Annihilation

A Feynman diagram showing the mutual annihilation of a bound state electron positron pair into two photons. This bound state is more commonly known as positronium.

Annihilation is defined as "total destruction" or "complete obliteration" of an object;^[1] having its root in the Latin nihil (nothing). A literal translation is "to make into nothing".

In physics, the word is used to denote the process that occurs when a subatomic particle collides with its respective antiparticle, such as an electron colliding with a positron.^[2] Energy and momentum are conserved, and the annihilated particles are replaced by photons, electromagnetic wave quanta with zero rest mass. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed. When a particle and its antiparticle collide, their energy is converted into a force carrier particle, such as a gluon, W/Z force carrier particle, or a photon. These particles are afterwards transformed into other particles.^[3]

During a low-energy annihilation, photon production is favored, since these particles have no mass. However, high-energy particle colliders produce annihilations where a wide variety of exotic heavy particles are created.

This is an example of renormalization in quantum field theory— the field theory being necessary because the number of particles changes from one to two and back again.

Examples of annihilation

Electron–positron annihilation

e− + e+ → γ + γ

When a low-energy electron annihilates a low-energy positron (antielectron), they can only produce two or more gamma ray photons, since the electron and positron do not carry enough mass-energy to produce heavier particles, and conservation of energy and linear momentum forbid the creation of only one photon. When an electron and a positron collide to annihilate and create gamma rays, energy is given off. Both particles have a rest energy of 0.511 mega electron volts (MeV). When the mass of the two particles is converted entirely into energy, this rest energy is what is given off. The energy is given off in the form of the aforementioned gamma rays. Each of the gamma rays has an energy of 0.511 MeV. Since the positron and electron are both briefly at rest during this annihilation, the system has no momentum during that moment. This is the reason that two gamma rays are created. Conservation of momentum would not be achieved if only one photon was created in this particular reaction. Momentum and energy are both conserved with 1.022 MeV of gamma rays (accounting for the rest energy of the particles) moving in opposite directions (accounting for the total zero momentum of the system).^[4] However, if one or both particles carry a larger amount of kinetic energy, various other particle pairs can be produced. The annihilation (or decay) of an electron-positron pair into a single photon cannot occur in free space because momentum and energy cannot both be conserved in this process. The reverse reaction is also impossible for this reason, except in the presence of another particle that can carry away the excess momentum. However, in quantum field theory this process is allowed as an intermediate quantum state. Some authors justify this by saying that the photon exists for a time which is short enough that the violation of conservation of momentum can be accommodated by the uncertainty principle. Others choose to assign the intermediate photon a non-zero mass. (The mathematics of the theory are unaffected by which view is taken.) This opens the way for virtual pair production or annihilation in which a one-particle quantum state may fluctuate into a two-particle state and back again (coherent superposition). These processes are important in the vacuum state and renormalization of a quantum field theory. It also allows neutral particle mixing through processes such as the one pictured here.

Proton-antiproton annihilation

When a proton encounters its antiparticle (and more generally, if any species of baryon encounters any species of antibaryon), the reaction is not as simple as electron-positron annihilation. Unlike an electron, a proton is a composite particle consisting of three "valence quarks" and an indeterminate number of "sea quarks" bound by gluons. Thus, when a proton encounters an antiproton, one of its constituent valence quarks may annihilate with an antiquark, while the remaining quarks and antiquarks will undergo rearrangement into a number of mesons (mostly pions and kaons), which will fly away from the annihilation point. The newly created mesons are unstable, and will decay in a series of reactions that ultimately produce nothing but gamma rays, electrons, positrons, and neutrinos. This type of reaction will occur between any baryon (particle consisting of three quarks) and any antibaryon (consisting of three antiquarks). Antiprotons can and do annihilate with neutrons, and likewise antineutrons can annihilate with protons, as discussed below.

Here are the specifics of the reaction that produces the mesons. Protons consist of two up quarks and one down quark, while antiprotons consist of two anti-ups and an anti-down. Similarly, neutrons consist of two down quarks and an up quark, while antineutrons consist of two anti-downs and an anti-up. The strong nuclear force provides a strong attraction between quarks and antiquarks, so when a proton and antiproton approach to within a distance where this force is operative (less than 1 fm), the quarks tend to pair up with the antiquarks, forming three pions. The energy released in this reaction is substantial, as the rest mass of three pions is much less than the mass of a proton and an antiproton. Energy may also be released by the direct annihilation of a quark with an antiquark. The extra energy can go to the kinetic energy of the released pions, be radiated as gamma rays, or into down or strange quarks. The other flavors of quarks are too massive to be created in this reaction, unless the incident antiproton has kinetic energy far exceeding its rest mass, i.e. is moving close to the speed of light. The newly created quarks and antiquarks pair into mesons, producing additional pions and kaons. Reactions in which proton-antiproton annihilation produces as many as nine mesons have been observed, while production of thirteen mesons is theoretically possible. The generated mesons leave the site of the annihilation at moderate fractions of the speed of light, and decay with whatever lifetime is appropriate for their type of meson.^[5]

Similar reactions will occur when an antinucleon annihilates within a more complex atomic nucleus, save that the resulting mesons, being strong-interacting, have a significant probability of being absorbed by one of the remaining "spectator" nucleons rather than escaping. Since the absorbed energy can be as much as ~2 GeV, it can in principle exceed the binding energy of even the heaviest nuclei. Thus, when an antiproton annihilates inside a heavy nucleus such as uranium or plutonium, partial or complete disruption of the nucleus can occur, releasing large numbers of fast neutrons.^[6] Such reactions open the possibility for triggering a significant number of secondary fission reactions in a subcritical mass, and may potentially be useful for spacecraft propulsion.

See also

• Pair production
• Creation and annihilation operators

References

Notations

• Kragh, H. (1999). Quantum Generations : A history of physics in the twentieth century. Princeton University Press. ISBN 0-691-01206-7. 

Footnotes