Physics and Engineering of Radiation Detection

2.5. Interaction of Electrons with Matter 127

For an electron withz= 1, the above equation becomes

dN

dx

= 490 sin^2 Θcm−^1. (2.5.14)

Example:

An electron moving in water emits Cherenkov radiation in a cone making

an angle of 40^0 with electron’s direction of motion. Compute the number of

photons emitted per centimeter by the electron.

Solution:

Using equation 2.5.14 withθ=40^0 ,weget

dN

dx

= 490 sin^2 Θ

= 490 sin^2 (40^0 )≈ 272 cm−^1.

Discriminating such a small number of photons from background is a very

difficult task. Generally, the conic signature of the Cherenkov radiation is

used to discriminate the Cherenkov photons from the background radiation.

2.5.B PassageofElectronsthroughMatter..............

As compared to heavy charged particles, electrons behave quite differently when
passing through matter. The main reason for this difference is, of course, the very
small mass of electrons as compared to heavy charged particles. Due to their low
mass, electrons travel so fast that their velocity may become very close to the velocity
of light. Since in such a situation the relativistic effects must be taken into account
to deduce meaningful results, therefore the computations become more complicated
than for the heavy charged particles.
We saw earlier that in certain situations an electron may even attain a velocity
greater than the velocity of light in the same material. If this happens, a special kind
of radiation, called Cherenkov radiation, with a specific cone signature is emitted.
As electrons pass through matter they rapidly lose energy and hence decelerate.
This deceleration gives rise to another type of radiation called Bremsstrahlung.
Whenever an electron beam passes through a material, the individual electrons
in the beam can interact with the target atoms or molecules in a number of ways,
most of which we have already discussed in the preceding sections. Fig.2.5.1 shows
the contributions of various types of interactions on the stopping power of lead for
electrons of various energies. It is interesting to note that except for the ionization
process, the Bremsstrahlung remains the dominant mode of interaction from low to
high energies. Therefore the radiative component of the stopping power can not be
neglected in case of electrons.
At low to moderate energies the collisional energy loss of electrons is quite signif-
icant and up to a certain energy is higher than the radiative energy loss. Hence the
stopping power of a material for electrons consists of two components: collisional
and radiative.

Selectron=Scollisional+Sradiative