1. Introduction to Pair Production
Pair production is a process where a photon with energy greater than the threshold energy interacts with an atom, leading to the creation of an electron-positron pair. The photon must have energy exceeding \( 2m_e c^2 = 1.022 \, \text{MeV} \), where \( m_e \) is the electron rest mass.
Fig. 1.9(d): Schematic diagram of nuclear pair production.
2. Conditions for Pair Production
For pair production to occur, three conservation laws must be respected:
- Energy Conservation: The total energy before and after the interaction must be equal.
- Momentum Conservation: The momentum must be conserved in the interaction.
- Charge Conservation: The charge must be conserved, meaning a neutral photon will create an electron (\( -1 \)) and a positron (\( +1 \)).
Additionally, pair production cannot occur in free space because both energy and momentum must be conserved simultaneously. Thus, it occurs in the Coulomb field of an atom’s nucleus or an orbital electron, which absorbs a fraction of the photon’s momentum.
3. Types of Pair Production
There are two types of pair production based on the interaction partner:
- Nuclear Pair Production: Involves the interaction between the photon and an atomic nucleus. This type of pair production has a threshold photon energy of approximately \( 2m_e c^2 = 1.022 \, \text{MeV} \).
- Electronic Pair Production (Triplet Production): This is less probable, where the photon interacts with an orbital electron instead of a nucleus. The threshold energy for this process is \( 4m_e c^2 = 2.044 \, \text{MeV} \), which is higher than the threshold for nuclear pair production.
4. Pair Production Attenuation Coefficients
The probability of pair production is zero for photon energies below the threshold value. Above the threshold, the probability increases rapidly with photon energy. The two types of pair production (nuclear and electronic) are usually combined and referred to as the pair production attenuation coefficient.
The attenuation coefficients are influenced by the atomic number \( Z \) of the absorber. The nuclear pair production coefficient \( a_\kappa \) depends approximately on \( Z^2 \), while the mass attenuation coefficient \( \kappa/\rho \) is proportional to \( Z \), where \( \rho \) is the material's density.
5. Energy Threshold for Pair Production
The photon must have a minimum energy of \( 1.022 \, \text{MeV} \) for nuclear pair production and \( 2.044 \, \text{MeV} \) for electronic pair production (triplet production). The probability of pair production increases significantly as the photon energy rises above these thresholds.
Example: Photon Energy and Pair Production
If a photon with energy of \( 3 \, \text{MeV} \) interacts with an atom, the photon will have enough energy to produce an electron-positron pair, as the energy exceeds the threshold for nuclear pair production. The energy of the incident photon is shared between the creation of the pair and any recoil energy imparted to the nucleus or electron.
Energy threshold for pair production:
\[ E_{\gamma} > 2 m_e c^2 = 1.022 \, \text{MeV} \quad \text{(Nuclear Pair Production)} \]