Annihilation and Creation of Particle-Antiparticle Pairs

In physics, the term “annihilation” was adopted for the process in which a particle and its corresponding antiparticle are converted into electromagnetic radiation (photons) or into other particles (quanta of a physical field of another nature). Pair creation is the opposite process, in which a particle and an antiparticle evolve simultaneously as a result of interacting electromagnetic or other fields. For example, in the collision of an electron and its antiparticle—the positron—both can disappear, generating two photons (gamma quanta). The collision of a proton and an antiproton can lead to their interannihilation, which is accompanied by the simultaneous appearance of several much lighter particles, quanta of the nuclear field—pi-mesons. A gamma quantum, if it possesses sufficiently high energy, can, interacting with the electric field of the atomic nucleus, produce an electron-positron pair. Thus the question is not about the destruction or spontaneous evolution of matter but about the interconversion of particles. These interconversions are controlled by the fundamental laws of conservation, such as the laws of conservation of energy and of momentum, of angular momentum, of electrical charge, of the number of leptons and of the number of baryons. The possibility of pair annihilation and creation, as well as the very existence of antiparticles, was theoretically predicted in 1930 by the English physicist P. Dirac; the existence of antiparticles followed from the theory of the electron developed by Dirac. In 1932 the American physicist C. Anderson experimentally proved the existence of positrons in cosmic rays. In 1933, Irène and Frédéric Joliot-Curie, using a Wilson chamber in a magnetic field, observed the creation of electron-positron pairs by gamma quanta from a radioactive source. In the same year, cases of electron-positron pair annihilation were reliably recorded.

Contemporary interpretation of pair annihilation and creation is given in the quantum theory of fields.

The discovery of pair annihilation and creation is of deep interest not only in physics. It has important philosophical significance. For the first time in the history of natural science, it has been proven that indivisible particles—the ultimate “building-blocks of the universe”—from which all material objects are formed do not exist, as was thought until the 1930’s. Any form of matter can be transformed into other forms.

Annihilation of an electron-positron pair. Colliding with matter, a positron loses nearly all of its velocity as a result of the loss of energy in ionizing the atoms. Therefore, immediately before annihilation, the positron can be considered to be at rest—that is, the positron and the electron that is “doomed to destruction” are most likely found in a state in which the angular momentum (relative) of the particles is equal to 0. The subsequent fate of the pair is determined by the mutual orientation of the intrinsic angular momentum of the particles—their spins. If the spins of the electron and the positron (which are equal to 1/2) are directed in opposite directions (that is, the sum of the spins is equal to 0), then only an even number of photons will be formed as a result of annihilation; creation of an odd number of photons is prohibited by the law of conservation of so-called charge parity. However, the probability of annihilation with the evolution of four or more photons is negligibly small, and the overwhelming majority of pairs annihilate generating two photons. These photons fly in opposite directions, each of them acquiring half of the initial energy of the electron-positron system—that is, approximately the electron’s rest energy mc² = 0.51 MeV, where m is the mass of the electron and c is the velocity of light in a vacuum. In accordance with A. Einstein’s theory of relativity, a particle at rest with a mass M has an energy E₀ = Mc², which is called its rest energy.

If before annihilation the spins of the electron and positron are parallel, so that their total spin is equal to 1, then it is possible to form only an odd number of particles, usually three photons; annihilation of free electrons and positrons with the emission of one photon is prohibited by the law of conservation of momentum. Three-photon annihilation is a much rarer occurrence than two-photon annihilation; on the average, only two or three positrons per thousand colliding with matter annihilate into three photons.

A small percentage of positrons “succeed” in annihilating while maintaining a sufficiently high velocity. Moreover, the angle of emergence of the photons depends on this velocity. When the annihilating positrons have high energies, the emerging photons are emitted mostly in forward and backward directions with respect to the motion of the positron. The photon that flies ahead carries away almost all of the positron’s energy, while the photon that flies in the opposite direction acquires only the energy approximately equal to the electron’s rest energy mc². Thus, the transit of fast positrons through matter forms a beam of high-energy gamma quanta that fly in one direction. This can be used for obtaining monochromatic beams of high-energy photons.

In matter, positrons “live” a very short time. In typical solids, during the course of about 10^-10 second—negligible from the usual point of view of time intervals—the process of annihilation destroys more than two-thirds of all positrons that occur in the substance. The positron is a stable particle (it does not decay) and can exist infinitely long in a vacuum.

Frequently, especially in gases, annihilation passes through an intermediate stage—the formation of a short-lived system, a positronium—that is, a bound state of the electron and positron.

Creation of an electron-positron pair. Development of the opposite process of annihilation—creation of an electron-positron pair by photons—requires the presence of an external electromagnetic field (or a second photon), since, according to the laws of conservation of momentum and energy, a single free photon cannot be transformed into a particle-antiparticle pair. Usually, the formation of an electron-positron pair by a photon takes place in the Coulomb field of an atomic nucleus (or an electron). To accomplish such a reaction, the photon’s energy must not be less than the sum of the electron and positron rest masses—that is, 2mc² = 1.02 MeV. The probability of creating a pair in the Coulomb field of a nucleus is proportional to the square of the charge of the nucleus (or the atomic number) Z²; it grows rapidly with increasing gamma-quantum energy, approaching some finite value at very high energies.

The formation of an electron-positron pair plays a decisive role in the absorption of high-energy gamma quanta by matter and further, together with bremsstrahlung, in the generation of so-called electron-photon showers of cosmic rays.

Annihilation and creation of other particle pairs. If the energy of a photon is very high, then it can generate other types of particle-antiparticle pairs—for instance, a pair of muons. A pair of strongly interacting particles—for example, a proton-antiproton pair—is formed through the collisions of very fast protons with nucleons—that is, protons and neutrons—of the atomic nucleus.

In the annihilation of nucleons with antinucleons there is also a much more frequent evolution not of gamma-quanta but of massive particles the occurrence of which is not prohibited by the laws of conservation. As a rule, annihilation of such pairs occurs with the formation of four or five pi-mesons.

The processes of pair annihilation and creation have found application in scientific research. Thus, the distribution of the angles of emergence of the photons that arise through annihilation helps to determine the velocity distribution of electrons in a metal, since the probability of annihilation of a positron in matter greatly depends on the relative velocity of the positron and the electron involved in thermal motion. Knowledge of this distribution is necessary, for example, in calculating the specific heat of metals at very low temperatures. Another example: from the creation of an electron-positron pair it is possible to obtain information about the high-energy photons formed in the reactions. A photon, like every other uncharged particle, can never be directly observed, since it does not leave an observable track in particle detectors, such as a Wilson chamber, a bubble chamber, a nuclear photographic emulsion, or other devices. Its energy, momentum, and even the very fact of its formation can be determined only through the pair it creates and, for a photon of smaller energy, through emission of a Compton recoil electron.