Nuclear Engineering

Interaction of photons with matter

The electromagnetic radiation corresponding to nuclear transition is gamma ray, which are highly energetic (typically mega electron volt, MeV) photons. They interact with materials by three different processes, namely, photoelectric effect, Compton scattering and pair creation. All these processes lead to partial or complete transfer of the photo energy to the electrons. These three processes eventually remove the photon from the beam entirely, either by absorption or by scattering. If a gamma ray/X-ray photon beam of intensity I₀ falls on a material, then it will be attenuated by these three processes as per the following relation:

where d is the distance traverses by the photon beam inside the material and μ the absorption coefficient.

Let us now try to understand the above mentioned three physical processes by which the incident photons interact with the material and their contribution to the overall absorption cross section of photons inside the matter. The first process, i. e. photoelectric effect is basically is an absorption process where the incident photon interacts with atomic electron, gets absorbed, and subsequently the electron ejects out from one of the bound shells of the atom. If E_b.e. is the binding energy of the electron in an atomic shell, then the kinetic energy of the ejected electron would be

where hν is the energy of the incident photons. This is illustrated in Fig. m2.7.

FIGURE m2.7 (a) Ejection of electrons from the surface due to photoelectric effect and (b) variation of photoelectric effect cross section with incident ion energy.

For gamma rays of sufficient energy, the most probable origin of the photoelectron is the most tightly bound or K shell of the atom. The probability of occurrence of photoelectric effect or the cross section of photoelectric effect varies with incident photon energy as shown in the above. It is clear from this figure that the photoelectron emission probability increases with decrease in photon energy and attains a peak when it approaches to energy equal to the binding energy of K-shell of the atom. The cross section drops down just after that since K-electrons are not available for emission. Below this energy, the cross-section rises once again and dips as the L, M levels, etc. are passed. Photoelectric effect is dominant at relatively lower energy, and it is also enhanced for absorber material of high atomic number, Z.

Now we are going to discuss the second interaction process, i.e. Compton scattering, which is basically scattering of photons by free electrons. Though the electrons inside the material is bound, if the incident photon energy is higher enough with respect to the binding energy, this latter energy can be ignored and the electrons can be considered as essentially free. In Fig. m2.8 the kinetics of Compton scattering is shown, which clearly indicates that after scattering photon flies to a direction with an angle θ and the electron is kicked out from its position with an angle φ.

FIGURE m2.8 Schematic representation of Compton scattering

If the incident photon energy is hν and scattered photon’s energy is hν₁, then from energy-momentum conservation it can be shown that¹

where m₀c² is the rest mass energy of electron , which is equal to 0.511 MeV. Klein-Nishima made a detailed theoretical work on the probability of Compton scattering and have shown that the probability varies linearly with Z value of the scatterer. As it is an angle dependent process, in a typical spectrum, it appears as a broad spectrum, known as Compton background.

The third process, known as pair creation is basically generation of electron-positron pairs when a gamma ray photon of energy 1.02 MeV or more passes through a material. In order to conserve momentum, this process occurs only near a third body, usually a nucleus. The minimum energy required for pair creation is 1.02 MeV, which is basically addition of rest mass energies of electron and positron. All the excess energy carried by photon above 1.02 MeV, required to create the pair, goes into kinetic energy shared by electron and positron. It has been shown1 that the probability of pair creation varies approximately square of the absorber’s atomic number Z. The variation of pair production crosss section with incident photon energy is shown in Fig. m2.9.

FIGURE m2.9 Pair production cross section with incident photon energy

Now when a gamma ray or a beam of gamma photons enters inside the material, it undergoes all these three processes simultaneously. Therefore, it is important to understand the relative contribution of individual process. This is depicted in Fig. m2. 10, where cross section of these three processes versus incident photon energy is plotted. It is clear from this figure that photoelectric effect and Compton scattering are dominant at lower gamma energy, whereas at higher energy the contribution from pair production process enhances.

FIGURE m2.10 Cross section of photoelectric effect, Compton scattering and pair production versus incident gamma ray energy.

All the above three processes contribute additively to the total absorption coefficient of the gamma ray photons inside matter. Therefore, total cross-section

Probability per unit length can be defined by multiplying

_tot and the density of atoms D and is given below:

where N_a is the Avogadro’s number; ρ density of the material and A is the molecular weight. This is the total linear absorption coefficient and just the inverse of the mean free path of the photon.

Let us hold here for a moment and think about the situation when charged particles or photons interact with any compound or mixture. The question arises how to calculate energy loss by charged particles or absorption of photons in these cases?

In case of compounds, the energy loss can be obtained by averaging dE/dx over each element in the compound weighted by the fraction of each element (Bragg’s Rule)². Therefore,

Where w₁, w₂, etc. are the weight fractions of the elements 1,2 in the compound. If n_i is the number of atoms of the i^th element in the molecule m, then

where A_i is the atomic weight of the i^th element and

Similarly, the Bragg rule for the absorption of photons can be written as:

Nuclear Engineering

Nuclear Engineering

Curriculum

Interaction of photons with matter

Modal title