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{{Short description|Force that acts between the protons and neutrons of atoms}}
{{about|the force that holds nucleons together in a nucleus|the force that holds quarks together in a nucleon that is also called the '''strong nuclear force'''|Strong interaction}}
{{Distinguish|Weak nuclear force}}
{{Nuclear physics}}
[[File:ReidForce2.jpg|thumb|350px|Force (as multiples of {{val|10,000|u=N}}) between two nucleons as a function of distance as computed from the Reid potential (1968).<ref name="Reid">{{cite journal |last1=Reid |first1=R. V. |year=1968 |title=Local phenomenological nucleon–nucleon potentials |journal=Annals of Physics |volume=50 |issue=3 |pages=411–448 |bibcode = 1968AnPhy..50..411R |doi = 10.1016/0003-4916(68)90126-7 }}</ref> The spins of the neutron and proton are aligned, and they are in the [[term symbol|S]] angular momentum state. The attractive (negative) force has a maximum at a distance of about 1&nbsp;fm with a force of about {{val|25000|u=N}}. Particles much closer than a distance of 0.8&nbsp;fm experience a large repulsive (positive) force. Particles separated by a distance greater than 1&nbsp;fm are still attracted (Yukawa potential), but the force falls as an exponential function of distance.]]
[[File:ReidPotential.jpg|thumb|350px|Corresponding potential energy (in units of MeV) of two nucleons as a function of distance as computed from the Reid potential. The potential well has a minimum at a distance of about 0.8&nbsp;fm. With this potential nucleons can become bound with a negative "binding energy".]]

The '''nuclear force''' (or '''nucleon–nucleon interaction''', '''residual strong force''', or, historically, '''strong nuclear force''') is a force that acts between [[Hadron|hadrons]], most commonly observed between [[proton]]s and [[neutron]]s of [[atom]]s. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1&nbsp;''e'', they experience an [[Coulomb's law|electric force]] that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electrostatic force. The nuclear force binds nucleons into [[Atomic nucleus|atomic nuclei]].

The nuclear force is powerfully attractive between nucleons at distances of about 0.8&nbsp;[[femtometre]] (fm, or {{val|0.8||e=−15|ul=m}}), but it rapidly decreases to insignificance at distances beyond about 2.5&nbsp;fm. At distances less than 0.7&nbsp;fm, the nuclear force becomes repulsive. This repulsion is responsible for the size of nuclei, since nucleons can come no closer than the force allows. (The size of an atom, of size in the order of [[angstrom]]s (Å, or {{val|e=−10|u=m}}), is five orders of magnitude larger.) The nuclear force is not simple, though, as it depends on the nucleon spins, has a tensor component, and may depend on the relative momentum of the nucleons.<ref name="Krane">{{cite book | author=Kenneth S. Krane | title=Introductory Nuclear Physics | year= 1988 | publisher=Wiley & Sons | isbn=0-471-80553-X }}</ref>

The nuclear force has an essential role in storing energy that is used in [[nuclear power]] and [[nuclear weapons]]. [[Work (physics)|Work (energy)]] is required to bring charged protons together against their electric repulsion. This energy is stored when the protons and neutrons are bound together by the nuclear force to form a nucleus. The mass of a nucleus is less than the sum total of the individual masses of the protons and neutrons. The difference in masses is known as the [[mass defect]], which can be expressed as an energy equivalent. Energy is released when a heavy nucleus breaks apart into two or more lighter nuclei. This energy is the internucleon potential energy that is released when the nuclear force no longer holds the charged nuclear fragments together.<ref>[http://www.furryelephant.com/content/radioactivity/binding-energy-mass-defect/ Binding Energy, Mass Defect] {{webarchive |url=https://web.archive.org/web/20170618092355/http://www.furryelephant.com/content/radioactivity/binding-energy-mass-defect/ |date=2017-06-18 }}, Furry Elephant physics educational site, retrieved 2012-07-01.</ref><ref>[http://mragheb.com/NPRE%20402%20ME%20405%20Nuclear%20Power%20Engineering/Nuclear%20Processes%20The%20Strong%20Force.pdf Chapter 4. NUCLEAR PROCESSES, THE STRONG FORCE] {{webarchive |url=https://web.archive.org/web/20130903021557/http://mragheb.com/NPRE%20402%20ME%20405%20Nuclear%20Power%20Engineering/Nuclear%20Processes%20The%20Strong%20Force.pdf |date=2013-09-03 }}, M. Ragheb, 1/30/2013, University of Illinois.</ref>

A quantitative description of the nuclear force relies on equations that are partly [[empirical research|empirical]]. These equations model the internucleon potential energies, or potentials. (Generally, forces within a system of particles can be more simply modelled by describing the system's potential energy; the negative gradient of a [[scalar potential|potential]] is equal to the vector force.) The constants for the equations are phenomenological, that is, determined by fitting the equations to experimental data. The internucleon potentials attempt to describe the properties of nucleon–nucleon interaction. Once determined, any given potential can be used in, e.g., the [[Schrödinger equation]] to determine the [[Quantum mechanics|quantum mechanical]] properties of the nucleon system.

The [[discovery of the neutron]] in 1932 revealed that atomic nuclei were made of protons and neutrons, held together by an attractive force. By 1935 the nuclear force was conceived to be transmitted by particles called [[meson]]s. This theoretical development included a description of the [[Yukawa potential]], an early example of a nuclear potential. [[Pion]]s, fulfilling the prediction, were discovered experimentally in 1947. By the 1970s, the [[quark model]] had been developed, by which the mesons and nucleons were viewed as composed of quarks and gluons. By this new model, the nuclear force, resulting from the exchange of mesons between neighbouring nucleons, is a multiparticle interaction, the collective effect of [[Strong interaction|strong force]] on the underlining structure of the nucleons.

== Description ==
[[File:Nuclear Force.png|thumb|Comparison between the Nuclear Force and the Coulomb Force.
'''a''' – residual strong force (nuclear force), rapidly decreases to insignificance at distances beyond about 2.5 fm,
'''b''' – at distances less than ~ 0.7&nbsp;fm between nucleons centres the nuclear force becomes repulsive,
'''c''' – coulomb repulsion force between two protons (over 3&nbsp;fm, force becomes the main),
'''d''' – equilibrium position for proton – proton, 
'''r''' – radius of a nucleon (a cloud composed of three quarks).
Note: 1&nbsp;fm = {{val|e=-15|u=m}}]]
While the nuclear force is usually associated with nucleons, more generally this force is felt between [[hadron]]s, or particles composed of [[quark]]s. At small separations between nucleons (less than ~&nbsp;0.7&nbsp;fm between their centres, depending upon spin alignment) the force becomes repulsive, which keeps the nucleons at a certain average separation. For identical nucleons (such as two neutrons or two protons) this repulsion arises from the [[Pauli exclusion principle|Pauli exclusion]] force. A Pauli repulsion also occurs between quarks of the same [[flavour (particle physics)|flavour]] from different nucleons (a proton and a neutron).

===Field strength===
At distances larger than 0.7&nbsp;fm the force becomes attractive between spin-aligned nucleons, becoming maximal at a centre–centre distance of about 0.9&nbsp;fm. Beyond this distance the force drops exponentially, until beyond about 2.0&nbsp;fm separation, the force is negligible. Nucleons have a radius of about 0.8&nbsp;fm.<ref name="Povh">{{cite book | last1=Povh | first1=B.| last2=Rith| first2=K.| last3=Scholz| first3=C.| last4=Zetsche| first4=F. |title=Particles and Nuclei: An Introduction to the Physical Concepts | location=Berlin | publisher=Springer-Verlag |pages=73| year=2002 | isbn=978-3-540-43823-6 }}</ref>

At short distances (less than 1.7&nbsp;fm or so), the attractive nuclear force is stronger than the repulsive [[Coulomb force]] between protons; it thus overcomes the repulsion of protons within the nucleus. However, the Coulomb force between protons has a much greater range as it varies as the inverse square of the charge separation, and Coulomb repulsion thus becomes the only significant force between protons when their separation exceeds about {{val|2|to|2.5|u=fm}}.

The nuclear force has a spin-dependent component. The force is stronger for particles with their spins aligned than for those with their spins anti-aligned. If two particles are the same, such as two neutrons or two protons, the force is not enough to bind the particles, since the spin vectors of two particles of the same type must point in opposite directions when the particles are near each other and are (save for spin) in the same quantum state. This requirement for [[fermion]]s stems from the [[Pauli exclusion principle]]. For fermion particles of different types, such as a proton and neutron, particles may be close to each other and have aligned spins without violating the Pauli exclusion principle, and the nuclear force may bind them (in this case, into a [[deuteron]]), since the nuclear force is much stronger for spin-aligned particles. But if the particles' spins are anti-aligned, the nuclear force is too weak to bind them, even if they are of different types.

The nuclear force also has a tensor component which depends on the interaction between the nucleon spins and the angular momentum of the nucleons, leading to deformation from a simple spherical shape.

=== Nuclear binding ===
To disassemble a nucleus into unbound protons and neutrons requires work against the nuclear force. Conversely, energy is released when a nucleus is created from free nucleons or other nuclei: the [[nuclear binding energy]]. Because of [[mass–energy equivalence]] (i.e. Einstein's formula {{nowrap|1=''E'' = ''mc''<sup>2</sup>}}), releasing this energy causes the mass of the nucleus to be lower than the total mass of the individual nucleons, leading to the so-called "mass defect".<ref>
{{cite web
  | last = Stern | first = Dr. Swapnil Nikam
  | title = Nuclear Binding Energy
  | work = From Stargazers to Starships
  | publisher = NASA website
  | date = February 11, 2009
  | url = http://www-istp.gsfc.nasa.gov/stargaze/SnucEnerA-2.htm
  | access-date = 2010-12-30
  | archive-date = 2016-04-09
  | archive-url = https://web.archive.org/web/20160409112854/http://www-istp.gsfc.nasa.gov/stargaze/SnucEnerA-2.htm
  | url-status = live
}}</ref>

The nuclear force is nearly independent of whether the nucleons are neutrons or protons. This property is called ''charge independence''. The force depends on whether the [[Spin (physics)|spins]] of the nucleons are parallel or antiparallel, as it has a non-central or ''[[tensor]]'' component. This part of the force does not conserve orbital [[angular momentum]], which under the action of [[central forces]] is conserved.

The symmetry resulting in the strong force, proposed by [[Werner Heisenberg]], is that protons and neutrons are identical in every respect, other than their charge. This is not completely true, because neutrons are a tiny bit heavier, but it is an approximate symmetry. Protons and neutrons are therefore viewed as the same particle, but with different [[isospin]] quantum numbers; conventionally, the proton is ''isospin up,'' while the neutron is ''isospin down''. The strong force is invariant under SU(2) isospin transformations, just as other interactions between particles are invariant under SU(2) transformations of [[Spin (physics)|intrinsic spin]]. In other words, both isospin and intrinsic spin transformations are [[Group isomorphism|isomorphic]] to the [[Representation theory of SU(2)|SU(2) symmetry group.]] There are only strong attractions when the total isospin of the set of interacting particles is 0, which is confirmed by experiment.<ref>Griffiths, David, Introduction to Elementary Particles</ref>

Our understanding of the nuclear force is obtained by scattering experiments and the binding energy of light nuclei.

[[File:pn scatter pi0.svg|thumb|300px|A simplified [[Feynman diagram]] of a strong [[proton]]–[[neutron]] interaction mediated by a [[virtual particle|virtual]] neutral [[pion]]. Time proceeds from left to right.]] The nuclear force occurs by the exchange of virtual light [[meson]]s, such as the [[virtual particle|virtual]] [[pion]]s, as well as two types of virtual mesons with spin ([[vector meson]]s), the [[rho meson]]s and the [[omega meson]]s. The vector mesons account for the spin-dependence of the nuclear force in this "virtual meson" picture.

The nuclear force is distinct from what historically was known as the [[weak nuclear force]]. The [[weak interaction]] is one of the four [[fundamental interactions]], and plays a role in processes such as [[beta decay]]. The weak force plays no role in the interaction of nucleons, though it is responsible for the decay of neutrons to protons and vice versa.

== History ==
The nuclear force has been at the heart of [[nuclear physics]] ever since the field was born in 1932 with the discovery of the [[neutron]] by [[James Chadwick]]. The traditional goal of nuclear physics is to understand the properties of [[atomic nuclei]] in terms of the "bare" interaction between pairs of nucleons, or nucleon–nucleon forces (NN&nbsp;forces).

Within months after the discovery of the neutron, [[Werner Heisenberg]]<ref>{{cite journal |last=Heisenberg |first=W. |title=Über den Bau der Atomkerne. I |language=de |journal=[[Z. Phys.]] |volume=77 |pages=1–11 |year=1932 |issue=1–2 |doi=10.1007/BF01342433 |ref={{harvid|Heisenberg|1932 I}} |bibcode=1932ZPhy...77....1H |s2cid=186218053 }}</ref><ref>{{cite journal |last=Heisenberg |first=W. |title=Über den Bau der Atomkerne. II |language=de |journal=Z. Phys. |volume=78 |pages=156–164 |year=1932 |doi=10.1007/BF01337585 |issue=3–4 |ref={{harvid|Heisenberg|1932 II}} |bibcode=1932ZPhy...78..156H |s2cid=186221789 }}</ref><ref>{{cite journal |last=Heisenberg |first=W. |title=Über den Bau der Atomkerne. III |language=de |journal=Z. Phys. |volume=80 |pages=587–596 |year=1933 |doi=10.1007/BF01335696 |issue=9–10 |ref={{harvid|Heisenberg|1933 III}} |bibcode=1933ZPhy...80..587H |s2cid=126422047 }}</ref> and [[Dmitri Ivanenko]]<ref>Iwanenko, D. D., The neutron hypothesis, Nature '''129''' (1932) 798.</ref> had proposed proton–neutron models for the nucleus.<ref>Miller A. I. ''Early Quantum Electrodynamics: A Sourcebook'', Cambridge University Press, Cambridge, 1995, {{ISBN|0521568919}}, pp.&nbsp;84–88.</ref> Heisenberg approached the description of protons and neutrons in the nucleus through quantum mechanics, an approach that was not at all obvious at the time. Heisenberg's theory for protons and neutrons in the nucleus was a "major step toward understanding the nucleus as a quantum mechanical system".<ref name="BrownRechenberg">{{cite book |last1=Brown |first1=L. M. |last2=Rechenberg |first2=H. |author-link2=Helmut Rechenberg |year=1996 |title=The Origin of the Concept of Nuclear Forces |location=Bristol and Philadelphia |publisher=Institute of Physics Publishing |url=https://books.google.com/books?id=IJPTgDTOmgMC&q=heisenberg+proton+neutron+model&pg=PA33 |isbn=0750303735 |access-date=2020-10-19 |archive-date=2023-12-30 |archive-url=https://web.archive.org/web/20231230135136/https://books.google.com/books?id=IJPTgDTOmgMC&q=heisenberg+proton+neutron+model&pg=PA33#v=snippet&q=heisenberg%20proton%20neutron%20model&f=false |url-status=live }}</ref> Heisenberg introduced the first theory of nuclear exchange forces that bind the nucleons. He considered protons and neutrons to be different quantum states of the same particle, i.e., nucleons distinguished by the value of their nuclear [[isospin]] quantum numbers.

One of the earliest models for the nucleus was the [[Semi-empirical mass formula#The liquid-drop model|liquid-drop model]] developed in the 1930s. One property of nuclei is that the average binding energy per nucleon is approximately the same for all stable nuclei, which is similar to a liquid drop. The liquid-drop model treated the nucleus as a drop of incompressible nuclear fluid, with nucleons behaving like molecules in a liquid. The model was first proposed by [[George Gamow]] and then developed by [[Niels Bohr]], [[Werner Heisenberg]], and [[Carl Friedrich von Weizsäcker]]. This crude model did not explain all the properties of the nucleus, but it did explain the spherical shape of most nuclei. The model also gave good predictions for the binding energy of nuclei.

In 1934, [[Hideki Yukawa]] made the earliest attempt to explain the nature of the nuclear force. According to his theory, massive [[boson]]s ([[meson]]s) mediate the interaction between two nucleons. In light of [[quantum chromodynamics]] (QCD)—and, by extension, the [[Standard Model]]—meson theory is no longer perceived as fundamental. But the meson-exchange concept (where [[hadron]]s are treated as [[elementary particles]]) continues to represent the best working model for a quantitative ''NN'' potential. The Yukawa potential (also called a screened [[Coulomb potential]]) is a potential of the form
: <math>V_\text{Yukawa}(r) = -g^2 \frac{e^{-\mu r}}{r},</math>
where ''g'' is a magnitude scaling constant, i.e., the amplitude of potential, <math>\mu</math> is the Yukawa particle mass, ''r'' is the radial distance to the particle. The potential is [[Monotonic function|monotone increasing]], [[Force#Potential energy|implying]] that the force is always attractive. The constants are determined empirically. The Yukawa potential depends only on the distance ''r'' between particles, hence it models a [[central force]].

Throughout the 1930s a group at [[Columbia University]] led by [[I.&nbsp;I. Rabi]] developed magnetic-resonance techniques to determine the magnetic moments of nuclei. These measurements led to the discovery in 1939 that the [[deuteron]] also possessed an [[quadrupole|electric quadrupole moment]].<ref name="Rigden">{{cite book | author=John S. Rigden | author-link=John S. Rigden | title=Rabi, Scientist and Citizen | location=New York | publisher=Basic Books, Inc. | pages=99–114 | year=1987 | url=https://books.google.com/books?id=Qgv9Xjv8_LYC&q=rabi+kellogg+zacharias+magnetic+moment+neutron&pg=PA106 | isbn=9780674004351 | access-date=May 9, 2015 | archive-date=December 30, 2023 | archive-url=https://web.archive.org/web/20231230135203/https://books.google.com/books?id=Qgv9Xjv8_LYC&q=rabi+kellogg+zacharias+magnetic+moment+neutron&pg=PA106#v=snippet&q=rabi%20kellogg%20zacharias%20magnetic%20moment%20neutron&f=false | url-status=live }}</ref><ref name="KRRZ">{{cite journal |last1=Kellogg |first1=J. M. |last2=Rabi |first2=I. I. |last3=Ramsey |first3=N. F. |last4=Zacharias |first4=J. R. |year=1939 |title=An electrical quadrupole moment of the deuteron |journal=Physical Review |url=http://journals.aps.org/pr/abstract/10.1103/PhysRev.55.318 |volume=55 |issue=3 |pages=318–319 |doi=10.1103/physrev.55.318 |access-date=May 9, 2015 |bibcode=1939PhRv...55..318K |archive-date=May 12, 2017 |archive-url=https://web.archive.org/web/20170512174358/https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.318 |url-status=live }}</ref> This electrical property of the deuteron had been interfering with the measurements by the Rabi group. The deuteron, composed of a proton and a neutron, is one of the simplest nuclear systems. The discovery meant that the physical shape of the deuteron was not symmetric, which provided valuable insight into the nature of the nuclear force binding nucleons. In particular, the result showed that the nuclear force was not a [[central force]], but had a tensor character.<ref name="Reid"/> [[Hans Bethe]] identified the discovery of the deuteron's quadrupole moment as one of the important events during the formative years of nuclear physics.<ref name="Rigden"/>

Historically, the task of describing the nuclear force phenomenologically was formidable. The first semi-empirical quantitative models came in the mid-1950s,<ref name="Reid"/> such as the [[Woods–Saxon potential]] (1954). There was substantial progress in experiment and theory related to the nuclear force in the 1960s and 1970s. One influential model was the [[Reid potential]] (1968)<ref name="Reid"/>
: <math>V_\text{Reid}(r) = -10.463 \frac{e^{-\mu r}}{\mu r} - 1650.6 \frac{e^{-4\mu r}}{\mu r} + 6484.2 \frac{e^{-7\mu r}}{\mu r},</math>
where <math>\mu = 0.7~\text{fm}^{-1},</math> and where the potential is given in units of [[MeV]]. In recent years,{{when|date=August 2019}} experimenters have concentrated on the subtleties of the nuclear force, such as its charge dependence, the precise value of the π''NN'' coupling constant, improved [[phase-shift analysis]], high-precision ''NN'' [[Nuclear data|data]], high-precision ''NN'' potentials, ''NN'' scattering at intermediate and high energies, and attempts to derive the nuclear force from QCD.{{citation needed|date=October 2019}}

== As a residual of strong force ==
[[File:Nuclear Force anim smaller.gif|thumb|350px|An animation of the interaction. The coloured double circles are gluons. Anticolours are shown as per [[:File:Quark Anticolours.png|this diagram]] ([[:File: Nulcear Force anim.gif|larger version]]).]]

[[File:Pn Scatter Quarks.svg|thumb|300px|The same diagram as that above with the individual [[quark]] constituents shown, to illustrate how the ''fundamental'' [[strong interaction]] gives rise to the '''nuclear force'''. Straight lines are quarks, while multi-coloured loops are [[gluon]]s (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion "in flight", are not shown.]]

The nuclear force is a residual effect of the more fundamental strong force, or [[strong interaction]]. The strong interaction is the attractive force that binds the elementary particles called [[quark]]s together to form the nucleons (protons and neutrons) themselves. This more powerful force, one of the [[fundamental interaction|fundamental forces]] of nature, is mediated by particles called [[gluon]]s. Gluons hold quarks together through [[colour charge]] which is analogous to electric charge, but far stronger. Quarks, gluons, and their dynamics are mostly confined within nucleons, but residual influences extend slightly beyond nucleon boundaries to give rise to the nuclear force.

The nuclear forces arising between nucleons are analogous to the forces in chemistry between neutral atoms or molecules called [[London dispersion force]]s. Such forces between atoms are much weaker than the attractive electrical forces that hold the atoms themselves together (i.e., that bind electrons to the nucleus), and their range between atoms is shorter, because they arise from small separation of charges inside the neutral atom.{{Explain|date=March 2021}} Similarly, even though nucleons are made of quarks in combinations which cancel most gluon forces (they are "colour neutral"), some combinations of quarks and gluons nevertheless leak away from nucleons, in the form of short-range nuclear force fields that extend from one nucleon to another nearby nucleon. These nuclear forces are very weak compared to direct gluon forces ("colour forces" or [[strong force]]s) inside nucleons, and the nuclear forces extend only over a few nuclear diameters, falling exponentially with distance. Nevertheless, they are strong enough to bind neutrons and protons over short distances, and overcome the electrical repulsion between protons in the nucleus.

Sometimes, the nuclear force is called the '''residual strong force''', in contrast to the [[strong interaction]]s which arise from QCD. This phrasing arose during the 1970s when QCD was being established. Before that time, the ''strong nuclear force'' referred to the inter-nucleon potential. After the verification of the [[quark model]], ''strong interaction'' has come to mean QCD.

== Nucleon–nucleon potentials ==
Two-nucleon systems such as the [[deuteron]], the nucleus of a deuterium atom, as well as proton–proton or neutron–proton scattering are ideal for studying the ''NN'' force. Such systems can be described by attributing a ''[[potential]]'' (such as the [[Yukawa potential]]) to the nucleons and using the potentials in a [[Schrödinger equation]]. The form of the potential is derived phenomenologically (by measurement), although for the long-range interaction, meson-exchange theories help to construct the potential. The parameters of the potential are determined by fitting to [[Nuclear data|experimental data]] such as the deuteron binding energy or ''NN'' [[elastic scattering]] [[cross section (physics)|cross sections]] (or, equivalently in this context, so-called ''NN'' phase shifts).

The most widely used ''NN'' potentials are the [[Paris potential]], the [[Argonne AV18 potential]],<ref>{{cite journal |last1=Wiringa |first1=R. B. |last2=Stoks |first2=V. G. J. |last3=Schiavilla |first3=R. |title=Accurate nucleon–nucleon potential with charge-independence breaking |journal=Physical Review C |volume=51 |year=1995 |issue=1 |pages=38–51 |doi=10.1103/PhysRevC.51.38 |pmid=9970037 |bibcode=1995PhRvC..51...38W |arxiv=nucl-th/9408016|s2cid=118937727 }}</ref> the [[CD-Bonn potential]], and the [[Nijmegen potentials]].

A more recent approach is to develop [[effective field theory|effective field theories]] for a consistent description of nucleon–nucleon and three-nucleon forces. [[Quantum hadrodynamics]] is an effective field theory of the nuclear force, comparable to QCD for colour interactions and [[quantum electrodynamics|QED]] for electromagnetic interactions. Additionally, [[chiral symmetry breaking]] can be analyzed in terms of an effective field theory (called [[chiral perturbation theory]]) which allows [[perturbation theory|perturbative calculations]] of the interactions between nucleons with pions as exchange particles.

=== From nucleons to nuclei ===
The ultimate goal of [[nuclear physics]] would be to describe all [[Nuclear reaction|nuclear interactions]] from the basic interactions between nucleons. This is called the ''microscopic'' or [[ab initio methods (nuclear physics)|''ab initio'']] approach of nuclear physics. There are two major obstacles to overcome:
* Calculations in [[many-body system]]s are difficult (because of multi-particle interactions) and require advanced computation techniques.
* There is evidence that [[Three-body force|three-nucleon force]]s (and possibly higher multi-particle interactions) play a significant role. This means that three-nucleon potentials must be included into the model.
This is an active area of research with ongoing advances in computational techniques leading to better first-principles calculations of the [[nuclear shell]] structure. Two- and three-nucleon potentials have been implemented for nuclides up to ''[[mass number|A]]''&nbsp;=&nbsp;12.

=== Nuclear potentials ===
A successful way of describing nuclear interactions is to construct one potential for the whole nucleus instead of considering all its nucleon components. This is called the ''macroscopic'' approach. For example, scattering of neutrons from nuclei can be described by considering a plane wave in the potential of the nucleus, which comprises a real part and an imaginary part. This model is often called the optical model since it resembles the case of light scattered by an opaque glass sphere.

Nuclear potentials can be ''local'' or ''global'': local potentials are limited to a narrow energy range and/or a narrow nuclear mass range, while global potentials, which have more parameters and are usually less accurate, are functions of the energy and the nuclear mass and can therefore be used in a wider range of applications.

== See also ==
* {{Portal-inline|Physics}}
* [[Nuclear binding energy]]

== References ==
{{reflist}}

== Bibliography ==
{{refbegin}}
* Gerald Edward Brown and A. D. Jackson (1976). ''The Nucleon–Nucleon Interaction''. Amsterdam North-Holland Publishing. {{ISBN|0-7204-0335-9}}.
* [[Ruprecht Machleidt|R. Machleidt]] and I. Slaus, [https://cds.cern.ch/record/485107/files/0101056.pdf "The nucleon–nucleon interaction"] {{Webarchive|url=https://web.archive.org/web/20210507021533/http://cds.cern.ch/record/485107/files/0101056.pdf |date=2021-05-07 }}, ''J. Phys. G'' '''27''' (May 2001) R69. {{doi|10.1088/0954-3899/27/5/201}}. (Topical review.)
* E. A. Nersesov (1990). ''Fundamentals of atomic and nuclear physics''. Moscow: Mir Publishers. {{ISBN|5-06-001249-2}}.
* {{cite journal |arxiv=nucl-th/0305090 |bibcode=2003PhRvC..68c4305N |doi=10.1103/PhysRevC.68.034305|title=Ab initio shell model with a genuine three-nucleon force for the p-shell nuclei|journal=Physical Review C|volume=68|issue=3|year=2003|last1=Navrátil|first1=Petr|last2=Ormand|first2=W. Erich|page=034305 |s2cid=119091461 }}
{{refend}}

== Further reading ==
* [[Ruprecht Machleidt]], [http://www.scholarpedia.org/article/Nuclear_Forces "Nuclear Forces"], ''[[Scholarpedia]]'', 9(1):30710. {{doi|10.4249/scholarpedia.30710}}.
{{Fundamental interactions}}
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[[Category:Quantum chromodynamics]]
[[Category:Nuclear physics]]

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