Interactions within Detector

All the introduced photon interactions (photoelectric effect, Compton effect, and pair production) occur in the photon detectors which are presented in this thesis. The relative importance of these effects is dependent on the photon energy and the absorber (detector) material.

The intensity of incident radiation is

I = φ hν, (5.15)

where φ is a number of primary photons per time unit (radiation flux) and hν their energy [101]. In passing a distance dx within the absorber, the number of primary

2_{The pair production could occur also in the field of an electron, but the probability is much}

38 CHAPTER 5. RADIATION INTERACTIONS

photons suffering collisions is

dφ = φ µ dx, (5.16)

where µ is the total linear attenuation coefficient [101]. Solution of this equation is as follows

φ = φ0e−µd (5.17)

and

I = I0e−µd, (5.18)

where φ0 is the initial radiation flux, I0 is the initial intensity of the radiation, and d

is a passed distance in the detector. The total linear attenuation coefficient consists of all above-mentioned interactions of photons with matter [92, 99, 101]:

µ = τ + σ + κ (5.19)

where τ is the photoelectric linear attenuation coefficient, σ is the Compton linear attenuation coefficient and κ is the pair production linear attenuation coefficient [101]. The Compton linear attenuation coefficient is given by σa and σs Compton

linear absorption coefficient and Compton linear scattering coefficient, respectively [101]

σ = σa+ σs. (5.20)

As shown in fig. 5.1, each of linear attenuation components depends on the energy of the photons and material of the detector [101]. At low energies of the photons the photoelectric linear attenuation dominates, but it decreases rapidly with increasing energy and grows with the atomic number Z. However, at heavy elements, τ may be still significant up to photon energy of a few MeV. For photon energies of more than a few hundred keV and less than several MeV, the Compton effect component σ predominates. We note that the σ is significant at all energies of photons observed in this work. The coefficient κ predominates at the many-MeV photon energy [92, 100, 101].

In the photoelectric collisions, the energy of the photoelectrons is (hν − Be),

where Beis the average binding energy of the atomic electron [101]. In the Compton

collisions, the average kinetic energy of the Compton electrons is (hνσs/σ), and the

Compton linear absorption coefficient σa is of the order of 1/2σ for (1 – 2)-Mev

5.1. INTERACTIONS OF PHOTONS 39

Figure 5.1: Relative importance of the three major photon interactions with a de- tector [101].

positron-electron pair is (hν − 2m0c2) [101]. Combining these considerations with

equations (5.16) and (5.19), we find the energy absorption in a thickness dx [101]: dI = nhτ (hν − Be) + σhν

σa

σ + κ(hν − 2m0c

2₎i_{dx. (5.21)}

In the case of usual detector materials, Be and 2m0c2 could be neglected3 [101].

Thus, the approximate expression of energy absorption becomes

dI = I(τ + σa+ κ) dx = Iµadx, (5.22)

Where µa is the linear absorption coefficient. Obviously, µais smaller than the total

linear attenuation coefficient µ, since µ includes the linear absorption coefficient µa

and the linear scattering coefficient µs [101]:

µ = µa+ µs (5.23)

The linear absorption coefficient µa represents the photon energy which is converted

into the kinetic energy of secondary electrons. The linear scattering coefficient µs

represents the total energy of all secondary photons (Compton, x-rays, and annihi- lation radiation) [101].

3_{At the light elements, the electron binding energy is much smaller than the photon energy}

at the region in which the Compton effect is significant and 2m0c2

.

= 1.02 MeV is very small in comparison with photon energy in the region in which the pair production is significant [101].

40 CHAPTER 5. RADIATION INTERACTIONS

In the real detector, all the mentioned photon interactions could contribute to the full-energy peak formation which is the most important in the gamma-ray spec- troscopy, but especially the Compton collisions could lead also to the formation of continuum background or “false” peaks in the measured spectrum. Hypothetically, if the detector will be so large that each secondary photon has an opportunity to interact by any effect which we have mentioned, the total energy of entered photons will be completely converted into kinetic energy of electrons. Because a time scale of such process is much shorter than the response of the practical detector, each pri- mary photon of a monoenergetic radiation will produce identical detector response and the full energy peak will be formed by all mentioned interactions. In the real detector with limited dimensions, some of scattered or annihilation photons may escape. Thus, the energy of an original photon is not always fully absorbed. The random losses of energy lead to the formation of continuum background, meanwhile, the precise losses lead to the formation of peaks in the measured spectrum.

The most significant continuum is caused by the Compton interaction of primary photons when the secondary photons are not absorbed. The Compton continuum is spread out between the zero energy (when the primary photon is scattered to the infinitely small angle) and the Compton edge (when the primary photon is backscattered to 180◦) [99]. Substituting hν = Eγ, ECE = hν − hν0, and ϑ = 180◦

in formula (5.12) we obtain the Compton edge energy ECE =

2E2 γ

mec2+ 2Eγ

(5.24) where Eγ is the energy of the primary photon, me is the rest-mass of electron and c

the speed of light (mec2 = 0.511 MeV). It should be noted that the second Compton

edge may be formed by the Compton edge of double Compton scattering to 180◦:

E2CE =

4E_γ2 mec2+ 4Eγ

. (5.25)

Between the Compton edge and the full energy peak is the continuum of multiple Compton events. The background with an energy above the full-energy peak is caused by pile-up effects which rest in false coincidence summing (detecting of two photons at the same time from different decays) and true coincidence summing (detecting of photons from the same decay). If both coincidence photons are fully absorbed, a “false” peak is formed. Other “false peaks” could be associated with the