Introduction to Pair Production
There are many ways in which photons can interact with atoms, electrons and matter. Pair production is one among those, through which a photon can interact with the atoms and electrons. In pair production, a photon creates an electron and a positron in such a way that during this process the photon involved in the interaction will disappear.
Basically, during the process of pair production, we are creating an elementary particle and its antiparticle with the help of a photon (or sometimes another neutral boson). Pair production is actually an exact opposite process of annihilation and it is useful in demonstrating the conservation of charges. Pair production is a chief method through which energy from gamma-ray is observed in a given condensed matter. Let us understand pair production, what is pair production along illustrations.
What is Pair Production?
Now, let us understand what is pair production. Before we start with pair production, let us have a look at the what is annihilation process. Both annihilation and the pair production process explain the interaction of photons with matter.
Annihilation
Electron-positron annihilation occurs when an electron and a positron (the antiparticle of the electron) collide. The result of the collision is the conversion of the electron and positron and the creation of gamma-ray photons or, less often, other particles. The process must satisfy a number of conservation laws, including:
Conservation of charge. The net charge before and after is zero
Conservation of linear momentum and total energy This forbids the creation of a single gamma-ray.
Conservation of angular momentum.
So, now we will focus on what is pair production with the help of the annihilation process. When a gamma-ray photon interacts with any nucleus and it will lose its energy. Technically, pair production is a mode of interaction of gamma rays with the matter and during this process, they will result in loss of energy. During pair production, the energy of the incident photon will get converted into matter. The pair production can take place if and only if the energy of the photon is more than or equal to 102 MeV.
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As positron is a highly unstable particle and has a very short lifespan, it will recombine with an available electron in the surrounding. The combination of a positron (the antiparticle of the electron) and an electron will lead to the formation of -rays which are at an angle of 180° to each other. The overall energy of initial -rays would be distributed equally i.e. for example if the original energy were 1.02 MeV then the two -rays (formed after the combination of the Positron and Electron) which are at an angle of 180° to each other would have 0.51 MeV of energy each. Any additional energy available will be conserved as kinetic energy in the produced particles.
Therefore, the pair production reaction is given by:
⇒Y ⟶ e- + e+ ≃1.02 MeV
After understanding what is pair production we can note certain important facts about the pair production process as following:
The pair production interactions are ruled by three major types of the law of conservation, i.e., conservation of total energy, conservation of momentum, and finally the conservation of electric charge. Soon after the collision, a pair of electrons and a positron will be created.
In this collision, the antiparticle of an electron i.e., the positron (e+)as a particle, has the same physical properties which electron has, except its charge parity, these two particles, electron and positron have the opposite charge, and thus their magnetic momentum will also be of the opposite parity. Having an opposite charge parity means that the total sum of the net charge of pairs is zero, which is actually equal to the photon before the interaction. Therefore, the conservation of electric charge will be conserved and is evident.
The momentum in the pair production can be ignored because the atomic nucleus is thousands of times more massive than just a pair of electrons and positrons, and thus, the photon momentum can be absorbed. Thus, it is possible to predict that absorbing momentum occurs without absorbing much energy. So, it is can be represented by an equation that shows the conservation of total energy and is given by:
⇒hv = E+ + E- = (Total energy of positron) + (Total energy of electron)
⇒hv = (m0c2 + K-) + (m0c2 + K+)
⇒ hv = 2m0c2 + K- + K+………(2)
Where,
K+ -The kinetic energy of Positron
K- -The kinetic energy of the electron
Did You Know?
Do you know that the pair production can not take place in space!!!
Reason: The pair production can not take place in a vacuum or space. The pair production can happen only in the presence of an external object like an atomic nucleus which can experience some recoil during the collision process to conserve the energy and the momentum at the same time. Thus, the pair production can not take place in space or a vacuum, as the energy and the momentum can not be conserved at the same time.
FAQs on Pair Production
1. What is pair production in Physics?
Pair production is a phenomenon in which a high-energy photon, such as a gamma ray, interacts with the strong electric field of an atomic nucleus and converts its energy into matter. This results in the creation of an electron-positron pair (e⁻ and e⁺). The original photon disappears in the process, demonstrating the conversion of energy into mass as described by Einstein's equation, E=mc².
2. What is the minimum energy a photon must have for pair production to occur, and why is there a threshold?
A photon must have a minimum energy of 1.02 MeV (Mega-electron Volts) to cause pair production. This threshold exists because this is the exact amount of energy required to create the rest mass of both an electron and its antiparticle, the positron. According to the principle of mass-energy equivalence, the rest mass energy of each particle is 0.51 MeV, so creating the pair requires at least 0.51 + 0.51 = 1.02 MeV.
3. Why can't pair production happen in a vacuum or empty space?
Pair production cannot occur in a vacuum because it would violate the law of conservation of momentum. A photon has momentum, but if it were to transform into an electron-positron pair in empty space, it's impossible to conserve both energy and momentum simultaneously. The presence of a heavy nucleus is essential, as it recoils and absorbs the initial photon's momentum without taking a significant amount of its energy, allowing both physical laws to be satisfied.
4. How does pair production differ from the Compton effect?
The main differences between pair production and the Compton effect lie in the interaction and its outcome:
- Interaction: In pair production, a photon interacts with a nucleus and is completely absorbed. In the Compton effect, a photon collides with a loosely bound outer-shell electron and is scattered, not absorbed.
- Outcome: Pair production creates new particles (an electron-positron pair) from the photon's energy. The Compton effect results in the same photon existing with reduced energy and a recoiling electron.
- Energy Threshold: Pair production has a strict energy threshold of 1.02 MeV, while the Compton effect can occur at lower energies.
5. What happens to the energy if the incident photon has more than the 1.02 MeV threshold?
If an incident photon possesses energy greater than 1.02 MeV, the first 1.02 MeV is used to create the rest mass of the electron and positron. Any excess energy is converted directly into the kinetic energy of the newly created electron and positron, causing them to move away from the point of creation at high speeds. The distribution of this kinetic energy between the two particles is not necessarily equal.
6. What is the relationship between pair production and pair annihilation?
Pair production and pair annihilation are inverse processes. Pair production is the creation of a matter-antimatter pair (electron and positron) from energy (a photon). Conversely, pair annihilation occurs when a particle and its antiparticle (like an electron and positron) collide and are destroyed, converting their total mass and kinetic energy back into energy, typically in the form of two or more gamma-ray photons.
7. What is the role of the nucleus in the pair production process?
The nucleus plays a crucial, non-participatory role. Its primary function is to enable the conservation of momentum. As a massive body, the nucleus can recoil and absorb the momentum of the incident photon without gaining a significant amount of kinetic energy. This allows the photon's energy to be almost entirely converted into the mass and kinetic energy of the new particle pair, fulfilling the requirements of both energy and momentum conservation.
8. What is the formula representing the energy conservation in pair production?
The energy conservation in pair production is described by the equation: hv = (m₀c² + K⁻) + (m₀c² + K⁺). In this formula:
- hv represents the energy of the incident photon.
- m₀c² is the rest mass energy of an electron (or positron), which is 0.51 MeV.
- K⁻ and K⁺ are the kinetic energies of the created electron and positron, respectively.
The equation can be simplified to hv = 2m₀c² + K_total.
