![ReidForce2](https://upload.wikimedia.org/wikipedia/commons/5/53/ReidForce2.jpg)
The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the
protons and
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 atoms. Since protons and neutrons beh ...
s of
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, ...
s. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 ''e'', they experience an
electric force
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electromagnetic force. The nuclear force binds nucleons into
atomic nuclei
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 gold foil experiment. After the discovery of the neutron ...
.
The nuclear force is powerfully attractive between nucleons at distances of about 0.8
femtometre (fm, or 0.8×10
−15 metre
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
), but it rapidly decreases to insignificance at distances beyond about 2.5 fm. At distances less than 0.7 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, measured in
angstrom
The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...
s (Å, or 10
−10 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.
The nuclear force has an essential role in storing energy that is used in
nuclear power
Nuclear power is the use of nuclear reactions to produce electricity. Nuclear power can be obtained from nuclear fission, nuclear decay and nuclear fusion reactions. Presently, the vast majority of electricity from nuclear power is produced ...
and
nuclear weapons.
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
Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always ...
, 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 electromagnetic potential energy that is released when the nuclear force no longer holds the charged nuclear fragments together.
A quantitative description of the nuclear force relies on equations that are partly
empirical. These equations model the internucleon potential energies, or potentials. (Generally, forces within a system of particles can be more simply modeled by describing the system's potential energy; the negative gradient of a
potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...
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
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
to determine the
quantum mechanical
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
properties of the nucleon system.
The
discovery of the neutron
The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford developed a crude model of the atom, based on the go ...
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
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, ...
s. This theoretical development included a description of the
Yukawa potential
In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form:
:V_\text(r)= -g^2\frac,
where is a ...
, an early example of a nuclear potential.
Pion
In particle physics, a pion (or a pi meson, denoted with the Greek 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 lightest mesons and, more gene ...
s, fulfilling the prediction, were discovered experimentally in 1947. By the 1970s, 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 "flavor SU(3)", or the Ei ...
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 neighboring nucleons, is a residual effect of the
strong force
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the ...
.
Description
![Nuclear Force](https://upload.wikimedia.org/wikipedia/commons/c/c6/Nuclear_force.png)
While the nuclear force is usually associated with nucleons, more generally this force is felt between
hadron
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
s, or particles composed of
quarks. At small separations between nucleons (less than ~ 0.7 fm between their centers, 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
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated ...
force. A Pauli repulsion also occurs between quarks of the same
flavour from different nucleons (a proton and a neutron).
Field strength
At distances larger than 0.7 fm the force becomes attractive between spin-aligned nucleons, becoming maximal at a center–center distance of about 0.9 fm. Beyond this distance the force drops exponentially, until beyond about 2.0 fm separation, the force is negligible. Nucleons have a radius of about 0.8 fm.
At short distances (less than 1.7 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 2 to 2.5 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
fermions stems from the
Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulat ...
. 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
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one n ...
), 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
In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physici ...
(i.e. Einstein's formula ), 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".
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
spins
The spins (as in having "the spins")Diane Marie Leiva. ''The Florida State University College of Education''Women's Voices on College Drinking: The First-Year College Experience"/ref> is an adverse reaction of intoxication that causes a state of ...
of the nucleons are parallel or antiparallel, as it has a non-central or ''
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
'' component. This part of the force does not conserve orbital
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
, which under the action of
central forces is conserved.
The symmetry resulting in the strong force, proposed by
Werner Heisenberg
Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent serie ...
, 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
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 ...
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
intrinsic spin. In other words, both isospin and intrinsic spin transformations are
isomorphic to the
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.
Our understanding of the nuclear force is obtained by scattering experiments and the binding energy of light nuclei.
![pn scatter pi0](https://upload.wikimedia.org/wikipedia/commons/c/c1/Pn_scatter_pi0.svg)
The nuclear force occurs by the exchange of virtual light
meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, ...
s, such as the
virtual pion
In particle physics, a pion (or a pi meson, denoted with the Greek 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 lightest mesons and, more gene ...
s, as well as two types of virtual mesons with spin (
vector meson
In high energy physics, a vector meson is a meson with total spin 1 and odd parity (usually noted as ). Vector mesons have been seen in experiments since the 1960s, and are well known for their spectroscopic pattern of masses.
The vector meson ...
s), the
rho meson
Rho (uppercase Ρ, lowercase ρ or ; el, ρο or el, ρω, label=none) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the sa ...
s and the
omega meson
The omega meson () is a flavourless meson formed from a superposition of an up quark–antiquark and a down quark–antiquark pair. It is part of the vector meson nonet and mediates the nuclear force along with pions and rho mesons.
Propert ...
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
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
. The
weak interaction
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
is one of the four
fundamental interactions
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
, and plays a role in processes such as
beta decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
. 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
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 ...
ever since the field was born in 1932 with the discovery of 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 nuclei of atoms. Since protons and neutrons beh ...
by
James Chadwick
Sir James Chadwick, (20 October 1891 – 24 July 1974) was an English physicist who was awarded the 1935 Nobel Prize in Physics for his discovery of the neutron in 1932. In 1941, he wrote the final draft of the MAUD Report, which inspi ...
. The traditional goal of nuclear physics is to understand the properties of
atomic nuclei
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 gold foil experiment. After the discovery of the neutron ...
in terms of the "bare" interaction between pairs of nucleons, or nucleon–nucleon forces (NN forces).
Within months after the discovery of the neutron,
Werner Heisenberg
Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent serie ...
and
Dmitri Ivanenko had proposed proton–neutron models for the nucleus. 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".
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
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 ...
quantum numbers.
One of the earliest models for the nucleus was the
liquid-drop model
In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approxi ...
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
George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoret ...
and then developed by
Niels Bohr
Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922 ...
,
Werner Heisenberg
Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent serie ...
, and
Carl Friedrich von Weizsäcker
Carl Friedrich Freiherr von Weizsäcker (; 28 June 1912 – 28 April 2007) was a German physicist and philosopher. He was the longest-living member of the team which performed nuclear research in Germany during the Second World War, under ...
. 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
was a Japanese theoretical physicist and the first Japanese Nobel laureate for his prediction of the pi meson, or pion.
Biography
He was born as Hideki Ogawa in Tokyo and grew up in Kyoto with two older brothers, two older sisters, and two yo ...
made the earliest attempt to explain the nature of the nuclear force. According to his theory, massive
boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...
s (
meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, ...
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
In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
s are treated as
elementary particles
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, anti ...
) 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
:
where ''g'' is a magnitude scaling constant, i.e., the amplitude of potential,
is the Yukawa particle mass, ''r'' is the radial distance to the particle. The potential is
monotone increasing
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of orde ...
,
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
In classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force.
: \vec = \mathbf(\mathbf) = \left\vert F( \mathbf ) \right\vert \hat
where \vec F is the force, F is a vecto ...
.
Throughout the 1930s a group at
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...
led by
I. I. Rabi developed magnetic-resonance techniques to determine the magnetic moments of nuclei. These measurements led to the discovery in 1939 that the
deuteron
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one n ...
also possessed an
electric quadrupole moment.
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
In classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force.
: \vec = \mathbf(\mathbf) = \left\vert F( \mathbf ) \right\vert \hat
where \vec F is the force, F is a vecto ...
, but had a tensor character.
Hans Bethe
Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel ...
identified the discovery of the deuteron's quadrupole moment as one of the important events during the formative years of nuclear physics.
Historically, the task of describing the nuclear force phenomenologically was formidable. The first semi-empirical quantitative models came in the mid-1950s,
such as the
Woods–Saxon potential
The Woods–Saxon potential is a mean field potential for the nucleons ( protons and neutrons) inside the atomic nucleus, which is used to describe approximately the forces applied on each nucleon, in the nuclear shell model for the structure of ...
(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)
:
where
and where the potential is given in units of
MeV
In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacu ...
. In recent years, 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
In physics and mathematics, the phase of a periodic function F of some real number, real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a sca ...
, high-precision ''NN''
data
In the pursuit of knowledge, data (; ) is a collection of discrete Value_(semiotics), values that convey information, describing quantity, qualitative property, quality, fact, statistics, other basic units of meaning, or simply sequences of sy ...
, high-precision ''NN'' potentials, ''NN'' scattering at intermediate and high energies, and attempts to derive the nuclear force from QCD.
The nuclear force as a residual of the strong force
![Nuclear Force anim smaller](https://upload.wikimedia.org/wikipedia/commons/3/35/Nuclear_Force_anim_smaller.gif)
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
quarks together to form the nucleons (protons and neutrons) themselves. This more powerful force, one of the
fundamental forces
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
of nature, is mediated by particles called
gluons. Gluons hold quarks together through
color charge
Color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics (QCD).
The "color charge" of quarks and gluons is completely unrelated to the everyday meanings of colo ...
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
London dispersion forces (LDF, also known as dispersion forces, London forces, instantaneous dipole–induced dipole forces, fluctuating induced dipole bonds or loosely as van der Waals forces) are a type of intermolecular force acting between a ...
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. Similarly, even though nucleons are made of quarks in combinations which cancel most gluon forces (they are "color 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 ("color forces" or
strong force
The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the ...
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 interactions 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
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 "flavor SU(3)", or the Ei ...
, ''strong interaction'' has come to mean QCD.
Nucleon–nucleon potentials
Two-nucleon systems such as the
deuteron
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one n ...
, 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
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...
'' (such as the
Yukawa potential
In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form:
:V_\text(r)= -g^2\frac,
where is a ...
) to the nucleons and using the potentials in a
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
. 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
experimental data
Experimental data in science and engineering is data produced by a measurement, test method, experimental design or quasi-experimental design. In clinical research any data produced are the result of a clinical trial. Experimental data may be qua ...
such as the deuteron binding energy or ''NN''
elastic scattering
Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modif ...
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,
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.
Quantum hadrodynamics
Quantum hadrodynamics is an effective field theory pertaining to interactions between hadrons, that is, hadron-hadron interactions or the inter-hadron force. It is "a framework for describing the nuclear many-body problem as a relativistic syste ...
is an effective field theory of the nuclear force, comparable to QCD for color interactions and
QED for electromagnetic interactions. Additionally,
chiral symmetry breaking
In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was awar ...
can be analyzed 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.
From nucleons to nuclei
The ultimate goal of
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 ...
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:
*Calculations in
many-body system
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of many interacting particles. ''Microscopic'' here implies that quantum mechanics has to be used to provid ...
s are difficult (because of multi-particle interactions) and require advanced computation techniques.
*There is evidence that
three-nucleon force
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 general, if the behaviour of a system of more than two objects cannot be described by the two-body interactions between all possib ...
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
In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels. The first shell mod ...
structure. Two- and three-nucleon potentials have been implemented for nuclides up to ''
A'' = 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
*
*
Nuclear binding energy
References
Bibliography
* Gerald Edward Brown and A. D. Jackson (1976). ''The Nucleon–Nucleon Interaction''. Amsterdam North-Holland Publishing. .
*
R. Machleidt and I. Slaus
"The nucleon–nucleon interaction" ''J. Phys. G'' 27 (May 2001) R69. . (Topical review.)
* E. A. Nersesov (1990). ''Fundamentals of atomic and nuclear physics''. Moscow: Mir Publishers. .
*
Further reading
*
Ruprecht Machleidt"Nuclear Forces" ''
Scholarpedia
''Scholarpedia'' is an English-language wiki-based online encyclopedia with features commonly associated with open-access online academic journals, which aims to have quality content in science and medicine.
''Scholarpedia'' articles are written ...
'', 9(1):30710. .
{{Authority control
Quantum chromodynamics
Nuclear physics
yi:שטארקע נוקלעארע קראפט