Physics and Engineering of Radiation Detection

2.2. Types of Particle Interactions 81

It is also possible that a high energy charged particle with non-zero rest mass,
such as an electron, travels faster than speed of light in that medium. If this hap-
pens, the particle emits a special kind of radiation called Cherenkov radiation. The
wavelengths of Cherenkov photons lie in and around the visible region of electro-
magnetic spectrum. In fact, the first Cherenkov radiation was observed by Pavel
Cherenkov in 1934 as blue light comingfrom a bottle of water undergoing bom-
bardment by particles from a radioactive source. This discovery and his subsequent
explanation of the process earned him Nobel Prize in Physics in 1958.
Cherenkov radiation has a certain geometric signature: it is emitted in the form
of a cone having an angleθdefined by

cosθ=

1

βn

, (2.2.6)

wherenis the refractive index of the medium andβ=v/cwithvas the velocity of
the particle in the medium.
Since Cherenkov radiation is always emitted in the form of a cone therefore the
above equation can be used to determine a value ofβ(and hencev)belowwhich
the particle will not emit any radiation. Since cosθ<1 for a cone, therefore using
the above relation we can conclude that a necessary condition for the emission of
Cherenkov radiation is that

β>

1

n

. (2.2.7)

Now, sinceβ=v/c, this condition can be translated into

v>

c

n

. (2.2.8)

Herec/nis the velocity of lightin the medium. This shows that the emission of
Cherenkov radiation depends on two factors: the refractive indexnof the medium
and the velocityvof the particle in that medium. Using this condition one can
determine the minimum kinetic energy a particle must possess in order to emit
Cherenkov radiation in a medium (see example below).

Example:

Compute the threshold energies an electron and a proton must possess in

light water to emit Cherenkov radiation.

Solution:

For both particles the threshold velocityvthcan be computed from equation

2.2.8.

v>

c

n

=

2. 99 × 108

1. 3

⇒vth =2. 3 × 108 ms−^1

Here we have takenn=1.3forwaterandc=2. 99 × 108 ms−^1 is the velocity

of lightin vacuum. Since particles are relativistic, we must use the relativistic

kinetic energy relation

T=

[(

1 −

v^2

c^2

)− 1 / 2

− 1

]

m 0 c^2.