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This article is about the force sometimes called the residual strong force. For the "strong nuclear force" see strong interaction; for the "weak nuclear force", see weak interaction.

A Feynman diagram of a strong proton-neutron interaction mediated by a neutral pion. Time proceeds from left to right.

The same diagram 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-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion "in-flight," are not shown.

The nuclear force (or nucleon-nucleon interaction or residual strong force) is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. To a large extent, this force can be understood in terms of the exchange of virtual light mesons, such as the pions. Sometimes the nuclear force is called the residual strong force, in contrast to the strong interactions which are now understood to arise from quantum chromodynamics (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. The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ... For other uses, see Proton (disambiguation). ... This article or section does not adequately cite its references or sources. ... In particle physics, pion (short for pi meson) is the collective name for three subatomic particles: π0, π+ and π−. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force. ... Image File history File links Size of this preview: 800 × 510 pixelsFull resolution (810 × 516 pixel, file size: 25 KB, MIME type: image/png) Feynman diagram of proton-neutron scattering mediated by a pion, with individual quarks shown. ... Image File history File links Size of this preview: 800 × 510 pixelsFull resolution (810 × 516 pixel, file size: 25 KB, MIME type: image/png) Feynman diagram of proton-neutron scattering mediated by a pion, with individual quarks shown. ... For other uses, see Quark (disambiguation). ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... For other uses, see Proton (disambiguation). ... This article or section does not adequately cite its references or sources. ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ... Mesons of spin 1 form a nonet In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ... In particle physics, pion (short for pi meson) is the collective name for three subatomic particles: π0, π+ and π−. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, i. ...

Since nucleons have no color charge, the nuclear force does not directly involve the force carriers of quantum chromodynamics, the gluons. However, just as electrically neutral atoms (each composed of cancelling charges) attract each other via the second-order effects of electrical polarization, via the van der Waals forces (London forces), so by analogy, "color-neutral" nucleons may attract each other by a type of polarization which allows some basically gluon-mediated effects to be carried from one color-neutral nucleon to another, via the virtual mesons which transmit the forces, and which themselves are held together by virtual gluons. It is this van der Waals-like nature which is responsible for the term "residual" in the term "residual strong force." The basic idea is that while the nucleons are "color-neutral," just as atoms are "charge-neutral," in both cases, polarization effects acting between near-by neutral particles allow a "residual" charge effect to cause net charge-mediated attraction between uncharged species, although it is necessarily of a much weaker and less direct nature than the basic forces which act internally within the particles. ^[1] In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... In particle physics, gluons are subatomic particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ... The title given to this article is incorrect due to technical limitations. ...

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 forces). Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... This article or section does not adequately cite its references or sources. ... Sir James Chadwick, CH (20 October 1891 – 24 July 1974) was an English physicist and Nobel laureate who is best known for discovering the neutron. ... The nucleus (atomic nucleus) is the center of an atom. ...

In 1935, Hideki Yukawa made the earliest attempt to explain the nature of the nuclear force. According to his theory, massive bosons (mesons) mediate the interaction between two nucleons. Although, in light of QCD, meson theory is no longer perceived as fundamental, the meson-exchange concept (where hadrons are treated as elementary particles) continues to represent the best working model for a quantitative NN potential. Hideki Yukawa Hideki Yukawa FRSE (湯川 秀樹, January 23, 1907 - September 8, 1981) was a Japanese theoretical physicist and the first Japanese to win the Nobel prize. ... In particle physics, bosons, named after Satyendra Nath Bose, are particles having integer spin. ... Mesons of spin 1 form a nonet In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ... The initialism QCD can mean: Quantum chromodynamics Quintessential Player, formerly known as Quintessential CD Quality, Cost, Delivery, A three-letter acronym used in lean manufacturing This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... In particle physics, an elementary particle is a particle of which other, larger particles are composed. ...

Historically, it was a formidable task to describe the nuclear force phenomenologically, and the first semi-empirical quantitative models came in the mid-1950s. There has been substantial progress in experiment and theory related to the nuclear force. Most basic questions were settled in the 1960s and 1970s. In recent years, experimenters have concentrated on the subtleties of the nuclear force, such as its charge dependence, the precise value of the πNN coupling constant, improved phase shift analysis, high-precision NN data, high-precision NN potentials, NN scattering at intermediate and high energies, and attempts to derive the nuclear force from QCD.

Basic properties of the nuclear force

• The nuclear force is only felt among hadrons.
• At much smaller separations between nucleons the force is very powerfully repulsive, which keeps the nucleons at a certain average separation.
• Beyond about 1.3 fm separation, the force drops to negligibly small values.
• At short distances, the nuclear force is stronger than the Coulomb force; it can overcome the Coulomb repulsion of protons inside the nucleus. However, the Coulomb force between protons has a much larger range and becomes the only significant force between protons when their separation exceeds about 2.5 fm.
• The NN force is nearly independent of whether the nucleons are neutrons or protons. This property is called charge independence.
• The NN force depends on whether the spins of the nucleons are parallel or antiparallel.
• The NN force has a noncentral or tensor component. This part of the force does not conserve orbital angular momentum, which is a constant of motion under central forces.

A hadron, in particle physics, is a subatomic particle which experiences the nuclear force. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume (ideally, a point source) exerts on another. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... The Azimuthal quantum number (or orbital angular momentum quantum number) l is a quantum number for an atomic orbital which determines its orbital angular momentum. ... A central force acting on an object is one whose magnitude depends only on the scalar distance r of the object from the origin and whose direction is along the position vector from the origin to the object. ...

Nucleon-nucleon potentials

Two-nucleon systems such as the deuteron 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, although for the long-range interaction, meson-exchange theories help to construct the potential. The parameters of the potential are determined by fitting to experimental data such as the deuteron binding energy or NN elastic scattering cross sections (or, equivalently in this context, so-called NN phase shifts). Deuterium (symbol 2H) is a stable isotope of hydrogen with a natural abundance of one atom in 6500 of hydrogen. ... In physics, a potential may refer to the scalar potential or to the vector potential. ... A Yukawa potential (also called a screened Coulomb potential) is a potential of the form Hideki Yukawa showed in the 1930s that such a potential arises from the exchange of a massive scalar field such as the field of the pion whose mass is . ... For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... In scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. ... In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ...

The most widely used NN potentials are the Paris potential, the Argonne AV18 potential, the CD-Bonn potential and the Nijmegen potentials.

A more recent approach is to develop effective field theories for a consistent description of nucleon-nucleon and three-nucleon forces. In particular, chiral symmetry breaking can be analysed in terms of an effective field theory (called chiral perturbation theory) which allows perturbative calculations of the interactions between nucleons with pions as exchange particles. In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies). ... In particle physics, chiral symmetry breaking is an example of spontaneous symmetry breaking affecting the chiral symmetry of gauge theory such as Quantum Chromodynamics. ... In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies). ... Chiral perturbation theory (ChPT) is an effective field theory constructed with a lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics (QCD), as well as the other symmetries of parity and charge conjugation. ... Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem. ...

From nucleons to nuclei

The ultimate goal of nuclear physics would be to describe all nuclear interactions from the basic interactions between nucleons. This is called the microscopic or ab initio approach of nuclear physics. There are two major obstacles to overcome before this dream can become reality: Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... The nuclear force (or nucleon-nucleon interaction) is the force between two or more nucleons. ...

• Calculations in many-body systems are difficult and require advanced computation techniques.
• There is evidence that three-nucleon forces (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 nuclear masses up to A=12. The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i. ... A three-body force is a force that does not exist in a system of two objects but appears in a three-body system. ... In nuclear physics, the nuclear shell model is a model of the atomic nucleus. ... The atomic mass (ma) is the mass of an atom at rest, most often expressed in unified atomic mass units. ...

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. The nuclear force (or nucleon-nucleon interaction) is the force between two or more nucleons. ...

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

• Yukawa potential
• Nuclear reaction
• Nuclear data
• Three-nucleon force

A Yukawa potential (also called a screened Coulomb potential) is a potential of the form Hideki Yukawa showed in the 1930s that such a potential arises from the exchange of a massive scalar field such as the field of the pion whose mass is . ... In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide to produce products different from the initial particles. ... Nuclear data groups all experimental data relevant for nuclear physics and nuclear applications. ... A three-body force is a force that does not exist in a system of two objects but appears in a three-body system. ...

References

• Gerald Edward Brown and A. D. Jackson, The Nucleon-Nucleon Interaction, (1976) North-Holland Publishing, Amsterdam ISBN 0-7204-0335-9
• R. Machleidt and I. Slaus, "The nucleon-nucleon interaction", J. Phys. G 27 (2001) R69 (topical review).
• Kenneth S. Krane, "Introductory Nuclear Physics", (1988) Wiley & Sons ISBN 0-471-80553-X
• P. Navrátil and W.E. Ormand, "Ab initio shell model with a genuine three-nucleon force for the p-shell nuclei", Phys. Rev. C 68, 034305 (2003).