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In
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...

physics
and
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ...

chemistry
, a nucleon is either a
proton 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 that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...

proton
or a
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...

neutron
, considered in its role as a component of an
atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden experiments, Geiger–Marsden gold foil experiment. After th ...
. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were thought to be
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, antiqu ...
s, not made up of smaller parts. Now they are known to be
composite particle This is a list of known and hypothesized particles. Elementary particles Elementary particles are particles with no measurable internal structure; that is, it is unknown whether they are composed of other particles. They are the fundamental ob ...
s, made of three
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...

quark
s bound together by the
strong interaction The strong interaction or strong force is a fundamental interaction that confines Quark, quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is calle ...
. The interaction between two or more nucleons is called internucleon interaction or
nuclear force The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nucle ...

nuclear force
, which is also ultimately caused by the strong interaction. (Before the discovery of quarks, the term "strong interaction" referred to just internucleon interactions.) Nucleons sit at the boundary where
particle physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standa ...
and
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the ...
overlap. Particle physics, particularly
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory 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 o ...
, provides the fundamental equations that describe the properties of quarks and of the strong interaction. These equations describe quantitatively how quarks can bind together into protons and neutrons (and all the other
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite particle, composite subatomic particle made of two or more quarks bound state, held together by the strong interaction. They are analogous to molecules tha ...
s). However, when multiple nucleons are assembled into an atomic nucleus (
nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was co ...

nuclide
), these fundamental equations become too difficult to solve directly (see lattice QCD). Instead, nuclides are studied within
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the ...
, which studies nucleons and their interactions by approximations and models, such as the
nuclear shell model In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model is a nuclear model, model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels. The ...
. These models can successfully describe nuclide properties, as for example, whether or not a particular nuclide undergoes
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive Decay chain, disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nucl ...

radioactive decay
. The proton and neutron are in a scheme of categories being at once
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks ...
s,
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite particle, composite subatomic particle made of two or more quarks bound state, held together by the strong interaction. They are analogous to molecules tha ...
s and
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron list of particles, family of particles; hadrons are composed o ...
s. The proton carries a positive net charge, and the neutron carries a zero net charge; the proton's
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
is only about 0.13% less than the neutron's. Thus, they can be viewed as two states of the same nucleon, and together form an
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions o ...
doublet (). In isospin space, neutrons can be transformed into protons and conversely by
SU(2) In mathematics, the special unitary group of degree , denoted , is the Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold. A manifold is a space that locally resembl ...
symmetries. These nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space. According to the Noether theorem, isospin is conserved with respect to the strong interaction.


Overview


Properties

Protons and neutrons are best known in their role as nucleons, i.e., as the components of atomic nuclei, but they also exist as free particles. Free neutrons are unstable, with a half-life of around 13 minutes, but they have important applications (see
neutron radiation Neutron radiation is a form of ionizing radiation Ionizing radiation (or ionising radiation), including nuclear radiation, consists of subatomic particles or electromagnetic waves that have sufficient energy to ionization, ionize atoms or molecu ...
and
neutron scattering Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. Th ...
). Protons not bound to other nucleons are the nuclei of hydrogen atoms when bound with an
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...

electron
or if not bound to anything are ions or cosmic rays. Both the proton and the neutron are
composite particle This is a list of known and hypothesized particles. Elementary particles Elementary particles are particles with no measurable internal structure; that is, it is unknown whether they are composed of other particles. They are the fundamental ob ...
s, meaning that each is composed of smaller parts, namely three
quarks A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...

quarks
each; although once thought to be so, neither is an
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, antiqu ...
. A proton is composed of two
up quark The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quark ...

up quark
s and one
down quark The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up q ...

down quark
, while the neutron has one up quark and two down quarks. Quarks are held together by the
strong force The strong interaction or strong force is a fundamental interaction that confines Quark, quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is calle ...
, or equivalently, by
gluon A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong interaction, strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged partic ...

gluon
s, which mediate the strong force at the quark level. An up quark has
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electron ...
  ''e'', and a down quark has charge  ''e'', so the summed electric charges of proton and neutron are + ''e'' and 0, respectively. Thus, the neutron has a charge of 0 (zero), and therefore is electrically neutral; indeed, the term "neutron" comes from the fact that a neutron is electrically neutral. The masses of the proton and neutron are similar: for the proton it is (), while for the neutron it is (); the neutron is roughly 0.13% heavier. The similarity in mass can be explained roughly by the slight difference in masses of up quarks and down quarks composing the nucleons. However, a detailed description remains an unsolved problem in particle physics. The spin of the nucleon is , which means that they are
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks ...
s and, like
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...

electron
s, are subject to the
Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spin (physics), spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle ...
: no more than one nucleon, e.g. in an atomic nucleus, may occupy the same
quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement in quantum mechanics, measurement on a system. Knowledge of the quantum state together with the rul ...
. The
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions o ...
and spin quantum numbers of the nucleon have two states each, resulting in four combinations in total. An
alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than tha ...

alpha particle
is composed of four nucleons occupying all four combinations, namely, it has two protons (having opposite spin) and two neutrons (also having opposite spin), and its net
nuclear spin In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin (physics), spin) of an electron or other Elementary particle, particle. The phra ...
is zero. In larger nuclei constituent nucleons, by Pauli exclusion, are compelled to have relative
motion In physics, motion is the phenomenon in which an object changes its Position (geometry), position with respect to time. Motion is mathematically described in terms of Displacement (geometry), displacement, distance, velocity, acceleration, speed ...

motion
, which may also contribute to nuclear spin via the
orbital quantum number The azimuthal quantum number is a quantum number for an atomic orbital that determines its angular momentum operator, orbital angular momentum and describes the shape of the orbital. The wikt:azimuthal, azimuthal quantum number is the second of ...
. They spread out into nuclear shells analogous to
electron shell In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's Atomic nucleus, nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by t ...
s known from chemistry. Both the proton and neutron have
magnetic moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...

magnetic moment
s, though the nucleon magnetic moments are anomalous and were unexpected when they were discovered in the 1930s. The proton's magnetic moment, symbol ''μ'', is , whereas, if the proton were an elementary Dirac particle, it should have a magnetic moment of . Here the unit for the magnetic moments is the
nuclear magneton The nuclear magneton (symbol ''μ'') is a physical constant of magnetic moment, defined in SI units by: :\mu_\text = and in Gaussian units, Gaussian Centimetre gram second system of units, CGS units by: :\mu_\text = where: :''e'' is the el ...
, symbol ''μ'', an atomic-scale
unit of measure A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
. The neutron's magnetic moment is ''μ'' = , whereas, since the neutron lacks an electric charge, it should have no magnetic moment. The value of the neutron's magnetic moment is negative because the direction of the moment is opposite to the neutron's spin. The nucleon magnetic moments arise from the quark substructure of the nucleons. The proton magnetic moment is exploited for NMR / MRI scanning.


Stability

A neutron in free state is an unstable particle, with a
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
around ten minutes. It undergoes (a type of
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive Decay chain, disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nucl ...

radioactive decay
) by turning into a proton while emitting an electron and an
electron antineutrino The electron neutrino () is an elementary particle which has zero electric charge and a spin (physics), spin of . Together with the electron, it forms the first generation (physics), generation of Lepton, leptons, hence the name electron neutrino ...
. This reaction can occur because the mass of the neutron is slightly greater than that of the proton. (See the
Neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...

Neutron
article for more discussion of neutron decay.) A proton by itself is thought to be stable, or at least its lifetime is too long to measure. This is an important discussion in particle physics (see ''
Proton decay In particle physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are ...

Proton decay
''). Inside a nucleus, on the other hand, combined protons and neutrons (nucleons) can be stable or unstable depending on the
nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was co ...

nuclide
, or nuclear species. Inside some nuclides, a neutron can turn into a proton (producing other particles) as described above; the reverse can happen inside other nuclides, where a proton turns into a neutron (producing other particles) through or
electron capture Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. Thi ...

electron capture
. And inside still other nuclides, both protons and neutrons are stable and do not change form.


Antinucleons

Both nucleons have corresponding
antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite charge (physics), physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also ...
s: the
antiproton The antiproton, , (pronounced ''p-bar'') is the antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite charge (physics), physical charges (such as electric charge). For ...

antiproton
and the
antineutron The antineutron is the antiparticle of the neutron with symbol . It differs from the neutron only in that some of its properties have additive inverse, equal magnitude but opposite sign. It has the same mass as the neutron, and no net electric ch ...

antineutron
, which have the same mass and opposite charge as the proton and neutron respectively, and they interact in the same way. (This is generally believed to be ''exactly'' true, due to
CPT symmetry Charge, parity, and time reversal symmetry is a fundamental symmetry in physics, symmetry of physical laws under the simultaneous transformation (mathematics), transformations of charge conjugation (C), parity transformation (P), and T-symmetry, ...
. If there is a difference, it is too small to measure in all experiments to date.) In particular, antinucleons can bind into an "antinucleus". So far, scientists have created antideuterium and antihelium-3 nuclei.


Tables of detailed properties


Nucleons

The masses of the proton and neutron are known with far greater precision in
dalton Dalton may refer to: Science * Dalton (crater), a lunar crater * Dalton (program), chemistry software * Dalton (unit) (Da), the atomic mass unit * John Dalton, chemist, physicist and meteorologist Entertainment * Dalton (Buffyverse), minor cha ...
s (Da) than in MeV/''c''2 due to the way in which these are defined. The conversion factor used is 1 Da = . At least 1035 years. See
proton decay In particle physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are ...

proton decay
. For
free neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atom Every atom is composed of ...

free neutron
s; in most common nuclei, neutrons are stable. The masses of their antiparticles are assumed to be identical, and no experiments have refuted this to date. Current experiments show any relative difference between the masses of the proton and antiproton must be less than and the difference between the neutron and antineutron masses is on the order of .


Nucleon resonances

Nucleon resonances are
excited state In quantum mechanics, an excited state of a system (such as an atom, molecule or Atomic nucleus, nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excita ...
s of nucleon particles, often corresponding to one of the quarks having a flipped spin state, or with different orbital angular momentum when the particle decays. Only resonances with a 3- or 4-star rating at the Particle Data Group (PDG) are included in this table. Due to their extraordinarily short lifetimes, many properties of these particles are still under investigation. The symbol format is given as N() , where is the particle's approximate mass, is the orbital angular momentum (in the
spectroscopic notation Spectroscopic notation provides a way to specify atomic ionization states, atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a Function (mathematics), function describing the location and wave-like behavior of an elec ...
) of the nucleon–meson pair, produced when it decays, and and are the particle's
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions o ...
and
total angular momentum In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given Subatomic particle, particle, by combining its angular momentum operator#Orbital angular momentum, orbital angular momentum and its ...
respectively. Since nucleons are defined as having isospin, the first number will always be 1, and the second number will always be odd. When discussing nucleon resonances, sometimes the N is omitted and the order is reversed, in the form (); for example, a proton can be denoted as "N(939) S11" or "S11 (939)". The table below lists only the base resonance; each individual entry represents 4 
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron list of particles, family of particles; hadrons are composed o ...
s: 2 nucleon resonances particles and their 2 antiparticles. Each resonance exists in a form with a positive
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electron ...
(), with a quark composition of like the proton, and a neutral form, with a quark composition of like the neutron, as well as the corresponding antiparticles with antiquark compositions of and respectively. Since they contain no , , , or
top A spinning top, or simply a top, is a toy with a squat body and a sharp point at the bottom, designed to be spun on its vertical axis, balancing on the tip due to the gyroscopic effect. Once set in motion, a top will usually wobble for a f ...

top
quarks, these particles do not possess
strangeness In particle physics, strangeness ("''S''") is a Physical property, property of Particle, particles, expressed as a quantum number, for describing Particle decay, decay of particles in Strong interaction, strong and Electromagnetic interaction, ele ...
, etc. The table only lists the resonances with an
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions o ...
= . For resonances with
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions o ...
= , see the article on Delta baryons. † ''The P11(939) nucleon represents the excited state of a normal proton or neutron. Such a particle may be stable when in an atomic nucleus, e.g. in
lithium-6 Naturally occurring lithium Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the Symbol (chemistry), symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard temperature and ...

lithium-6
.''


Quark model classification

In the
quark model In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies Flavour (particle physics), ...
with
SU(2) In mathematics, the special unitary group of degree , denoted , is the Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold. A manifold is a space that locally resembl ...
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) In mathematics, the special unitary group of degree , denoted , is the Lie group of Unitary matrix, unitary Matrix (mathematics), matrices with determinant 1. The more general Unitary group, unitary matrices may have complex determinants with ...
flavour, they are part of the ground-state octet (8) of spin-
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron list of particles, family of particles; hadrons are composed o ...
s, known as the Eightfold way. The other members of this octet are the hyperons strange isotriplet , , , the and the strange isodoublet , . One can extend this multiplet in SU(4) flavour (with the inclusion of the
charm quark The charm quark, charmed quark or c quark (from its symbol, c) is the third-most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks. Examples of hadrons containin ...
) to the ground-state 20-plet, or to SU(6) flavour (with the inclusion of the
top A spinning top, or simply a top, is a toy with a squat body and a sharp point at the bottom, designed to be spun on its vertical axis, balancing on the tip due to the gyroscopic effect. Once set in motion, a top will usually wobble for a f ...

top
and
bottom quark The bottom quark or b quark, also known as the beauty quark, is a third-generation heavy quark with a charge of − elementary charge, ''e''. All quarks are described in a similar way by Electroweak interaction, electroweak and quantum chr ...
s) to the ground-state 56-plet. The article on
isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions o ...
provides an explicit expression for the nucleon wave functions in terms of the quark flavour eigenstates.


Models

Although it is known that the nucleon is made from three quarks, , it is not known how to solve the
equations of motion In physics, equations of motion are equations that describe the behavior of a physical system in terms of its Motion (physics), motion as a function (mathematics), function of time.''Encyclopaedia of Physics'' (second Edition), Rita G. Lerner, R ...
for
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory 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 o ...
. 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
supercomputer A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions p ...
s. However, several analytic models also exist:


Skyrmion models

The skyrmion models the nucleon as a topological soliton in a nonlinear
SU(2) In mathematics, the special unitary group of degree , denoted , is the Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold. A manifold is a space that locally resembl ...
pion In particle physics, a pion (or a pi meson, denoted with the Greek alphabet, Greek letter pi (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 li ...
field. The topological stability of the skyrmion is interpreted as the conservation of
baryon number In particle physics, the baryon number is a Conservation law (physics), strictly conserved additive quantum number of a system. It is defined as ::B = \frac\left(n_\text - n_\bar\right), where ''n''q is the number of quarks, and ''n'' is the n ...
, that is, the non-decay of the nucleon. The local topological winding number density is identified with the local
baryon number In particle physics, the baryon number is a Conservation law (physics), strictly conserved additive quantum number of a system. It is defined as ::B = \frac\left(n_\text - n_\bar\right), where ''n''q is the number of quarks, and ''n'' is the n ...
density of the nucleon. With the pion isospin vector field oriented in the shape of a hedgehog space, 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.


MIT bag model

The ''MIT bag model'' confines quarks and gluons interacting through
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory 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 o ...
to a region of space determined by balancing the pressure exerted by the quarks and gluons against a hypothetical pressure exerted by the vacuum on all colored quantum fields. The simplest approximation to the model confines three non-interacting quarks to a spherical cavity, with the
boundary condition In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in m ...
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 In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its Dirac equation#Covariant form and relativistic invariance, free form, or including Dirac equation#Comparison with the ...
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. Although the basic bag model does not provide a pion-mediated interaction, it describes excellently the nucleon–nucleon forces through the 6 quark bag ''s''-channel mechanism using the ''P''-matrix.


Chiral bag model

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. , this remarkable trade-off between
topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
and the spectrum of an operator does not have any grounding or explanation in the mathematical theory of
Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally ...
s and their relationship to
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
. 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 of
Lewis Carroll Charles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet and mathematician. His most notable works are ''Alice's Adventures in Wonderland'' (1865) and its sequel ...
's
Cheshire Cat The Cheshire Cat ( or ) is a List of fictional felines, fictional cat popularised by Lewis Carroll in ''Alice's Adventures in Wonderland'' and known for its distinctive mischievous grin. While now most often used in ''Alice''-related contexts ...
to just its smile. It is expected that a first-principles solution of the equations of QCD will demonstrate a similar duality of quark–
meson In particle physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are ...
descriptions.


See also

*
Hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite particle, composite subatomic particle made of two or more quarks bound state, held together by the strong interaction. They are analogous to molecules tha ...
s *
Electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified field theory, unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two force ...


Footnotes


References


Particle listings


Further reading

* * * {{Authority control Hadrons Baryons Neutron