Sanford–Wang Parameterisation
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Sanford–Wang Parameterisation
The Sanford–Wang parameterisation is an empirical formula used to model the production of pions in nuclear interaction of the form p+A → \pi^++X where a beam of high-energy protons hit a material. Its formula for the double-differential Cross section (physics), cross section with respect to momentum (p) and solid angle (\Omega) is as follows. \frac(p,\theta) = c_1 p^ \left(1-\frac\right)\exp\left[-c_3\frac-c_6\theta(p-c_7 p_ (\cos\theta)^)\right] Where p and \theta are the momentum of the outgoing pion and its angle from the direction of the incident proton. The numbers c_1\ldots c_8 are the ''Sanford-Wang parameters'' and are typically varied to give a good fit with experimental data. References

* J. R. Sanford and C. L. Wang, Brookhaven National Laboratory, AGS internal report, 1967 (unpublished) * * {{DEFAULTSORT:Sanford-Wang Parameterisation Quantum chromodynamics Scattering Experimental particle physics ...
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Pions
In particle physics, a pion (, ) or pi meson, denoted with the Greek letter pi (), is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more generally, the lightest hadrons. They are unstable, with the charged pions and decaying after a mean lifetime of 26.033  nanoseconds ( seconds), and the neutral pion decaying after a much shorter lifetime of 85  attoseconds ( seconds). Charged pions most often decay into muons and muon neutrinos, while neutral pions generally decay into gamma rays. The exchange of virtual pions, along with vector, rho and omega mesons, provides an explanation for the residual strong force between nucleons. Pions are not produced in radioactive decay, but commonly are in high-energy collisions between hadrons. Pions also result from some matter–antimatter annihilation events. All types of pions are also produced in ...
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Protons
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 the mass of a neutron and approximately times the mass of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of approximately one dalton, are jointly referred to as '' nucleons'' (particles present in atomic nuclei). One or more protons are present in the nucleus of every atom. They provide the attractive electrostatic central force which binds the atomic electrons. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol ''Z''). Since each element is identified by the number of protons in its nucleus, each element has its own atomic number, which determines the number of atomic electrons and consequently the chemical characteristics of the element. The word ''proton'' is Greek for "first ...
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Cross Section (physics)
In physics, the cross section is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process. When two discrete particles interact in classical physics, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other. If the particles are hard inelastic sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is ...
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Quantum Chromodynamics
In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group special unitary group, SU(3). The QCD analog of electric charge is a property called ''color''. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of Quantum chromodynamics#Experimental tests, experimental evidence for QCD has been gathered over the years. QCD exhibits three salient properties: * Color confinement. Due to the force between two color charges remaining constant as they are separated, the energy grows until a quark–antiquark pair is mass–energy equivalence, spontaneously produced, turning ...
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Scattering
In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called ''diffuse reflections'' and unscattered reflections are called ''specular'' (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering research, noted the connecti ...
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