KAHIBARO
Table of Contents
When a Particle Meets Its Antiparticle
Annihilation is the process in which a particle and its antiparticle meet and disappear as separate matter objects, converting their mass and motion into other particles. Most often, the final products are photons, but other particle pairs can also be produced if energy and conservation laws allow it.
A classic example is electron-positron annihilation. An electron, $e^-$, and a positron, $e^+$, are antiparticles of each other. When they come together, they can annihilate and produce gamma ray photons:
$$
e^- + e^+ \to \gamma + \gamma
$$
This does not mean that energy vanishes. Instead, the rest mass energy and any kinetic energy are transformed into the energy of the outgoing particles.
Annihilation does not destroy energy or momentum. It converts the particle and antiparticle into other forms of energy and matter while obeying all conservation laws.
Energy in Annihilation
Each particle has rest energy given by Einstein’s relation:
$$
E_0 = mc^2
$$
For an electron or positron,
$$
m_e c^2 = 0.511 \, \text{MeV}
$$
So if an electron and positron annihilate while essentially at rest, the total available energy is
$$
E_{\text{total}} = 2 m_e c^2 = 1.022 \, \text{MeV}
$$
This energy appears in the outgoing photons. In the simplest case, two photons are produced, each with energy
$$
E_\gamma = 0.511 \, \text{MeV}
$$
if the initial pair had no kinetic energy.
For electron-positron annihilation at rest,
$$
e^- + e^+ \to 2\gamma
$$
and each photon carries
$$
0.511 \, \text{MeV}
$$
of energy.
If the electron and positron are moving before annihilation, then their kinetic energy also contributes. The photons or other final particles then carry more than just the rest energy.
Why Two Photons Are Common
A single photon cannot usually be the final product when an electron and positron annihilate in empty space. The reason is conservation of momentum. If the initial electron and positron are at rest together, the total momentum is zero. A single photon always has momentum, so one photon alone cannot satisfy both energy and momentum conservation.
Two photons can solve this. They move in opposite directions with equal momentum, so the total momentum remains zero.
In the special case where the pair is exactly at rest before annihilation, the two photons go in opposite directions, back to back.
Conservation Laws in Annihilation
Annihilation must obey the same conservation laws as every other particle interaction. The most important ones here are energy, momentum, and electric charge.
For electron-positron annihilation,
$$
e^- + e^+ \to \gamma + \gamma
$$
the initial electric charge is
$$
(-1) + (+1) = 0
$$
and photons have zero charge, so charge is conserved.
The total lepton number is also zero at the start, because the electron has lepton number $+1$ and the positron has $-1$. The final photons have lepton number $0$, so this is also consistent.
The same idea applies to other annihilation reactions. The final state must match all conserved quantities of the initial state.
In any annihilation process, always check conservation of energy, momentum, charge, and all relevant quantum numbers.
Other Annihilation Outcomes
Although two-photon annihilation is the simplest and most famous case, it is not the only possibility. If enough energy is available, a particle-antiparticle pair can annihilate into other particles.
For example, a proton and antiproton can annihilate into several mesons:
$$
p + \bar{p} \to \pi^+ + \pi^- + \pi^0 + \cdots
$$
This happens because protons are much more massive than electrons, so much more energy is available. The annihilation products are often several particles rather than just two photons.
Electron-positron annihilation at high energy can also produce heavier pairs, such as
$$
e^- + e^+ \to \mu^- + \mu^+
$$
if the total energy is large enough.
This shows an important idea. The matter and antimatter do not need to turn only into light. They can turn into any allowed set of particles whose total energy and quantum numbers match the initial state.
Matter to Radiation
Annihilation is one of the clearest demonstrations that mass can be converted into radiation. In everyday chemistry, only tiny fractions of energy are exchanged compared with rest mass energy. In annihilation, the conversion is much more direct.
This is why antimatter is associated with very large energy release per unit mass. If a mass $m$ of matter annihilates with a mass $m$ of antimatter, the total energy released is
$$
E = 2mc^2
$$
For example, if $1 \, \text{g}$ of matter annihilates with $1 \, \text{g}$ of antimatter, then the total mass converted is
$$
2 \times 10^{-3} \, \text{kg}
$$
and the energy is
$$
E = 2 \times 10^{-3} \times (3.0 \times 10^8)^2
$$
$$
E = 1.8 \times 10^{14} \, \text{J}
$$
This is an enormous amount of energy.
If equal masses of matter and antimatter annihilate completely,
$$
E = 2mc^2
$$
where $m$ is the mass of either one alone.
Annihilation Compared with Pair Production
Annihilation is closely related to pair production, but in reverse. In pair production, enough energy is converted into a particle and an antiparticle. In annihilation, a particle and antiparticle convert into radiation or other particles.
These two processes reflect the same deep principle, mass and energy are interchangeable when conservation laws are satisfied.
| Process | Example | Main idea |
|---|---|---|
| Annihilation | $e^- + e^+ \to \gamma + \gamma$ | Matter and antimatter convert into radiation |
| Pair production | $\gamma \to e^- + e^+$, in the presence of a nucleus | Radiation converts into matter and antimatter |
Practical Importance
Annihilation is not just a theoretical idea. It appears in experiments and applications. Positron emission tomography, often called PET, uses positrons produced by radioactive decay. When a positron meets an electron in the body, they annihilate and emit two gamma photons moving in nearly opposite directions. Detecting these photons helps form medical images.
In particle physics, electron-positron colliders are also important. They allow controlled annihilation events that can produce new particles, making them powerful tools for studying fundamental interactions.
Summary Idea
Annihilation happens when a particle meets its antiparticle and they convert into other particles, often photons. The process is governed by conservation laws, especially energy and momentum. For an electron and positron at rest, the usual result is two gamma photons, each with energy $0.511 \, \text{MeV}$. Annihilation is one of the most direct examples of mass becoming energy.