Pair Production
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Pair production is the creation of a
subatomic particle In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a pr ...
and its
antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
from a
neutral Neutral or neutrality may refer to: Mathematics and natural science Biology * Neutral organisms, in ecology, those that obey the unified neutral theory of biodiversity Chemistry and physics * Neutralization (chemistry), a chemical reaction in ...
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...
. Examples include creating an
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
and a
positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collides ...
, a
muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wi ...
and an
antimuon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wit ...
, or a
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
and an
antiproton The antiproton, , (pronounced ''p-bar'') is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived, since any collision with a proton will cause both particles to be annihilated in a burst of energy. The exis ...
. Pair production often refers specifically to a
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
creating an electron–positron pair near a nucleus. As energy must be conserved, for pair production to occur, the incoming
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
of the photon must be above a threshold of at least the total
rest mass energy Rest or REST may refer to: Relief from activity * Sleep ** Bed rest * Kneeling * Lying (position) * Sitting * Squatting position Structural support * Structural support ** Rest (cue sports) ** Armrest ** Headrest ** Footrest Arts and entertain ...
of the two particles created. (As the electron is the lightest, hence, lowest mass/energy, elementary particle, it requires the least energetic photons of all possible pair-production processes.) Conservation of energy and
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
are the principal constraints on the process. All other conserved quantum numbers (
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
,
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
,
lepton number In particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. Lepton number ...
) of the produced particles must sum to zero thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has
strangeness In particle physics, strangeness ("''S''") is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic interactions which occur in a short period of time. The strangeness of a parti ...
of +1 then another one must have strangeness of −1. The probability of pair production in photon–matter interactions increases with
photon energy Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, ...
and also increases approximately as the square of
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of (hence, number of protons in) the nearby atom.


Photon to electron and positron

For photons with high
photon energy Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, ...
(
MeV In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacu ...
scale and higher), pair production is the dominant mode of photon interaction with matter. These interactions were first observed in
Patrick Blackett Patrick Maynard Stuart Blackett, Baron Blackett (18 November 1897 – 13 July 1974) was a British experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism, winning the Nobel Prize for Physics in 1948. ...
's counter-controlled
cloud chamber A cloud chamber, also known as a Wilson cloud chamber, is a particle detector used for visualizing the passage of ionizing radiation. A cloud chamber consists of a sealed environment containing a supersaturated vapour of water or alcohol. An ...
, leading to the 1948
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
. If the photon is near an atomic nucleus, the energy of a photon can be converted into an electron–positron pair: (Z+) →  +  The photon's energy is converted to particle mass in accordance with Einstein's equation, ; where is
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
, is
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
and is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. The photon must have higher energy than the sum of the rest mass energies of an electron and positron (2 ⋅ 511 keV = 1.022 MeV, resulting in a photon-wavelength of 1.2132 picometer) for the production to occur. (Thus, pair production does not occur in medical X-ray imaging because these X-rays only contain ~150 keV.) The photon must be near a nucleus in order to satisfy conservation of momentum, as an electron–positron pair produced in free space cannot satisfy conservation of both energy and momentum. Because of this, when pair production occurs, the atomic nucleus receives some
recoil Recoil (often called knockback, kickback or simply kick) is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, as according to Newton's third law the force requ ...
. The reverse of this process is
electron–positron annihilation Electron–positron annihilation occurs when an electron () and a positron (, the electron's antiparticle) collide. At low energies, the result of the collision is the annihilation of the electron and positron, and the creation of energetic photo ...
.


Basic kinematics

These properties can be derived through the kinematics of the interaction. Using
four vector In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a ...
notation, the conservation of energy-momentum before and after the interaction gives: :p_\gamma = p_ + p_ + p_ where p_\text is the recoil of the nuclei. Note the modulus of the four vector :A \equiv (A^0,\mathbf) is: :A^2 = A^ A_ = - (A^0)^2 + \mathbf \cdot \mathbf which implies that (p_\gamma)^2 = 0 for all cases and (p_)^2 = -m_\text^2 c^2 . We can square the conservation equation: :(p_\gamma)^2 = (p_ + p_ + p_\text)^2 However, in most cases the recoil of the nuclei is much smaller compared to the energy of the photon and can be neglected. Taking this approximation of p_ \approx 0 to simplify and expanding the remaining relation: :(p_\gamma)^2 \approx (p_)^2 + 2 p_ p_ + (p_)^2 :-2\, m_\text^2 c^2 + 2 \left( -\frac + \mathbf_ \cdot \mathbf_ \right) \approx 0 :2\,(\gamma^2 - 1)\,m_\text^2\,c^2\,(\cos \theta_\text - 1) \approx 0 Therefore, this approximation can only be satisfied if the electron and positron are emitted in very nearly the same direction, that is, \theta_\text \approx 0 . This derivation is a semi-classical approximation. An exact derivation of the kinematics can be done taking into account the full
quantum mechanical scattering of photon and nucleus In pair production, a photon creates an electron positron pair. In the process of photons scattering in air (e.g. in lightning discharges), the most important interaction is the scattering of photons at the nuclei of atoms or molecules. The full ...
.


Energy transfer

The energy transfer to electron and positron in pair production interactions is given by: :(E_k^)_\text = h \nu - 2\, m_\text c^2 where h is Planck's constant, \nu is the frequency of the photon and the 2\, m_\text c^2 is the combined rest mass of the electron–positron. In general, ignoring the nuclei recoil, the electron and positron can be emitted with different kinetic energies, but the average transferred to each is: :(\bar E_k^)_\text = \frac (h \nu - 2\, m_\text c^2)


Cross section

The exact analytic form for the cross section of pair production must be calculated through
quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
in the form of
Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...
s and results in a complicated function. To simplify, the cross section can be written as: :\sigma = \alpha \, r_\text^2 \, Z^2 \, P(E,Z) where \alpha is the
fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between ele ...
, r_\text is the
classical electron radius The classical electron radius is a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic self-interaction energ ...
, Z is the
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of the material, and P(E,Z) is some complex-valued function that depends on the energy and atomic number. Cross sections are tabulated for different materials and energies. In 2008 the Titan laser, aimed at a 1 millimeter-thick
gold Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...
target, was used to generate positron–electron pairs in large numbers.


Astronomy

Pair production is invoked in the heuristic explanation of hypothetical
Hawking radiation Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical a ...
. According to
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, particle pairs are constantly appearing and disappearing as a
quantum foam Quantum foam or spacetime foam is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at these small scales, particles of matter and antimatter are constantly created and destroye ...
. In a region of strong gravitational
tidal forces The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
, the two particles in a pair may sometimes be wrenched apart before they have a chance to mutually annihilate. When this happens in the region around a
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
, one particle may escape while its antiparticle partner is captured by the black hole. Pair production is also the mechanism behind the hypothesized
pair-instability supernova A pair-instability supernova is a type of supernova predicted to occur when pair production, the production of free electrons and positrons in the collision between atomic nuclei and energetic gamma rays, temporarily reduces the internal radiatio ...
type of stellar explosion, where pair production suddenly lowers the pressure inside a
supergiant star Supergiants are among the most massive and most luminous stars. Supergiant stars occupy the top region of the Hertzsprung–Russell diagram with absolute visual magnitudes between about −3 and −8. The temperature range of supergiant stars s ...
, leading to a partial implosion, and then explosive thermonuclear burning.
Supernova A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or when ...
SN 2006gy SN 2006gy was an extremely energetic supernova, also referred to as a hypernova or quark-nova, that was discovered on September 18, 2006. It was first observed by Robert Quimby and P. Mondol,
is hypothesized to have been a pair production type supernova.


See also

* Breit–Wheeler process *
Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac par ...
*
Matter creation Even restricting the discussion to physics, scientists do not have a unique definition of what matter is. In the currently known particle physics, summarised by the standard model of elementary particles and interactions, it is possible to distin ...
* Meitner–Hupfeld effect *
Landau–Pomeranchuk–Migdal effect In high-energy physics, the Landau–Pomeranchuk–Migdal effect, also known as the Landau–Pomeranchuk effect and the Pomeranchuk effect, or simply LPM effect, is a reduction of the bremsstrahlung and pair production cross sections at high energi ...
*
Two-photon physics Two-photon physics, also called gamma–gamma physics, is a branch of particle physics that describes the interactions between two photons. Normally, beams of light pass through each other unperturbed. Inside an optical material, and if the intens ...


References


External links


Theory of photon-impact bound-free pair production
{{DEFAULTSORT:Pair Production Particle physics Nuclear physics