User Contributed Dictionary
Noun
nucleons p Plural of nucleon
Extensive Definition
 This article is about subatomic particles in nuclear physics. For the fictional power source used in the Transformers Universes, see Nucleon (Transformers). For the Ford concept car, see Ford 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.
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.
The proton
With spin and
parity
1/2+, charge +1, and rest mass of 938 MeV, the proton is the
nucleus of a hydrogen
atom (). 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 0.54×1023 ecm.
In some speculative grand
unified theories it may decay. The halflife for this decay has
been limited to be greater than 2.1×1029 years. The charge radius
is measured mainly through elastic electronproton scattering and
is . For specific decay modes, into antilepton or lepton and a meson, the bound is often better
than 10 years. The proton is therefore taken to be a stable
particle, and baryon
number is assumed to be conserved.
The neutron
The neutron has no charge, has spin and
parity
of 1/2+, and rest mass of . 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 (about 15 minutes). It decays weakly through
the process

 → + +
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 . The meansquare charge radius
related to the scattering
length measured in low energy electronneutron scattering for
the neutron is .
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 . The much
poorer bound, as compared to protons, is related to the difficulty
of the observations.
A limit on electric
charge nonconservation comes from the observed lack of the
decay

 → + +
The observations which limit the branching
fraction of the neutron in this decay channel to less than are
all done looking for appropriate decays of nuclei (A→A and
Z→Z+1).
Antinucleons
CPTsymmetry 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 10). The equality of their masses is also tested to 10. By holding antiprotons in a Penning trap, the equality of the charge to mass ratio of the proton has been tested to . The magnetic moment of the antiproton has been found with error of nuclear Bohr magnetons, and is found to be equal and opposite to that of the proton. For the neutronantineutron system, the masses are equal to within .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 isodoublet Ξ0,. One can extend this multiplet in SU(4) flavour (with the inclusion of the charm quark) to the ground state 20plet.The article on isospin provides an explicit
expression for the nucleon wave functions in terms of the quark
flavour eigenstates.
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 lowenergy properties of
the nucleon are performed by means of models. The only
firstprinciples 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:
The Skyrmion models
the nucleon as a topological
soliton in a nonlinear SU(2) pion field. The topological
stability of the Skyrmion is interpreted as the conservation of
baryon
number, that is, the nondecay 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 lowenergy parameters, such as
the nucleon mass, radius and axial
coupling constant, to approximately 30% of experimental
values.
The MIT bag
model confines three noninteracting quarks to a spherical
cavity, with the boundary
condition that the quark vector
current vanish on the boundary. The noninteracting 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 pionmediated interaction.
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
nonzero vacuum
expectation value (or spectral
asymmetry) of the quark fields inside the bag. As of 2006,
this remarkable tradeoff 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 510%, 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 firstprinciples solution of the
equations of QCD will demonstrate a similar duality of quarkpion
descriptions.
See also
References
 Gerald Edward Brown and A. D. Jackson, The NucleonNucleon Interaction, (1976) NorthHolland Publishing, Amsterdam ISBN 0720403359
 Linas Vepstas, A.D. Jackson, A.S. Goldhaber, Twophase models of baryons and the chiral Casimir effect, Physics Letters B140 (1984) p. 280284.
 Linas Vepstas, A.D. Jackson, Justifying the Chiral Bag, Physics Reports, 187 (1990) p. 109143.
 Particle data group listing on the proton
 Particle data group listing on the neutron
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