Editing Nucleon

{{Short description|Component of an atomic nucleus}}
{{About||the Ford concept car|Ford Nucleon}}
[[File:Nucleus drawing.svg|thumb|An [[atomic nucleus]] is shown here as a compact bundle of the two types of nucleons, [[proton]]s (red) and [[neutron]]s (blue). In this picture, the protons and neutrons are shown as distinct, which is the conventional view in [[chemistry]], for example. But in an actual nucleus, as understood by modern [[nuclear physics]], the nucleons are partially delocalized and organize themselves according to the laws of [[quantum chromodynamics]].]]
In [[physics]] and [[chemistry]], a '''nucleon''' is either a [[proton]] or a [[neutron]], considered in its role as a component of an [[atomic nucleus]]. The number of nucleons in a nucleus defines the atom's [[mass number]].

Until the 1960s, nucleons were thought to be [[elementary particle]]s, not made up of smaller parts. Now they are understood as [[composite particle]]s, made of three [[quark]]s bound together by the [[strong interaction]]. The interaction between two or more nucleons is called [[internucleon interaction]] or [[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]] and [[nuclear physics]] overlap. Particle physics, particularly [[quantum chromodynamics]], 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]]s). However, when multiple nucleons are assembled into an atomic nucleus ([[nuclide]]), these fundamental equations become too difficult to solve directly (see [[lattice QCD]]). Instead, nuclides are studied within [[nuclear physics]], which studies nucleons and their interactions by approximations and models, such as the [[nuclear shell model]]. These models can successfully describe nuclide properties, as for example, whether or not a particular nuclide undergoes [[radioactive decay]].

The proton and neutron are in a scheme of categories being at once [[fermion]]s, [[hadron]]s and [[baryon]]s. The proton carries a positive net [[electric charge|charge]], and the neutron carries a zero net charge; the proton's [[mass]] 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]] doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by [[SU(2)]] symmetries. These nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space. According to [[Noether's theorem]], isospin is conserved with respect to the strong interaction.<ref name=Griffiths2008>{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}</ref>{{rp|129–130}}

==Overview==
{{Main article|Proton|Neutron}}

===Properties===
{{multiple image
   | align     = right
   | direction = vertical
   | header    = Quark composition of a nucleon
   | width1    = 183
   | image1    = Quark structure proton.svg
   | alt1      = Proton
   | caption1  = Proton ({{SubatomicParticle|proton}}): {{SubatomicParticle|Up quark}}{{SubatomicParticle|Up quark}}{{SubatomicParticle|Down quark}}
   | width2    = 183
   | image2    = Quark structure neutron.svg
   | alt2      = Neutron
   | caption2  = Neutron ({{SubatomicParticle|neutron}}): {{SubatomicParticle|Up quark}}{{SubatomicParticle|Down quark}}{{SubatomicParticle|Down quark}}
   | width3    = 183
   | image3    = Quark structure antiproton.svg
   | alt3      = Antiproton
   | caption3  = Antiproton ({{SubatomicParticle|antiproton}}): {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}}
   | width4    = 183
   | image4    = Quark structure antineutron.svg
   | alt4      = Antineutron
   | caption4  = Antineutron ({{SubatomicParticle|antineutron}}): {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}}{{SubatomicParticle|Down antiquark}}
   | footer    = A proton (p) is composed of two up quarks (u) and one down quark (d): uud. A neutron (n) has one up quark (u) and two down quarks (d): udd. An [[antiproton]] ({{SubatomicParticle|antiproton}}) has two up [[antiquarks]] ({{SubatomicParticle|Up antiquark}}) and one down antiquark ({{SubatomicParticle|Down antiquark}}): {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}}. An [[antineutron]] ({{SubatomicParticle|antineutron}}) has one up antiquark ({{SubatomicParticle|Up antiquark}}) and two down antiquarks ({{SubatomicParticle|Down antiquark}}): {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}}{{SubatomicParticle|Down antiquark}}. The [[color charge]] ([[color charge|color assignment]]) of individual quarks is arbitrary, but all three colors (red, green, blue) must be present.
}}
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&nbsp;minutes, but they have important applications (see [[neutron radiation]] and [[neutron scattering]]). Protons not bound to other nucleons are the nuclei of hydrogen atoms when bound with an [[electron]] or{{snd}} if not bound to anything{{snd}} are [[ion]]s or cosmic rays.<!-- particles in beams in a collider are frequently referred to as “ions”! -->

Both the proton and the neutron are [[composite particle]]s, meaning that each is composed of smaller parts, namely three [[quarks]] each; although once thought to be so, neither is an [[elementary particle]]. A proton is composed of two [[up quark]]s and one [[down quark]], while the neutron has one up quark and two down quarks. Quarks are held together by the [[strong interaction|strong force]], or equivalently, by [[gluon]]s, which mediate the strong force at the quark level.

An up quark has [[electric charge]] {{sfrac|+|2|3}}&nbsp;[[elementary charge|''e'']], and a down quark has charge {{sfrac|&minus;|1|3}}&nbsp;''e'', so the summed electric charges of proton and neutron are +[[elementary charge|''e'']] and 0, respectively.{{efn|name=coeffs|The resultant coefficients are obtained by summation of the component charges: {{math|1=<big>Σ</big>''Q'' = {{sfrac|2|3}} + {{sfrac|2|3}} + <big>(</big>{{sfrac|&minus;|1|3}}<big>)</big> = {{sfrac|3|3}} = +1}} for proton, and {{math|1=<big>Σ</big>''Q'' = {{sfrac|2|3}} + <big>(</big>{{sfrac|&minus;|1|3}}<big>)</big> + <big>(</big>{{sfrac|&minus;|1|3}}<big>)</big> = {{sfrac|0|3}} = 0}} for neutron.}} 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 {{val|1.6726|e=-27|ul=kg}} ({{val|938.27|ul=MeV/c2}}), while for the neutron it is {{val|1.6749|e=-27|ul=kg}} ({{val|939.57|ul=MeV/c2}}); 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.<ref name=Griffiths2008/>{{rp|135–136}}

The [[Spin (physics)|spin]] of the nucleon is {{sfrac|1|2}}, which means that they are [[fermion]]s and, like [[electron]]s, are subject to the [[Pauli exclusion principle]]: no more than one nucleon, e.g. in an atomic nucleus, may occupy the same [[quantum state]].

The [[isospin]] and [[spin quantum number|spin]] quantum numbers of the nucleon have two states each, resulting in four combinations in total. An [[alpha particle]] is composed of four nucleons occupying all four combinations, namely, it has two protons (having [[singlet state|opposite spin]]) and two neutrons (also having opposite spin), and its net [[nuclear spin]] is zero. In larger nuclei constituent nucleons, by Pauli exclusion, are compelled to have relative [[motion]], which may also contribute to nuclear spin via the [[orbital quantum number]]. They spread out into [[nuclear shell]]s analogous to [[electron shell]]s known from chemistry.

Both the proton and neutron have [[magnetic moment]]s, though the [[nucleon magnetic moment]]s are anomalous and were unexpected when they were discovered in the 1930s.  The proton's magnetic moment, symbol ''&mu;''{{sub|p}}, is {{val|2.79|u=''μ''{{sub|N}}}}, whereas, if the proton were an elementary [[Dirac particle]], it should have a magnetic moment of {{val|1.0|u=''μ''{{sub|N}}}}.  Here the unit for the magnetic moments is the [[nuclear magneton]], symbol ''μ''{{sub|N}}, an atomic-scale [[unit of measure]]. The neutron's magnetic moment is ''&mu;''{{sub|n}} = {{val|-1.91|u=''μ''{{sub|N}}}}, 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.<ref name="Perk">{{cite book |author1-last = Perkins |author1-first = Donald H. |title = Introduction to High Energy Physics |url  = https://archive.org/details/introductiontohi0000perk |url-access = registration |pages=[https://archive.org/details/introductiontohi0000perk/page/201 201–202] |publisher = Addison Wesley |location=Reading, Massachusetts |date = 1982 |isbn = 978-0-201-05757-7}}</ref><ref name="MagMom">{{cite web |url=http://phys.org/news/2015-02-magnetic-moments-nuclear.html |title=Pinpointing the magnetic moments of nuclear matter |last1=Kincade |first1=Kathy |date=2 February 2015 |publisher=Phys.org |access-date=May 8, 2015 |archive-date=2 May 2015 |archive-url=https://web.archive.org/web/20150502123656/http://phys.org/news/2015-02-magnetic-moments-nuclear.html |url-status=live }}</ref>  The proton magnetic moment is exploited for [[nuclear magnetic resonance|NMR / MRI]] scanning.

===Stability===
A neutron in free state is an unstable particle, with a [[half-life]] around ten minutes. It undergoes [[beta decay|{{SubatomicParticle|Beta-}} decay]] (a type of [[radioactive decay]]) by turning into a proton while emitting an electron and an [[electron antineutrino]]. This reaction can occur because the mass of the neutron is slightly greater than that of the proton. (See the [[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]]'').

Inside a nucleus, on the other hand, combined protons and neutrons (nucleons) can be stable or unstable depending on the [[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 [[beta decay|{{SubatomicParticle|Beta+}} decay]] or [[electron capture]]. And inside still other nuclides, both protons and neutrons are stable and do not change form.

===Antinucleons===
{{Main article|Antineutron|Antiproton|Antimatter}}

Both nucleons have corresponding [[antiparticle]]s: the [[antiproton]] and the [[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]]. 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]]<ref>{{cite journal|author = Massam, T|year = 1965 |title = Experimental observation of antideuteron production |journal = Il Nuovo Cimento |volume = 39|issue = 1 |pages = 10–14 |doi = 10.1007/BF02814251|last2 = Muller|first2 = Th.|last3 = Righini|first3 = B.|last4 = Schneegans|first4 = M.|last5 = Zichichi|first5 = A.|bibcode = 1965NCimS..39...10M |s2cid = 122952224 }}</ref><ref>{{cite journal|author = Dorfan, D. E|date=June 1965|title = Observation of Antideuterons|journal = Phys. Rev. Lett.|volume = 14|issue = 24 |pages = 1003–1006| doi = 10.1103/PhysRevLett.14.1003|last2 = Eades|first2 = J.|last3 = Lederman|first3 = L. M.|last4 = Lee|first4 = W.|last5 = Ting|first5 = C. C.|bibcode=1965PhRvL..14.1003D}}</ref> and antihelium-3<ref>
{{cite journal
 |author=R. Arsenescu|year=2003
 |title=Antihelium-3 production in lead-lead collisions at 158 ''A'' GeV/''c''
 |journal=[[New Journal of Physics]]
 |volume=5 |issue=1
 |page=1
 |doi=10.1088/1367-2630/5/1/301
|bibcode = 2003NJPh....5....1A |display-authors=etal|doi-access=free}}</ref> nuclei.

==Tables of detailed properties==

===Nucleons===
{| class="wikitable sortable"  style="text-align:center; width:100%;"
|+ Nucleons (''[[Isospin|I]]'' = {{sfrac|1|2}}; ''[[strangeness|S]]'' = ''[[charm (quantum number)|C]]'' = ''[[bottomness|B]]'' = 0)
|-
! Particle <br />name
! class="unsortable" | Symbol
! class="unsortable" | Quark <br />content
! [[Mass]]<sup>{{ref|nucleonmass|[a]}}</sup>
! ''[[Isospin|I]]''<sub>3</sub>
! ''[[Total angular momentum|J]]''<sup>''[[Parity (physics)|P]]''</sup>
! ''[[Electric charge|Q]]''
! [[Magnetic moment]] ([[Nuclear magneton|''μ''<sub>N</sub>]])
! [[Mean lifetime]]
! class="unsortable" | Commonly decays to
|-
| style="text-align:left;" | [[proton]]<ref name=PDGProton group="PDG">[http://pdg.lbl.gov/2010/listings/rpp2010-list-p.pdf Particle listings – {{SubatomicParticle|Proton}}] {{Webarchive|url=https://web.archive.org/web/20170127034547/http://pdg.lbl.gov/2010/listings/rpp2010-list-p.pdf |date=2017-01-27 }}.</ref>
| {{SubatomicParticle|Proton}} / {{SubatomicParticle|Proton+}} / {{SubatomicParticle|Nucleon+}}
| {{SubatomicParticle|link=yes|Up quark}}{{SubatomicParticle|Up quark}}{{SubatomicParticle|link=yes|Down quark}}
| {{sort|1.00727646688|{{val|938.272013|(23)|ul=MeV/c2}} {{val|1.00727646677|(10)|ul=Da}}}}
| {{sort|0.5|+{{sfrac|1|2}}}}
| {{sort|0.5|{{sfrac|1|2}}}}<sup>+</sup>
| {{sort|1|{{val|+1|ul=e}}}}
| {{sort|2.7|{{val|2.792847356|(23)}}}}
| {{sort|+10|stable}}<sup>{{ref|protonlifetime|[b]}}</sup>
| unobserved
|-
| style="text-align:left;" | [[neutron]]<ref name=PDGNeutron group="PDG">[http://pdg.lbl.gov/2010/listings/rpp2010-list-n.pdf Particle listings – {{SubatomicParticle|Neutron}}] {{Webarchive|url=https://web.archive.org/web/20181003230501/http://pdg.lbl.gov/2010/listings/rpp2010-list-n.pdf |date=2018-10-03 }}.</ref>
| {{SubatomicParticle|Neutron}} / {{SubatomicParticle|Neutron0}} / {{SubatomicParticle|Nucleon0}}
| {{SubatomicParticle|Up quark}}{{SubatomicParticle|Down quark}}{{SubatomicParticle|Down quark}}
| {{sort|1.00866491560|{{val|939.565346|(23)|ul=MeV/c2}} {{val|1.00866491597|(43)|ul=Da}}}}
| {{sort|-0.5|{{sfrac|−|1|2}}}}
| {{sort|0.5|{{sfrac|1|2}}}}<sup>+</sup>
| {{sort|0|{{val|0|ul=e}}}}
| {{sort|-1.9|{{val|-1.91304273|(45)}}}}
| {{sort|+2|{{val|885.7|(8)|ul=s}}}}<sup>{{ref|neutronlifetime|[c]}}</sup>
| {{nowrap|{{SubatomicParticle|link=yes|Proton}} + {{SubatomicParticle|link=yes|Electron}} + {{SubatomicParticle|link=yes|Electron antineutrino}}}}
|-
| style="text-align:left;" | [[antiproton]]
| {{SubatomicParticle|Antiproton}} / {{PhysicsParticle|p|TR=−}} / {{PhysicsParticle|N|TR=−}}
| {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}}
| {{sort|1.00727646688|{{val|938.272013|(23)|ul=MeV/c2}} {{val|1.00727646677|(10)|ul=Da}}}}
| {{sort|-0.5|{{sfrac|−|1|2}}}}
| {{sort|0.5|{{sfrac|1|2}}}}<sup>+</sup>
| {{sort|-1|{{val|-1|ul=e}}}}
| {{sort|-2.7|{{val|-2.793|(6)}}}}
| {{sort|+10|stable}}<sup>{{ref|protonlifetime|[b]}}</sup>
| unobserved
|-
| style="text-align:left;" | [[antineutron]]
| {{SubatomicParticle|Antineutron}} / {{SubatomicParticle|Antineutron0}} / {{SubatomicParticle|Antinucleon0}}
| {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}}{{SubatomicParticle|Down antiquark}}
| {{sort|1.00866491560|{{val|939.485|(51)|ul=MeV/c2}} {{val|1.00866491597|(43)|ul=Da}}}}
| {{sort|0.5|{{sfrac|+|1|2}}}}
| {{sort|0.5|{{sfrac|1|2}}}}<sup>+</sup>
| {{sort|0|{{val|0|ul=e}}}}
| ?
| {{sort|+2|{{val|885.7|(8)|ul=s}}}}<sup>{{ref|neutronlifetime|[c]}}</sup>
| {{nowrap|{{SubatomicParticle|link=yes|Antiproton}} + {{SubatomicParticle|link=yes|Positron}} + {{SubatomicParticle|link=yes|Electron neutrino}}}}
|}
{{note|nucleonmass|a}} The masses of the proton and neutron are known with far greater precision in [[Dalton (unit)|dalton]]s (Da) than in MeV/''c''<sup>2</sup> due to the way in which these are defined. The conversion factor used is 1&nbsp;Da&nbsp;=&nbsp;{{val|931.494028|(23)|u=MeV/c2}}.

{{note|protonlifetime|b}} At least 10<sup>35</sup> years. See [[proton decay]].

{{note|neutronlifetime|c}} For [[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 {{val|2|e=-9}}<ref group="PDG" name="PDGProton" /> and the difference between the neutron and antineutron masses is on the order of {{val|9|6|e=-5|u=MeV/c2}}.<ref name=PDGNeutron group="PDG"/>

{| class="wikitable"
|+ Proton–antiproton CPT invariance tests
|-
! Test
! Formula
! PDG result<ref name=PDGProton group="PDG"/>
|-
| [[Mass]]
| <math>\frac{|m_{\rm p}-m_\bar{\rm p}|}{m_{\rm p}}</math>
| <{{val|2|e=-9}}
|-
| [[Charge-to-mass ratio]]
| <math>\frac{\left|\frac{q_\bar{\rm p}}{m_\bar{\rm p}}\right|}{\left(\frac{q_{\rm p}}{m_{\rm p}}\right)}</math>
| {{val|0.99999999991|(9)}}
|-
| Charge-to-mass-to-mass ratio
| <math>\frac{\left|\frac{q_\bar{\rm p}}{m_\bar{\rm p}}\right| - \frac{q_{\rm p}}{m_{\rm p}}}{\frac{q_{\rm p}}{m_{\rm p}}}</math>
| {{val|-9|9|e=-11}}
|-
| Charge
| <math>\frac{\left|q_{\rm p} + q_\bar{\rm p}\right|}{e}</math>
| <{{val|2|e=-9}}
|-
| Electron charge
| <math>\frac{\left|q_{\rm p} + q_{\rm e}\right|}{e}</math>
| <{{val|1|e=-21}}
|-
| Magnetic moment
| <math>\frac{\left|\mu_{\rm p} + \mu_\bar{p}\right|}{\mu_{\rm p}}</math>
| {{val|-0.1|2.1|e=-3}}
|}

===Nucleon resonances===
'''Nucleon resonances''' are [[excited state]]s of nucleon particles, often corresponding to one of the quarks having a flipped [[Spin (physics)|spin]] state, or with different [[Azimuthal quantum number|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({{mvar|m}}) {{mvar|L<sub>IJ</sub>}}, where {{mvar|m}} is the particle's approximate mass, {{mvar|L}} is the orbital angular momentum (in the [[spectroscopic notation]]) of the nucleon–meson pair, produced when it decays, and {{mvar|I}} and {{mvar|J}} are the particle's [[isospin]] and [[total angular momentum]] respectively. Since nucleons are defined as having {{sfrac|1|2}} 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 {{mvar|L<sub>IJ</sub>}} ({{mvar|m}}); for example, a proton can be denoted as "N(939) S<sub>11</sub>" or "S<sub>11</sub> (939)".

The table below lists only the base resonance; each individual entry represents 4&nbsp;[[baryon]]s: 2&nbsp;nucleon resonances particles and their 2&nbsp;antiparticles. Each resonance exists in a form with a positive [[electric charge]] ({{mvar|Q}}), with a quark composition of {{SubatomicParticle|Up quark}}{{SubatomicParticle|Up quark}}{{SubatomicParticle|Down quark}} like the proton, and a neutral form, with a quark composition of {{SubatomicParticle|Up quark}}{{SubatomicParticle|Down quark}}{{SubatomicParticle|Down quark}} like the neutron, as well as the corresponding antiparticles with antiquark compositions of {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}} and {{SubatomicParticle|Up antiquark}}{{SubatomicParticle|Down antiquark}}{{SubatomicParticle|Down antiquark}} respectively. Since they contain no [[strange quark|strange]], [[charm quark|charm]], [[bottom quark|bottom]], or [[top quark|top]] quarks, these particles do not possess [[strangeness]], etc.

The table only lists the resonances with an [[isospin]] = {{sfrac|1|2}}. For resonances with [[isospin]] = {{sfrac|3|2}}, see the [[Delta baryon|article on Delta baryons]].

{| class="wikitable sortable"  style="text-align:center"
|+ Nucleon resonances with [[Isospin|I]] = {{sfrac|1|2}}
|-
! Symbol
! &nbsp;''[[Total angular momentum|J]]''<sup>''[[Parity (physics)|P]]''</sup>&nbsp;
! PDG [[mass]] average<br />([[electron volt|MeV]]/[[speed of light|''c'']]<sup>2</sup>)
! [[Relativistic Breit–Wigner distribution|Full width]]<br />(MeV/''c''<sup>2</sup>)
! Pole position<br />(real part)
! Pole position<br />(−2 × imaginary part)
! class=unsortable | Common decays <br />(Γ<sub>i</sub>/Γ > 50%)
|-
| N(939) P<sub>11</sub><br /><ref name="PDGN939" group="PDG">[http://pdg.lbl.gov/2011/reviews/rpp2011-rev-n-delta-resonances.pdf Particle listings — Note on N and Delta Resonances] {{Webarchive|url=https://web.archive.org/web/20210327004538/https://pdg.lbl.gov/2011/reviews/rpp2011-rev-n-delta-resonances.pdf |date=2021-03-27 }}.</ref>†
| {{sort|0.5|{{sfrac|1|2}}}}<sup>+</sup>
| 939
| †
| †
| †
| †
|-
| N(1440) P<sub>11</sub><br /><ref name="PDGN1440" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1440-P11.pdf Particle listings — N(1440)] {{Webarchive|url=https://web.archive.org/web/20210330015434/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1440-P11.pdf |date=2021-03-30 }}.</ref><br /> (the [[Roper resonance]])
| {{sort|0.5|{{sfrac|1|2}}}}<sup>+</sup>
| 1440<br />(1420–1470) 
| 300<br />(200–450) 
| 1365<br />(1350–1380)
| 190<br />(160–220)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}}}}
|-
| N(1520) D<sub>13</sub><br /><ref name="PDGN1520" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1520-D13.pdf Particle listings — N(1520)] {{Webarchive|url=https://web.archive.org/web/20210329120821/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1520-D13.pdf |date=2021-03-29 }}.</ref>
| {{sort|1.5|{{sfrac|3|2}}}}<sup>−</sup>
| 1520<br />(1515–1525)
| 115<br />(100–125)
| 1510<br />(1505–1515)
| 110<br />(105–120)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}}}}
|-
| N(1535) S<sub>11</sub><br /><ref name="PDGN1535" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1535-S11.pdf Particle listings — N(1535)] {{Webarchive|url=https://web.archive.org/web/20210329222330/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1535-S11.pdf |date=2021-03-29 }}.</ref>
| {{sort|0.5|{{sfrac|1|2}}}}<sup>−</sup>
| 1535<br />(1525–1545)
| 150<br />(125–175)
| 1510<br />(1490–1530)
| 170<br />(90–250)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} or}} <br />{{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Eta}}}}
|-
| N(1650) S<sub>11</sub><br /><ref name="PDGN1650" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1650-S11.pdf Particle listings — N(1650)] {{Webarchive|url=https://web.archive.org/web/20210330004339/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1650-S11.pdf |date=2021-03-30 }}.</ref>
| {{sort|0.5|{{sfrac|1|2}}}}<sup>−</sup>
| 1650<br />(1645–1670)
| 165<br />(145–185)
| 1665<br />(1640–1670)
| 165<br />(150–180)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}}}}
|-
| N(1675) D<sub>15</sub><br /><ref name="PDGN1675" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1675-D15.pdf Particle listings — N(1675)] {{Webarchive|url=https://web.archive.org/web/20210328054543/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1675-D15.pdf |date=2021-03-28 }}.</ref>
| {{sort|2.5|{{sfrac|5|2}}}}<sup>−</sup>
| 1675<br />(1670–1680)
| 150<br />(135–165)
| 1660<br />(1655–1665)
| 135<br />(125–150)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} + {{SubatomicParticle|link=yes|Pion}} or}} <br />{{nowrap|{{SubatomicParticle|link=yes|Delta}} + {{SubatomicParticle|link=yes|Pion}}}}
|-
| N(1680) F<sub>15</sub><br /><ref name="PDGN1680" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1680-F15.pdf Particle listings — N(1680)] {{Webarchive|url=https://web.archive.org/web/20210329051338/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1680-F15.pdf |date=2021-03-29 }}.</ref>
| {{sort|2.5|{{sfrac|5|2}}}}<sup>+</sup>
| 1685<br />(1680–1690)
| 130<br />(120–140)
| 1675<br />(1665–1680)
| 120<br />(110–135)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}}}}
|-
| N(1700) D<sub>13</sub><br /><ref name="PDGN1700" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1700-D13.pdf Particle listings — N(1700)] {{Webarchive|url=https://web.archive.org/web/20210328060307/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1700-D13.pdf |date=2021-03-28 }}.</ref>
| {{sort|1.5|{{sfrac|3|2}}}}<sup>−</sup>
| 1700<br />(1650–1750)
| 100<br />(50–150)
| 1680<br />(1630–1730)
| 100<br />(50–150)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} + {{SubatomicParticle|link=yes|Pion}}}}
|-
| N(1710) P<sub>11</sub><br /><ref name="PDGN1710" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1710-P11.pdf Particle listings — N(1710)] {{Webarchive|url=https://web.archive.org/web/20210328131441/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1710-P11.pdf |date=2021-03-28 }}.</ref>
| {{sort|0.5|{{sfrac|1|2}}}}<sup>+</sup>
| 1710<br />(1680–1740)
| 100<br />(50–250)
| 1720<br />(1670–1770)
| 230<br />(80–380)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} + {{SubatomicParticle|link=yes|Pion}}}}
|-
| N(1720) P<sub>13</sub><br /><ref name="PDGN1720" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-1720-P13.pdf Particle listings — N(1720)] {{Webarchive|url=https://web.archive.org/web/20210330022733/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-1720-P13.pdf |date=2021-03-30 }}.</ref>
| {{sort|1.5|{{sfrac|3|2}}}}<sup>+</sup>
| 1720<br />(1700–1750)
| 200<br />(150–300)
| 1675<br />(1660–1690)
| 115–275
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} + {{SubatomicParticle|link=yes|Pion}} or}} <br />{{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Rho}}}}
|-
| N(2190) G<sub>17</sub><br /><ref name="PDGN2190" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-2190-G17.pdf Particle listings — N(2190)] {{Webarchive|url=https://web.archive.org/web/20210329020350/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-2190-G17.pdf |date=2021-03-29 }}.</ref>
| {{sort|3.5|{{sfrac|7|2}}}}<sup>−</sup>
| 2190<br />(2100–2200)
| 500<br />(300–700)
| 2075<br />(2050–2100)
| 450<br />(400–520)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} (10—20%)}}
<!-- ** http://pdg.lbl.gov/2011/listings/rpp2011-list-N-2200-D15.pdf -->
|-
| N(2220) H<sub>19</sub><br /><ref name="PDGN2220" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-2220-H19.pdf Particle listings — N(2220)] {{Webarchive|url=https://web.archive.org/web/20210329192105/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-2220-H19.pdf |date=2021-03-29 }}.</ref>
| {{sort|4.5|{{sfrac|9|2}}}}<sup>+</sup>
| 2250<br />(2200–2300)
| 400<br />(350–500)
| 2170<br />(2130–2200)
| 480<br />(400–560)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} (10—20%)}}
|-
| N(2250) G<sub>19</sub><br /><ref name="PDGN2250" group="PDG">[http://pdg.lbl.gov/2011/listings/rpp2011-list-N-2250-G19.pdf Particle listings — N(2250)] {{Webarchive|url=https://web.archive.org/web/20210329211112/https://pdg.lbl.gov/2011/listings/rpp2011-list-N-2250-G19.pdf |date=2021-03-29 }}.</ref>
| {{sort|4.5|{{sfrac|9|2}}}}<sup>−</sup>
| 2250<br />(2200–2350)
| 500<br />(230–800)
| 2200<br />(2150–2250)
| 450<br />(350–550)
| {{nowrap|{{SubatomicParticle|link=yes|Nucleon}} + {{SubatomicParticle|link=yes|Pion}} (5—15%)}}
|}
† ''The P<sub>11</sub>(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]].''<ref>{{cite web |url=https://pubchem.ncbi.nlm.nih.gov/compound/Lithium-6 |title=Lithium-6. Compound summary |website=PubChem |publisher=National Library of Medicine |access-date=2021-04-08 |archive-date=2021-11-19 |archive-url=https://web.archive.org/web/20211119032317/https://pubchem.ncbi.nlm.nih.gov/compound/Lithium-6 |url-status=live }}</ref>

==Quark model classification==
In the [[quark model]] with [[SU(2)]] [[flavour (particle physics)|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 (physics)|spin]]-{{sfrac|1|2}} [[baryon]]s, known as the [[eightfold way (physics)|Eightfold way]]. The other members of this octet are the [[hyperon]]s [[strangeness|strange]] [[isospin|isotriplet]] [[Sigma baryon|{{SubatomicParticle|Sigma+}}, {{SubatomicParticle|Sigma0}}, {{SubatomicParticle|Sigma-}}]], the [[Lambda baryon|{{SubatomicParticle|Lambda}}]] and the strange isodoublet [[Xi baryon|{{SubatomicParticle|Xi0}}, {{SubatomicParticle|Xi-}}]]. One can extend this multiplet in [[SU(4)]] flavour (with the inclusion of the [[charm quark]]) to the ground-state '''20'''-plet, or to [[SU(6)]] flavour (with the inclusion of the [[top quark|top]] and [[bottom quark]]s) to the ground-state '''56'''-plet.

The article on [[isospin]] provides an explicit expression for the nucleon wave functions in terms of the quark flavour eigenstates.

==Models==<!-- This section is linked from [[Casimir effect]] -->
{{confusing|section|date=August 2007}}

Although it is known that the nucleon is made from three quarks, {{As of|2006|lc=on}}, 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 [[supercomputer]]s. However, several analytic models also exist:

===Skyrmion models===
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 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 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''<ref>Chodos et al. [https://doi.org/10.1103/PhysRevD.9.3471 "New extended model of hadrons"] {{Webarchive|url=https://web.archive.org/web/20231230134936/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.9.3471 |date=2023-12-30 }}, Phys. Rev. D 9, 3471 (1974).</ref><ref>Chodos et al. [https://doi.org/10.1103/PhysRevD.10.2599 "Baryon structure in the bag theory"] {{Webarchive|url=https://web.archive.org/web/20231230134924/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.10.2599 |date=2023-12-30 }}, Phys. Rev. D 10, 2599 (1974).</ref><ref>DeGrand et al. [https://doi.org/10.1103/PhysRevD.12.2060 "Masses and other parameters of the light hadrons"] {{Webarchive|url=https://web.archive.org/web/20231230134817/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.12.2060 |date=2023-12-30 }}, Phys. Rev. D 12, 2060 (1975).</ref> confines quarks and gluons interacting through [[quantum chromodynamics]] 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]] 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.

Although the basic bag model does not provide a pion-mediated interaction, it describes excellently the nucleon–nucleon forces through the 6&nbsp;quark bag ''s''-channel mechanism using the ''P''-matrix.<ref>{{cite journal |last1=Jaffe |first1=R. L. |author1-link=Robert Jaffe (physicist) |author2-link=Francis E. Low |last2=Low |first2=F. E. |year=1979 |title=Connection between quark-model eigenstates and low-energy scattering |journal=Phys. Rev. D |volume=19 |issue=7| page=2105 |doi=10.1103/PhysRevD.19.2105 |bibcode=1979PhRvD..19.2105J }}</ref><ref>
{{cite journal |last1=Yu |last2=Simonov |first2=A. |year=1981 |title=The quark compound bag model and the Jaffe-Low ''P''-matrix |journal=[[Physics Letters B]] |volume=107 |issue=1–2 |page=1 |doi=10.1016/0370-2693(81)91133-3 |bibcode=1981PhLB..107....1S}}</ref>

===Chiral bag model===
The ''chiral bag model''<ref>{{cite journal
 |author1-link=Gerald E. Brown  |first1=Gerald E. |last1=Brown
 |author2-link=Mannque Rho  |first2=Mannque |last2=Rho
 |date=March 1979
 |title=The little bag
 |journal=[[Physics Letters B]]
 |volume=82  |issue=2  |pages=177–180
 |doi=10.1016/0370-2693(79)90729-9
 |bibcode=1979PhLB...82..177B
}}</ref><ref>{{cite journal
 |last1=Vepstas |first1=L.
 |last2=Jackson |first2=A. D.
 |last3=Goldhaber |first3=A. S.
 |year=1984
 |title=Two-phase models of baryons and the chiral Casimir effect
 |journal=[[Physics Letters B]]
 |volume=140  |issue=5–6  |pages=280–284
 |bibcode=1984PhLB..140..280V
 |doi=10.1016/0370-2693(84)90753-6
}}</ref> 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|2017}}, 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 space]]s 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'',<ref>{{cite journal
 |last1=Vepstas |first1=L.
 |last2=Jackson |first2=A. D.
 |year=1990
 |title=Justifying the chiral bag
 |journal=[[Physics Reports]]
 |volume=187  |issue=3  |pages=109–143
 |bibcode=1990PhR...187..109V
 |doi=10.1016/0370-1573(90)90056-8
}}</ref> after the fading of [[Lewis Carroll]]'s [[Cheshire Cat]] 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]] descriptions.

==See also==
* [[SLAC bag model]]
* [[Hadron]]s
* [[Electroweak interaction]]

==Footnotes==
{{notelist|1}}

==References==
{{Reflist}}

===Particle listings===
{{Reflist|group=PDG|liststyle=decimal-leading-zero}}

==Further reading==
* {{cite book
 |first1=A. W. |last1=Thomas 
 |first2=W. |last2=Weise
 |year=2001
 |title=The Structure of the Nucleon
 |publisher=Wiley-WCH |place=Berlin, DE
 |isbn=3-527-40297-7
}}
* {{cite book
 |last1=Brown |first1=G .E.
 |last2=Jackson |first2=A. D.
 |year=1976
 |title=The Nucleon–Nucleon Interaction
 |publisher=[[North-Holland Publishing]]
 |isbn=978-0-7204-0335-0
}}
* {{cite journal
 |last=Nakamura |first=N.
 |year=2011
 |author2=Particle Data Group
 |author2-link=Particle Data Group
 |display-authors=etal 
 |journal=[[Journal of Physics G]]
 |volume=37 |issue=7 |page=075021
 |doi=10.1088/0954-3899/37/7A/075021 |doi-access=free
 |title=Review of Particle Physics
 |bibcode = 2010JPhG...37g5021N|hdl=10481/34593
 |hdl-access=free
 }}

{{particles}}

{{Authority control}}

[[Category:Hadrons]]
[[Category:Baryons]]
[[Category:Neutron]]
[[Category:Nucleons| ]]