Physics and Engineering of Radiation Detection

96 Chapter 2. Interaction of Radiation with Matter

The reader might be wondering why this process is termed as triplet production
although only an electron and a positron are produced. It is true that only an
electron-positron pair is generated, however since the original electron also scatters
off therefore in the imaging detector three tracks become visible: two electrons and a
positron. Hence the process is called triplet production not because three particles
are produced but because of its unique signature of three particle tracks that it
produces. To avoid confusion, some authors use the termtriplet pair productionfor
this process. The triplet production has a threshold of 2.044MeV. Since there
are only a few radioactive sources that emitγ-rays having energies higher than
this threshold, therefore this process is not of much significance in usual radiation
measurements.
The positrons produced during the process of pair production have very short
mean lives. The reason is of course the occurrence of this reaction in materials,
which always have electrons in abundance. Thus the positrons quickly combine
with a nearby electrons to produce photons through the process of annihilation.

Example:

Determine the region of the electromagnetic spectrum for a photon to be able

to generate an electron-positron pair through the process of pair production.

Solution:

To determine the threshold wavelength for the process, we use the pair pro-

duction threshold relation 2.3.25 andEγ=hc/λ.

Eγ,thresh ≥ 2 mec^2

⇒

hc

λthresh

≥ 2 mec^2

⇒λthresh ≤

h

2 mec

Substitutingh=6. 625 × 10 −^34 Js,me=9. 11 × 10 −^31 kg,andc=2. 99 ×

108 ms−^1 in the above relation gives

λthresh≤ 1. 2 × 10 −^12 m=1. 2 fm

Looking at the electromagnetic spectrum 1.6.1, we conclude that onlyγ-rays

or high energy hard x-rays are capable of producing electron-positron pairs.

It is apparent that this process is not possible at all at low photon energies. If
we compare this with the usual photon energy of a few tens ofkeV generally used
in x-ray diagnostics, it is absolutely unnecessary to even consider this process as a
possibility. However in someγ-decays, photons of energy greater than this threshold
are emitted.
Now we turn our attention to the probability of occurrence of this process in any
material. The pair production cross section for high energy photonsE 20 MeV
has a roughlyZ^2 dependence,Zbeing the atomic number of the material.

σpair∝Z^2 (2.3.29)