(0.05174)^2
1 −(0.05174)^2
=2. 743 × 10 −^3 MeV
The mass attenuation coefficient, according to equation 2.4.12, can then be
written as
[
−1
ρdE
dx]
Bethe−Bloch=
0. 30548 Zq^2
Aβ^2[
ln(
Wmax
I)
−β^2]
.
=
(0.30548)(2)(2)^2
A(0.05174)^2
[
ln(
2. 743 × 10 −^3
I
)
−(0.05174)^2
]
=
912. 893
A
[
ln(
2. 743 × 10 −^3
I
)
− 2. 677 × 10 −^3
]
.
To calculate ionization potentials of nitrogen and oxygen we use equation
2.4.13.
I =12Z+7
⇒Initrogen = 12(7) + 7 = 91eV
Ioxygen = 12(8) + 7 = 103eV