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Encyclopedia > Nucleon

In physics a nucleon is a collective name for two baryons: the neutron and the proton. They are constituents of the atomic nucleus and until the 1960s were thought to be elementary particles. In those days their interactions (now called internucleon interactions) defined strong interactions. Now they are known to be composite particles, made of quarks and gluons. Understanding the nucleons' properties is one of the major goals of quantum chromodynamics, the modern theory of strong interactions. This is a discussion of a present category of science. ... Combinations of three u, d or s-quarks with a total spin of 3/2 form the so-called baryon decuplet. ... This article or section does not adequately cite its references or sources. ... In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ... In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ... The nuclear force (or inter-nucleon potential) is the force between two or more nucleons. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... Elementary particles An elementary particle is a particle with no measurable internal structure, that is, it is not a composite of other particles. ... The six flavours of quarks and their most likely decay modes. ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ...

The proton is the lightest baryon and its stability is a measure of baryon number conservation. The proton's lifetime thus puts strong constraints on speculative theories which try to extend the Standard Model of particle physics. The neutron decays into a proton through the weak decay. The two are members of an isospin I=1/2 doublet. Combinations of three u, d or s-quarks with a total spin of 3/2 form the so-called baryon decuplet. ... In particle physics, the baryon number is an approximate conserved quantum number. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. ... In physics, weak decay is the process of decomposing a heavier particle into lighter particles (plus energy) by means of a weak interaction. ... Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ...

## Contents

Main article: proton

With spin and parity 1/2+, charge +1, and mass of 938 MeV, the proton is the nucleus of a hydrogen atom (1H1). It has a magnetic moment of 2.79 nuclear magnetons. The electric dipole moment is consistent with zero; the bound on it is that it is less than 0.54×10-23 e-cm. In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3Ã—3 matrix representation of P would have determinant equal to â€“1, and hence cannot reduce to a rotation. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... For other uses, see Atom (disambiguation). ... A bar magnet. ... The nuclear magneton (symbol ), is a physical constant of magnetic moment, defined by: where: is the elementary charge, is the reduced Plancks constant, is the proton rest mass In the SI system of units its value is approximately: = 5. ... This article is about the electromagnetic phenomenon. ...

In some speculative grand unified theories it may decay. The half-life for this decay has been limited to be greater than 2.1×1029 years. The charge radius is measured mainly through elastic electron-proton scattering and is 0.870 fm. For specific decay modes, into antilepton or lepton and a meson, the bound is often better than 1032 years. The proton is therefore taken to be a stable particle, and baryon number is assumed to be conserved. Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ... For other uses, see Electron (disambiguation). ... In physics, a lepton is a particle with spin-1/2 (a fermion) that does not experience the strong interaction (that is, the strong nuclear force). ... Mesons of spin 1 form a nonet In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ... In particle physics, the baryon number is an approximate conserved quantum number. ...

## The neutron

Main article: neutron

The neutron has no charge, has spin and parity of 1/2+, and mass of 940 MeV. The most precise measurements of its decay lifetime are mainly from traps of various kinds and in beams. The lifetime of a free neutron outside the nucleus is 885.7±0.8 seconds (about 15 minutes). It decays weakly through the process This article or section does not adequately cite its references or sources. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3Ã—3 matrix representation of P would have determinant equal to â€“1, and hence cannot reduce to a rotation. ... A free neutron is a neutron that exists outside of an atomic nucleus. ... In physics, weak decay is the process of decomposing a heavier particle into lighter particles (plus energy) by means of a weak interaction. ...

$nto p+e+overlinenu_e$.

Its magnetic moment is −1.91 nuclear magnetons. Both time reversal and parity invariance of the strong interactions implies that the neutron's electric dipole moment must be zero; the current observational bound is that it is less than 0.63×10−23 e-cm. The mean-square charge radius related to the scattering length measured in low energy electron-neutron scattering for the neutron is −0.116 fm². The nuclear magneton (symbol ), is a physical constant of magnetic moment, defined by: where: is the elementary charge, is the reduced Plancks constant, is the proton rest mass In the SI system of units its value is approximately: = 5. ... Wikipedia does not have an article with this exact name. ... Look up Parity in Wiktionary, the free dictionary Parity is a concept of equality of status or functional equivalence. ... The scattering amplitude describes the amplitude of an outgoing, elementary, spherical wave relative to a plane, incoming wave scattered on a point size particle. ...

Violation of baryon number conservation may give rise to oscillations between the neutron and antineutron, through processes which change B by two units. Using free neutrons from nuclear reactors, as well as neutrons bound inside nuclei, the mean time for these transitions is found to be greater than 1.3×108 seconds. The much poorer bound, as compared to protons, is related to the difficulty of the observations. In particle physics, the baryon number is an approximate conserved quantum number. ... Core of a small nuclear reactor used for research. ...

A limit on electric charge non-conservation comes from the observed lack of the decay Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ...

$nto p+nu_e+overlinenu_e$

The observations which limit the branching fraction of the neutron in this decay channel to less than 8×10−27 are all done looking for appropriate decays of nuclei (AA and ZZ+1). In particle physics and nuclear physics, the branching fraction for a decay is the fraction of particles which decay by an individual decay mode with respect to the total number of particles which decay. ...

## Antinucleons

CPT-symmetry puts strong constraints on the relative properties of particles and antiparticles and, therefore, is open to stringent tests. For example, the charges of the proton and the antiproton have to be equal. (This equality has been tested to one part in 108). The equality of their masses is also tested to 10-8. By holding antiprotons in a Penning trap, the equality of the charge to mass ratio of the proton has been tested to 90×10-12. The magnetic moment of the antiproton has been found with error of 8×10-3 nuclear Bohr magnetons, and is found to be equal and opposite to that of the proton. For the neutron-antineutron system, the masses are equal to within 9×10-5. CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. ... For each kind of particle, there is an associated antiparticle with the same mass but opposite electromagnetic, weak, and strong charges, as well as spin. ... Penning traps are devices for the storage of charged particles using a constant magnetic field and a constant electric field. ...

## Quark model classification

In the quark model with SU(2) flavour, the two nucleons are part of the ground state doublet. The proton has quark content of uud, and the neutron, udd. In SU(3) flavour, they are part of the ground state octet (8) of spin 1/2 baryons, known as the Eightfold way. The other members of this octet are the hyperons strange isotriplet Σ0,±, the Λ and the strange iso-doublet Ξ0,-. One can extend this multiplet in SU(4) flavour (with the inclusion of the charm quark) to the ground state 20-plet. In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, i. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... Flavour (or flavor) is a quantum number of elementary particles related to their weak interactions. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... Combinations of three u, d or s-quarks with a total spin of 3/2 form the so-called baryon decuplet. ... It has been suggested that this article or section be merged into quark model. ... In particle physics, a hyperon is any subatomic particle which is a baryon (and hence a hadron and a fermion) with non-zero strangeness, but with zero charm and zero bottomness. ...

The article on isospin provides an explicit expression for the nucleon wave functions in terms of the quark flavour eigenstates. Isospin (isotopic spin, isobaric spin) is a physical quantity which is mathematically analogous to spin. ...

## Models of the nucleon

Although it is known that the nucleon is made from three quarks, as of 2006, it is not known how to solve the equations of motion for quantum chromodynamics. Thus, the study of the low-energy properties of the nucleon are performed by means of models. The only first-principles approach available is to attempt to solve the equations of QCD numerically, using lattice QCD. This requires complicated algorithms and very powerful supercomputers. However, several analytic models also exist: Image File history File links Confused. ... 2006 is a common year starting on Sunday of the Gregorian calendar. ... In advanced physics, equations of motion usually refer to the Euler-Lagrange equations, differential equations derived from the Lagrangian. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... It has been suggested that lattice field theory be merged into this article or section. ... A supercomputer is a computer that led the world (or was close to doing so) in terms of processing capacity, particularly speed of calculation, at the time of its introduction. ...

The Skyrmion models the nucleon as a topological soliton in a non-linear SU(2) pion field. The topological stability of the Skyrmion is interpreted as the conservation of baryon number, that is, the non-decay of the nucleon. The local topological winding number density is identified with the local baryon number density of the nucleon. With the pion isospin vector field oriented in the shape of a hedgehog, the model is readily solvable, and is thus sometimes called the hedgehog model. The hedgehog model is able to predict low-energy parameters, such as the nucleon mass, radius and axial coupling constant, to approximately 30% of experimental values. In theoretical physics, a skyrmion, named for Tony Skyrme, is a homotopically nontrivial classical solution of a nonlinear sigma model with a non-trivial target manifold topology i. ... A topological soliton is a solution of a system of partial differential equations (or alternatively, a quantum field theory), not so much because of the nature of the PDEs themselves, but because of the boundary conditions entailing the existence of homotopically distinct solutions. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... In particle physics, the baryon number is an approximate conserved quantum number. ... It has been suggested that this article or section be merged with Soliton (topological). ... In particle physics, the baryon number is an approximate conserved quantum number. ... Genera Atelerix Erinaceus Hemiechinus Mesechinus Paraechinus A hedgehog is any of the small spiny mammals of the subfamily Erinaceinaes and the order Erinaceomorpha. ...

The MIT bag model confines three non-interacting quarks to a spherical cavity, with the boundary condition that the quark vector current vanish on the boundary. The non-interacting treatment of the quarks is justified by appealing to the idea of asymptotic freedom, whereas the hard boundary condition is justified by quark confinement. Mathematically, the model vaguely resembles that of a radar cavity, with solutions to the Dirac equation standing in for solutions to the Maxwell equations and the vanishing vector current boundary condition standing for the conducting metal walls of the radar cavity. If the radius of the bag is set to the radius of the nucleon, the bag model predicts a nucleon mass that is within 30% of the actual mass. An important failure of the basic bag model is its failure to provide a pion-mediated interaction. In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ... In special and general relativity, the four-current is the Lorentz covariant four-vector that replaces the electromagnetic current density, or indeed any conventional current density. ... In physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances, i. ... This article refers to a particle physics phenomenon. ... A cavity magnetron is a high-powered vacuum tube that generates coherent microwaves. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-Â½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

The chiral bag model merges the MIT bag model and the Skyrmion model. In this model, a hole is punched out of the middle of the Skyrmion, and replaced with a bag model. The boundary condition is provided by the requirement of continuity of the axial vector current across the bag boundary. Very curiously, the missing part of the topological winding number (the baryon number) of the hole punched into the Skyrmion is exactly made up by the non-zero vacuum expectation value (or spectral asymmetry) of the quark fields inside the bag. As of 2006, this remarkable trade-off between topology and the spectrum of an operator does not have any grounding or explanation in the mathematical theory of Hilbert spaces and their relationship to geometry. Several other properties of the chiral bag are notable: it provides a better fit to the low energy nucleon properties, to within 5-10%, and these are almost completely independent of the chiral bag radius (as long as the radius is less than the nucleon radius). This independence of radius is referred to as the Cheshire Cat principle, after the fading to a smile of Lewis Carroll's Cheshire Cat. It is expected that a first-principles solution of the equations of QCD will demonstrate a similar duality of quark-pion descriptions. In quantum field theory the vacuum expectation value (also called condensate) of an operator is its average, expected value in the vacuum. ... In mathematics and physics, the spectral asymmetry is the asymmetry in the distribution of the spectrum of eigenvalues of an operator. ... 2006 is a common year starting on Sunday of the Gregorian calendar. ... A MÃ¶bius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ... In functional analysis, the concept of the spectrum of an operator is a generalisation of the concept of eigenvalues, which is much more useful in the case of operators on infinite-dimensional spaces. ... The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the plane and three-dimensional space to spaces of functions. ... Calabi-Yau manifold Geometry (Greek Î³ÎµÏ‰Î¼ÎµÏ„ÏÎ¯Î±; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... Charles Lutwidge Dodgson (Lewis Carroll) â€“ believed to be a self-portrait Charles Lutwidge Dodgson (IPA: ) (January 27, 1832 â€“ January 14, 1898), better known by the pen name Lewis Carroll, was an English author, mathematician, logician, Anglican clergyman and photographer. ... This article does not cite any references or sources. ...

## References

• Gerald Edward Brown and A. D. Jackson, The Nucleon-Nucleon Interaction, (1976) North-Holland Publishing, Amsterdam ISBN 0-7204-0335-9
• Linas Vepstas, A.D. Jackson, A.S. Goldhaber, Two-phase models of baryons and the chiral Casimir effect, Physics Letters B140 (1984) p. 280-284.
• Linas Vepstas, A.D. Jackson, Justifying the Chiral Bag, Physics Reports, 187 (1990) p. 109-143.
• Particle data group listing on the proton
• Particle data group listing on the neutron

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