WordNet

form a pair or pairs; "The two old friends paired off" (同)pair off, partner off, couple
a set of two similar things considered as a unit (同)brace
a poker hand with 2 cards of the same value
two people considered as a unit
arrange in pairs; "Pair these numbers" (同)geminate
occur in pairs (同)geminate
(economics) manufacturing or mining or growing something (usually in large quantities) for sale; "he introduced more efficient methods of production"
(law) the act of exhibiting in a court of law; "the appellate court demanded the production of all documents"
the act or process of producing something; "Shakespeares production of poetry was enormous"; "the production of white blood cells"
the creation of value or wealth by producing goods and services
a display that is exaggerated or unduly complicated; "she tends to make a big production out of nothing"
a presentation for the stage or screen or radio or television; "have you seen the new production of Hamlet?"
the act of grouping things or people in pairs
mated sexually

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(二つで一つに用いられる物の)『組』,『対』《+『of』+『名』》 / (対になる部分からなる物の)『1個』《+『of』+『名』》 / 《集合的に》《複数扱い》夫婦,婚約中の男女;(動物の)つがい《+『of』+『名』》 / 《集合的に》《複数扱い》(同種または何かの関係のある物の)二人(二つ,2頭など)の組《+『of』+『名』》 / …‘を'二人(2個)ずつ組にする《+『名』+『off』(『up』),+『off』(『up』)+『名』》,(…と)…‘を'組にする《+『名』+『with』+『名』》 / (…と)…‘を'結婚させる《+『名』+[『up』]『with』+『名』》 / 二人(2個)ずつ組になる《+『off』(『up』)》
〈U〉(…を)『生み出すこと』,(…の)『生産』,産出,製造《+『of』+『名』》 / 〈U〉『生産高』,産出額(量) / 〈C〉『産物』,製品 / 〈U〉(…の)提出,提示《+『of』+『名』》 / 〈C〉(劇・映画などの)製作;(文学などの)作品
とうちゃん(papa)

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/02/05 14:42:23」(JST)

wiki en

Pair production refers to the creation of an elementary particle and its antiparticle, usually when a photon (or another neutral boson) interacts with a nucleus or another boson. For example an electron and its antiparticle, the positron, may be created. This is allowed, provided there is enough energy available to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and momentum to be conserved. Other pairs produced could be a muon and anti-muon or a tau and anti-tau. However all other conserved quantum numbers (angular momentum, electric charge, 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 of +1 then another one must have strangeness of −1. The probability of pair production in photon-matter interactions increases with increasing photon energy and also increases with atomic number approximately as Z².

Examples[edit]

γ + γ → e− + e+

In nuclear physics, this occurs when a high-energy photon interacts with a nucleus. The energy of this photon can be converted into mass through Einstein’s equation, $E = mc 2$ ; where $E$ is energy, $m$ is mass and $c$ is the speed of light. The photon must have enough energy to create the mass of an electron plus a positron. The rest mass of an electron is 9.11 × 10⁻³¹ kg (0.511 MeV), the same as a positron. Without a nucleus to absorb momentum, a photon decaying into electron-positron pair (or other pairs for that matter) can never conserve energy and momentum simultaneously.^[1]

Photon–nucleus interaction[edit]

There are different processes how an electron-positron pair can be produced. In air (e.g. in lightning discharges) the most important one is the scattering of photons at the nuclei of atoms or molecules. Quantum mechanically, the process of pair production can be described by the quadruply differential cross section:^[2]

$\begin{align} d^4\sigma &= \frac{Z^2\alpha_{fine}^3c^2}{(2\pi)^2\hbar}|\mathbf{p}_+||\mathbf{p}_-| \frac{dE_+}{\omega^3}\frac{d\Omega_+ d\Omega_- d\Phi}{|\mathbf{q}|^4}\times \\ &\times\left[- \frac{\mathbf{p}_-^2\sin^2\Theta_-}{(E_--c|\mathbf{p}_-|\cos\Theta_-)^2}\left (4E_+^2-c^2\mathbf{q}^2\right)\right.\\ &-\frac{\mathbf{p}_+^2\sin^2\Theta_+}{(E_+-c|\mathbf{p}_+|\cos\Theta_+)^2}\left (4E_-^2-c^2\mathbf{q}^2\right) \\ &+2\hbar^2\omega^2\frac{\mathbf{p}_+^2\sin^2\Theta_++\mathbf{p}_-^2\sin^2\Theta_-}{(E_+-c|\mathbf{p}_+|\cos\Theta_+)(E_--c|\mathbf{p}_-|\cos\Theta_-)} \\ &+2\left.\frac{|\mathbf{p}_+||\mathbf{p}_-|\sin\Theta_+\sin\Theta_-\cos\Phi}{(E_+-c|\mathbf{p}_+|\cos\Theta_+)(E_--c|\mathbf{p}_-|\cos\Theta_-)}\left(2E_+^2+2E_-^2-c^2\mathbf{q}^2\right)\right]. \\ \end{align}$

with

$\begin{align} d\Omega_+&=\sin\Theta_+\ d\Theta_+,\\ d\Omega_-&=\sin\Theta_-\ d\Theta_-. \end{align}$

This expression can be derived by using a quantum mechanical symmetry between pair production and Bremsstrahlung.
is the atomic number, the fine structure constant, the reduced Planck's constant and the speed of light. The kinetic energies of the positron and electron relate to their total energies and momenta via

$E_{+,-}=E_{kin,+/-}+m_e c^2=\sqrt{m_e^2 c^4+\mathbf{p}_{+,-}^2 c^2}.$

Conservation of energy yields

$\hbar\omega=E_{+}+E_{-}.$

The momentum of the virtual photon between incident photon and nucleus is:

$\begin{align} -\mathbf{q}^2&=-|\mathbf{p}_+|^2-|\mathbf{p}_-|^2-\left(\frac{\hbar}{c}\omega\right)^2+2|\mathbf{p}_+|\frac{\hbar}{c} \omega\cos\Theta_+ +2|\mathbf{p}_-|\frac{\hbar}{c} \omega\cos\Theta_- \\ &-2|\mathbf{p}_+||\mathbf{p}_-|(\cos\Theta_+\cos\Theta_-+\sin\Theta_+\sin\Theta_-\cos\Phi), \end{align}$

where the directions are given via:

$\begin{align} \Theta_+&=\sphericalangle(\mathbf{p}_+,\mathbf{k}),\\ \Theta_-&=\sphericalangle(\mathbf{p}_-,\mathbf{k}),\\ \Phi&=\text{Angle between the planes } (\mathbf{p}_+,\mathbf{k}) \text{ and } (\mathbf{p}_-,\mathbf{k}), \end{align}$

where is the momentum of the incident photon.

In order to analyse the relation between the photon energy and the emission angle between photon and positron, Köhn and Ebert integrated ^[3] the quadruply differential cross section over and . The double differential cross section is:

$\begin{align} \frac{d^2\sigma (E_+,\omega,\Theta_+)}{dE_+d\Omega_+} = \sum\limits_{j=1}^{6} I_j \end{align}$

with

$\begin{align} I_1&=\frac{2\pi A}{\sqrt{(\Delta^{(p)}_2)^2+4p_+^2p_-^2\sin^2\Theta_+}} \\ &\times \ln\left(\frac{(\Delta^{(p)}_2)^2+4p_+^2p_-^2\sin^2\Theta_+-\sqrt{(\Delta^{(p)}_2)^2+4p_+^2p_-^2\sin^2 \Theta_+}(\Delta^{(p)}_1+\Delta^{(p)}_2)+\Delta^{(p)}_1\Delta^{(p)}_2}{-(\Delta^{(p)}_2) ^2-4p_+^2p_-^2\sin^2\Theta_+ -\sqrt{(\Delta^{(p)}_2)^2+4p_+^2p_-^2\sin^2 \Theta_+}(\Delta^{(p)}_1-\Delta^{(p)}_2)+\Delta^{(p)}_1\Delta^{(p)}_2 }\right) \\ &\times\left[-1-\frac{c\Delta^{(p)}_2}{p_-(E_+-cp_+\cos\Theta_+)}+\frac{p_+^2c^2\sin^2\Theta_+} {(E_+-cp_+\cos\Theta_+)^2}-\frac{2\hbar^2\omega^2p_-\Delta^{(p)}_2}{c(E_+-cp_+\cos \Theta_+)((\Delta^{(p)}_2)^2+4p_+^2p_-^2\sin^2\Theta_+)}\right], \\ I_2&=\frac{2\pi Ac}{p_-(E_+-cp_+\cos\Theta_+)}\ln\left( \frac{E_-+p_-c}{E_--p_-c}\right), \\ I_3&=\frac{2\pi A}{\sqrt{(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+ }} \\ &\times\ln\Bigg(\Big((E_-+p_-c)(4p_+^2p_-^2\sin^2\Theta_+(E_--p_-c)+(\Delta^{(p)}_1+\Delta^{(p)}_2) ((\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c) \\ &-\sqrt{(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+}))\Big)\Big((E_--p_-c) (4p_+^2p_-^2\sin^2\Theta_+(-E_--p_-c) \\ &+(\Delta^{(p)}_1-\Delta^{(p)}_2) ((\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)-\sqrt{(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+}))\Big)^{-1}\Bigg) \\ &\times\left[\frac{c(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)}{p_-(E_+-cp_+\cos\Theta_+)}\right.\\ &+\Big[((\Delta^{(p)}_2)^2+4p_+^2p_-^2\sin^2\Theta_+)(E_-^3+E_-p_-c)+p_-c(2 ((\Delta^{(p)}_1)^2-4p_+^2p_-^2\sin^2\Theta_+)E_-p_-c \\ &+\Delta^{(p)}_1\Delta^{(p)}_2(3E_-^2+p_-^2c^2))\Big]\Big[(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+\Big]^{-1} \\ &+\Big[-8p_+^2p_-^2m^2c^4\sin^2\Theta_+(E_+^2+E_-^2)-2\hbar^2\omega^2p_+^2\sin^2\Theta_+p_-c(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c) \\ &+2\hbar^2\omega^2p_- m^2c^3(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)\Big] \Big[(E_+-cp_+\cos\Theta_+)((\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+)\Big]^{-1} \\ &+\left.\frac{4E_+^2p_-^2(2(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2-4m^2c^4p_+^2p_-^2\sin^2\Theta_+)(\Delta^{(p)}_1E_-+\Delta^{(p)}_2p_-c)}{((\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+)^2}\right], \\ I_4&=\frac{4\pi Ap_-c(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)}{(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+}+\frac{16\pi E_+^2p_-^2 A(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2}{((\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+)^2}, \\ I_5&=\frac{4\pi A}{(-(\Delta^{(p)}_2)^2+(\Delta^{(p)}_1)^2-4p_+^2p_-^2\sin^2\Theta_+) ((\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+)} \\ &\times\left[\frac{\hbar^2\omega^2p_-^2}{E_+cp_+\cos\Theta_+} \Big[E_-[2(\Delta^{(p)}_2)^2((\Delta^{(p)}_2)^2-(\Delta^{(p)}_1)^2)+8p_+^2p_-^2\sin^2\Theta_+((\Delta^{(p)}_2)^2+(\Delta^{(p)}_1)^2)] \right.\\ &+p_-c[2\Delta^{(p)}_1\Delta^{(p)}_2((\Delta^{(p)}_2)^2-(\Delta^{(p)}_1)^2)+16\Delta^{(p)}_1\Delta^{(p)}_2p_+^2p_-^2\sin^2\Theta_+]\Big]\Big[(\Delta^{(p)}_2)^2+4p_+^2p_-^2\sin^2\Theta_+\Big]^{-1}\\ &+ \frac{2\hbar^2\omega^2 p_{+}^2 \sin^2\Theta_+(2\Delta^{(p)}_1\Delta^{(p)}_2 p_-c+2(\Delta^{(p)}_2)^2E_-+8p_+^2p_-^2\sin^2\Theta_+ E_-)}{E_+-cp_+\cos\Theta_+}\\ &-\Big[2E_+^2p_-^2\{2((\Delta^{(p)}_2)^2-(\Delta^{(p)}_1)^2)(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2 +8p_+^2p_-^2\sin^2\Theta_+[((\Delta^{(p)}_1)^2+(\Delta^{(p)}_2)^2)(E_-^2+p_-^2c^2)\\ &+4\Delta^{(p)}_1\Delta^{(p)}_2E_-p_-c]\}\Big]\Big[(\Delta^{(p)}_2E_-+\Delta^{(p)}_1p_-c)^2+4m^2c^4p_+^2p_-^2\sin^2\Theta_+\Big]^{-1}\\ &-\left.\frac{8p_+^2p_-^2\sin^2\Theta_+(E_+^2+E_-^2)(\Delta^{(p)}_2p_-c +\Delta^{(p)}_1 E_-)}{E_+-cp_+\cos\Theta_+}\right], \\ I_6&=-\frac{16\pi E_-^2p_+^2\sin^2\Theta_+ A}{(E_+-cp_+\cos\Theta_+)^2 (-(\Delta^{(p)}_2)^2+(\Delta^{(p)}_1)^2-4p_+^2p_-^2\sin^2\Theta_+)} \end{align}$

and

$\begin{align} A&=\frac{Z^2\alpha_{fine}^3c^2}{(2\pi)^2\hbar}\frac{|\mathbf{p}_+||\mathbf{p}_-|}{\omega^3},\\ \Delta^{(p)}_1&:=-|\mathbf{p}_+|^2-|\mathbf{p}_-|^2-\left(\frac{\hbar}{c}\omega\right) + 2\frac{\hbar}{c}\omega|\mathbf{p}_+|\cos\Theta_+,\\ \Delta^{(p)}_2&:=2\frac{\hbar}{c}\omega|\mathbf{p}_i|-2|\mathbf{p}_+||\mathbf{p}_-| \cos\Theta_+ + 2. \end{align}$

This cross section can be applied in Monte Carlo simulations. An analysis of this expression shows that positrons are mainly emitted in the direction of the incident photon.

Energy[edit]

Photon-nucleus pair production can only occur if the photons have an energy exceeding twice the rest energy ( $m e c 2$ ) of an electron (1.022 MeV). These interactions were first observed in Patrick Blackett's counter-controlled cloud chamber, leading to the 1948 Nobel Prize in Physics. The same conservation laws apply for the generation of other higher energy particles such as the muon and tau.

In semiclassical general relativity, pair production was invoked to predict hypothetical Hawking radiation. According to quantum mechanics, particle pairs are constantly appearing and disappearing as a quantum foam. In a region of strong gravitational tidal forces, 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, 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 type of stellar explosion, where pair production suddenly lowers the pressure inside a supergiant star, leading to a partial implosion, and then explosive thermonuclear burning. Supernova SN 2006gy is hypothesized to have been a pair production type supernova.

In 2008 the Titan laser aimed at a 1-millimeter-thick gold target was used to generate positron–electron pairs in large numbers.^[4]

References[edit]

^ Hubbell, J. H. (June 2006). "Electron positron pair production by photons: A historical overview". Radiation Physics and Chemistry 75 (6): 614–623. Bibcode:2006RaPC...75..614H. doi:10.1016/j.radphyschem.2005.10.008.
^ Bethe, H.A., Heitler, W., 1934. On the stopping of fast particles and on the creation of positive electrons. Proc. Phys. Soc. Lond. 146, 83–112
^ Koehn, C., Ebert, U., Angular distribution of Bremsstrahlung photons and of positrons for calculations of terrestrial gamma-ray flashes and positron beams, Atmos. Res. (2013), http://dx.doi.org/10.1016/j.atmosres.2013.03.012
^ "Laser technique produces bevy of antimatter". MSNBC. 2008. Retrieved 2008-12-04. "The LLNL scientists created the positrons by shooting the lab's high-powered Titan laser onto a one-millimeter-thick piece of gold."

External links[edit]

Theory of photon-impact bound-free pair production

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