Pair production is the creation of a subatomic particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production refers to a photon creating an electron–positron pair near a nucleus. For pair production to occur, the incoming energy of the interaction must be above a threshold of at least the total rest mass energy of the two particles, the situation must conserve both energy and momentum. However, all other conserved quantum numbers 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 another one must have strangeness of −1; the probability of pair production in photon–matter interactions increases with photon energy and increases as the square of atomic number of the nearby atom. For photons with high photon energy, pair production is the dominant mode of photon interaction with matter.
These interactions were first observed in Patrick Blackett's counter-controlled cloud chamber, leading to the 1948 Nobel Prize in Physics. If the photon is near an atomic nucleus, the energy of a photon can be converted into an electron–positron pair: γ → e− + e+The photon's energy is converted to particle mass in accordance with Einstein’s equation, E = m ⋅ c2; the photon must have higher energy than the sum of the rest mass energies of an electron and positron for the production to occur. The photon must be near a nucleus in order to satisfy conservation of momentum, as an electron–positron pair produced in free space cannot both satisfy conservation of energy and momentum; because of this, when pair production occurs, the atomic nucleus receives some recoil. The reverse of this process is electron positron annihilation; these properties can be derived through the kinematics of the interaction. Using four vector notation, the conservation of energy-momentum before and after the interaction gives: p γ = p e − + p e + + p R where p R is the recoil of the nuclei.
Note the modulus of the four vector A = is: A 2 = A μ A μ = − 2 + A ⋅ A which implies that 2 = 0 for all cases and 2 = − m e 2 c 2. We can square the conservation equation: 2 = 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 R ≈ 0 to simplify and expanding the remaining relation: 2 ≈ 2 + 2 p e − p e + + 2 − 2 m e 2 c 2 + 2 ≈ 0 2 m e 2 c 2 ≈ 0 Therefore, this approximation can only be satisfied if the electron and positron are emitted in nearly the same direction, that is, θ e ≈ 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; the energy transfer to electron and positron in pair production interactions is given by: ( E
The Paraíba State University is a public university in the Brazilian state of Paraíba. The university has eight campuses throughout the state, its main campus is located in the city of Campina Grande, it was founded by local ordinance n. 23, on March 15, 1966, as Regional University of Northeastern Brazil as a local autarky. On October 11, 1987 by State Law n. 4.977, sanctioned by Governor Tarcísio Burity, the URNe became the State University of Paraíba. The UEPB has eight campuses throughout the state, it is located in the city of Campina Grande. The campus was named after the economist Edvaldo de Souza do Ó, one of the founders of the university. On July, 1966, Edvaldo do Ó was first elected vice-rector and was rector of the Universidade Regional do Nordeste, which became the UEPB, until April 10, 1969; the campus I houses the administrative center of the University. Site
Live aus Berlin is a live album by German pop duo Rosenstolz, recorded in the Columbiahalle in Berlin during the band's 2002 Macht Liebe tour. The album was released in 2003 by Island Records on single CD, double CD, DVD; the double-CD edition of Live aus Berlin containing all 24 songs of the Columbiahalle concert was favourably reviewed by Linus Schwanke of German music magazine laut.de, who felt that the album faithfully captured the live performance. Felix Kosel of German music magazine bloom was impressed with the double-CD album, commenting that it reflected the feelings and atmosphere in the Columbiahalle. However, he was less impressed with the video recording on the DVD album, criticizing the unsharp pictures, the editing and the cinematography. By contrast, the DVD album was seen in a positive light by Anja Kesting of German women's magazine AVIVA-Berlin, as it provided a glimpse behind the scenes. "Intro: Macht Liebe / Fütter deine Angst" – 5:15 "Bastard" – 4:41 "Lass sie reden" – 3:43 "Sex im Hotel" – 4:11 "Laut" – 3:55 "Der Moment" – 4:50 "Komm doch mit" – 3:23 "Megapower" – 3:46 "Nur einmal noch" – 3:55 "Es tut immer noch weh" – 4:13 "Es könnt' ein Anfang sein" – 5:25 "Königin" – 4:29 "Sternraketen" – 5:08 "Die Schlampen sind müde" – 4:49 "Herzensschöner" – 4:22 "Tag in Berlin" – 3:01 "Was kann ich für eure Welt" – 3:51 The track listing for the DVD edition is identical to that for the double-CD edition.
Live aus Berlin at official Rosenstolz website