2.5. Interaction of Electrons with Matter 129
2 5 10 20 50 100 200
Copper
X 0 = 12.86 g cm−^2
Ec = 19.63 MeV
dE
/dx
×
X
(MeV) 0
Electron energy (MeV)
10
20
30
50
70
100
200
40
Brems = ionization
Ionization
Rossi:
Ionization per X 0
= electron energy
To
ta
l
Brems
≈
E
E
xa
ct
bre
m
sst
ra
hl
un
g
Figure 2.5.3: Energy loss per unit track length of electrons in copper as a
function of energy. The plot also shows two definitions of the critical energy
(19).using the values obtained by the energy loss equations to find the constantsaand
b. Such computations have been shown to give the following values for solids and
gases (19):
Solids: a= 610,b=1. 24
Gases: a= 710,b=0. 92Equation 2.5.17 clearly shows that, for materials with low atomic numbers and
low incident electron energies, the collisional component of the stopping power domi-
nates. Hence most of the electrons in a beam of low energy electrons passing through
a gas will loose their energy through collisions with the gas molecules. But for the
same electrons passing through a highZmaterial (such as Lead), the radiative losses
will be significant.
A very important point to note here is that these expressions are valid only for
electrons. For positrons, the cross sections for the interactions are quite different,
even though the underlying processes may be similar. The difference in cross sections
for electrons and positrons are mainly due to the fact that the positrons passing
through a material see an abundance of electrons with which they could combine
and annihilate. On the other hand, the electrons only seldom encounter a positron
along their paths.