Nuclear force

The nuclear force (or nucleon–nucleon interaction or residual strong force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience an electric force 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 nuclear force is powerfully attractive between nucleons at distances of about 1 femtometre (fm, or 1.0 × 10−15 metres), 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 repulsive component is responsible for the physical size of nuclei, since the nucleons can come no closer than the force allows. By comparison, the size of an atom, measured in angstroms (Å, or 1.0 × 10−10 m), is five orders of magnitude larger. The nuclear force is not simple, however, since it depends on the nucleon spins, has a tensor component, and may depend on the relative momentum of the nucleons.[2] The strong nuclear force is one of the fundamental forces of nature.

The nuclear force plays an essential role in storing energy that is used in nuclear power 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, 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.[3][4]

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 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 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 mesons. This theoretical development included a description of the Yukawa potential, an early example of a nuclear potential. Mesons, predicted by theory, 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 neighboring nucleons, is a residual effect of the strong force.

Force (in units of 10,000 N) between two nucleons as a function of distance as computed from the Reid potential (1968).[1] The spins of the neutron and proton are aligned, and they are in the S angular momentum state. The attractive (negative) force has a maximum at a distance of about 1 fm with a force of about 25,000 N. Particles much closer than a distance of 0.8 fm experience a large repulsive (positive) force. Particles separated by a distance greater than 1 fm are still attracted (Yukawa potential), but the force falls as an exponential function of distance.
Corresponding potential energy (in units of MeV) of two nucleons as a function of distance as computed from the Reid potential. The potential well is a minimum at a distance of about 0.8 fm. With this potential nucleons can become bound with a negative "binding energy."


While the nuclear force is usually associated with nucleons, more generally this force is felt between hadrons, 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, even if they are of different types. This repulsion arises from the Pauli exclusion force for identical nucleons (such as two neutrons or two protons). A Pauli exclusion force also occurs between quarks of the same type within nucleons, when the nucleons are different (a proton and a neutron, for example).

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.[5]

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. 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 famous formula E = mc2), 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".[6]

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 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 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.[7]

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

Pn scatter pi0
A Feynman diagram of a strong protonneutron interaction mediated by a neutral pion. Time proceeds from left to right.

The nuclear force occurs by the exchange of virtual light mesons, such as the virtual pions, as well as two types of virtual mesons with spin (vector mesons), the rho mesons and the omega mesons. 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 such processes 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.


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).

Within months after the discovery of the neutron, Werner Heisenberg[8][9][10] and Dmitri Ivanenko[11] had proposed proton–neutron models for the nucleus.[12] 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."[13] 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 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 nuclear 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 bosons (mesons) mediate the interaction between two nucleons. Although, in light of quantum chromodynamics (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. 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, implying that the force is always attractive. The constants are determined empirically. The Yukawa potential depends only on the distance between particles, r, hence it models a central force.

Throughout the 1930s a group at Columbia University 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 also possessed an electric quadrupole moment.[14][15] 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.[1] Hans Bethe identified the discovery of the deuteron's quadrupole moment as one of the important events during the formative years of nuclear physics.[14]

Historically, the task of describing the nuclear force phenomenologically was formidable. The first semi-empirical quantitative models came in the mid-1950s,[1] 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).[1]

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.

The nuclear force as a residual of the strong force

Nuclear Force anim smaller
An animation of the interaction. The colored double circles are gluons. Anticolors are shown as per this diagram (larger version).
Pn Scatter Quarks
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-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 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 is mediated by particles called gluons. Gluons hold quarks together through color 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 forces. 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 forces) 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, 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 experimental data such as the deuteron binding energy or NN elastic scattering 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 ,[16] 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 is an effective field theory of the nuclear force, comparable to QCD for color interactions and QED for electromagnetic interactions. Additionally, chiral symmetry breaking 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 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:

  • 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 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


  1. ^ a b c d Reid, R.V. (1968). "Local phenomenological nucleon–nucleon potentials". Annals of Physics. 50: 411–448. Bibcode:1968AnPhy..50..411R. doi:10.1016/0003-4916(68)90126-7.
  2. ^ Kenneth S. Krane (1988). Introductory Nuclear Physics. Wiley & Sons. ISBN 0-471-80553-X.
  3. ^ Binding Energy, Mass Defect, Furry Elephant physics educational site, retr 2012 7 1
  4. ^ Chapter 4 NUCLEAR PROCESSES, THE STRONG FORCE, M. Ragheb 1/30/2013, University of Illinois
  5. ^ Povh, B.; Rith, K.; Scholz, C.; Zetsche, F. (2002). Particles and Nuclei: An Introduction to the Physical Concepts. Berlin: Springer-Verlag. p. 73. ISBN 978-3-540-43823-6.
  6. ^ Stern, Dr. Swapnil Nikam (February 11, 2009). "Nuclear Binding Energy". "From Stargazers to Starships". NASA website. Retrieved 2010-12-30.
  7. ^ Griffiths, David, Introduction to Elementary Particles
  8. ^ Heisenberg, W. (1932). "Über den Bau der Atomkerne. I". Z. Phys. 77: 1–11. Bibcode:1932ZPhy...77....1H. doi:10.1007/BF01342433.
  9. ^ Heisenberg, W. (1932). "Über den Bau der Atomkerne. II". Z. Phys. 78 (3–4): 156–164. Bibcode:1932ZPhy...78..156H. doi:10.1007/BF01337585.
  10. ^ Heisenberg, W. (1933). "Über den Bau der Atomkerne. III". Z. Phys. 80 (9–10): 587–596. Bibcode:1933ZPhy...80..587H. doi:10.1007/BF01335696.
  11. ^ Iwanenko, D.D., The neutron hypothesis, Nature 129 (1932) 798.
  12. ^ Miller A. I. Early Quantum Electrodynamics: A Sourcebook, Cambridge University Press, Cambridge, 1995, ISBN 0521568919, pp. 84–88.
  13. ^ Brown, L.M.; Rechenberg, H. (1996). The Origin of the Concept of Nuclear Forces. Bristol and Philadelphia: Institute of Physics Publishing. ISBN 0750303735.
  14. ^ a b John S. Rigden (1987). Rabi, Scientist and Citizen. New York: Basic Books, Inc. pp. 99–114. ISBN 9780674004351. Retrieved May 9, 2015.
  15. ^ Kellogg, J.M.; Rabi, I.I.; Ramsey, N.F.; Zacharias, J.R. (1939). "An electrical quadrupole moment of the deuteron". Physical Review. 55: 318–319. Bibcode:1939PhRv...55..318K. doi:10.1103/physrev.55.318. Retrieved May 9, 2015.
  16. ^ Wiringa, R. B.; Stoks, V. G. J.; Schiavilla, R. (1995). "Accurate nucleon–nucleon potential with charge-independence breaking". Physical Review C. 51: 38. arXiv:nucl-th/9408016. Bibcode:1995PhRvC..51...38W. doi:10.1103/PhysRevC.51.38.


  • 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).
  • E.A. Nersesov, Fundamentals of atomic and nuclear physics, (1990), Mir Publishers, Moscow, ISBN 5-06-001249-2
  • 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).

Further reading

Alpha decay

Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two. An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. It has a charge of +2 e and a mass of 4 u. For example, uranium-238 decays to form thorium-234. Alpha particles have a charge +2 e, but as a nuclear equation describes a nuclear reaction without considering the electrons – a convention that does not imply that the nuclei necessarily occur in neutral atoms – the charge is not usually shown.

Alpha decay typically occurs in the heaviest nuclides. Theoretically, it can occur only in nuclei somewhat heavier than nickel (element 28), where the overall binding energy per nucleon is no longer a minimum and the nuclides are therefore unstable toward spontaneous fission-type processes. In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitters being the lightest isotopes (mass numbers 104–109) of tellurium (element 52). Exceptionally, however, beryllium-8 decays to two alpha particles.

Alpha decay is by far the most common form of cluster decay, where the parent atom ejects a defined daughter collection of nucleons, leaving another defined product behind. It is the most common form because of the combined extremely high nuclear binding energy and relatively small mass of the alpha particle. Like other cluster decays, alpha decay is fundamentally a quantum tunneling process. Unlike beta decay, it is governed by the interplay between both the nuclear force and the electromagnetic force.

Alpha particles have a typical kinetic energy of 5 MeV (or ≈ 0.13% of their total energy, 110 TJ/kg) and have a speed of about 15,000,000 m/s, or 5% of the speed of light. There is surprisingly small variation around this energy, due to the heavy dependence of the half-life of this process on the energy produced (see equations in the Geiger–Nuttall law). Because of their relatively large mass, electric charge of +2 e and relatively low velocity, alpha particles are very likely to interact with other atoms and lose their energy, and their forward motion can be stopped by a few centimeters of air. Approximately 99% of the helium produced on Earth is the result of the alpha decay of underground deposits of minerals containing uranium or thorium. The helium is brought to the surface as a by-product of natural gas production.


An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small; typical sizes are around 100 picometers (a ten-billionth of a meter, in the short scale).

Atoms are small enough that attempting to predict their behavior using classical physics – as if they were billiard balls, for example – gives noticeably incorrect predictions due to quantum effects. Through the development of physics, atomic models have incorporated quantum principles to better explain and predict this behavior.

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 typically a similar number of neutrons. Protons and neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, that atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively, and it is called an ion.

The electrons of an atom are attracted to the protons in an atomic nucleus by this electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by a different force, the nuclear force, which is usually stronger than the electromagnetic force repelling the positively charged protons from one another. Under certain circumstances, the repelling electromagnetic force becomes stronger than the nuclear force, and nucleons can be ejected from the nucleus, leaving behind a different element: nuclear decay resulting in nuclear transmutation.

The number of protons in the nucleus defines to what chemical element the atom belongs: for example, all copper atoms contain 29 protons. The number of neutrons defines the isotope of the element. The number of electrons influences the magnetic properties of an atom. Atoms can attach to one or more other atoms by chemical bonds to form chemical compounds such as molecules. The ability of atoms to associate and dissociate is responsible for most of the physical changes observed in nature and is the subject of the discipline of chemistry.

Atomic nucleus

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively-charged nucleus, with a cloud of negatively-charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.

The diameter of the nucleus is in the range of 1.7566 fm (1.7566×10−15 m) for hydrogen (the diameter of a single proton) to about 11.7142 fm for the heaviest atom uranium. These dimensions are much smaller than the diameter of the atom itself (nucleus + electron cloud), by a factor of about 26,634 (uranium atomic radius is about 156 pm (156×10−12 m)) to about 60,250 (hydrogen atomic radius is about 52.92 pm).The branch of physics concerned with the study and understanding of the atomic nucleus, including its composition and the forces which bind it together, is called nuclear physics.


In chemistry, an enantiomer ( ə-NAN-tee-ə-mər; from Greek, Modern ἐνάντιος (enántios), meaning 'opposite', and μέρος (méros), meaning 'part'), also known as an optical isomer (and archaically termed antipode or optical antipode), is one of two stereoisomers that are mirror images of each other that are non-superposable (not identical), much as one's left and right hands have the same shape except for being reversed along one axis (the hands cannot be made to appear identical simply by reorientation). A single chiral atom or similar structural feature in a compound causes that compound to have two possible structures which are non-superposable, each a mirror image of the other. Each member of the pair is termed an enantiomorph (enantio = opposite; morph = form); the structural property is termed enantiomerism. The presence of multiple chiral features in a given compound increases the number of geometric forms possible, though there may still be some perfect-mirror-image pairs.

A sample of a chemical is considered enantiopure when it has, within the limits of detection, molecules of only one chirality.When present in a symmetric environment, enantiomers have identical chemical and physical properties except for their ability to rotate plane-polarized light (+/−) by equal amounts but in opposite directions (although the polarized light can be considered an asymmetric medium). They are sometimes called optical isomers for this reason. A mixture of equal parts of an optically active isomer and its enantiomer is termed racemic and has zero net rotation of plane-polarized light, because the positive rotation of each (+) form is exactly counteracted by the negative rotation of a (−) one. For all intents and purposes, pairs of enantiomers have the same Gibbs free energy. However, theoretical physics predicts that due to parity violation of the weak nuclear force (the only force in nature that can "tell left from right"), there is actually a minute difference in energy between enantiomers (on the order of 10−12 eV or 10−10 kJ/mol or less) due to the weak neutral current mechanism. This difference in energy is far smaller than energy changes caused by even a trivial change in molecular conformation and far too small to measure by current technology, and is therefore chemically inconsequential.Enantiomer members often have different chemical reactions with other enantiomer substances. Since many biological molecules are enantiomers, there is sometimes a marked difference in the effects of two enantiomers on biological organisms. In drugs, for example, often only one of a drug's enantiomers is responsible for the desired physiological effects, while the other enantiomer is less active, inactive, or sometimes even productive of adverse effects. Owing to this discovery, drugs composed of only one enantiomer ("enantiopure") can be developed to make the drug work better and sometimes eliminate some side effects. An example is eszopiclone (Lunesta), which is just a single enantiomer of an older racemic drug called zopiclone. The is enantiomer is responsible for all the desired effects, while the other enantiomer seems to be inactive, and the so the dose of eszopiclone is half that of zopiclone.

In chemical synthesis of enantiomeric substances, non-enantiomeric precursors inevitably produce racemic mixtures. In the absence of an effective enantiomeric environment (precursor, chiral catalyst, or kinetic resolution), separation of a racemic mixture into its enantiomeric components is impossible.

Intermediate-Range Nuclear Forces Treaty

The Intermediate-Range Nuclear Forces Treaty (INF Treaty, formally Treaty Between the United States of America and the Union of Soviet Socialist Republics on the Elimination of Their Intermediate-Range and Shorter-Range Missiles; Russian: Договор о ликвидации ракет средней и меньшей дальности / ДРСМД, Dogovor o likvidatsiy raket sredney i menshey dalnosti / DRSMD) was an arms control treaty between the United States and the Soviet Union (and its successor state, the Russian Federation). U.S. President Ronald Reagan and Soviet General Secretary Mikhail Gorbachev signed the treaty on 8 December 1987. The United States Senate approved the treaty on 27 May 1988, and Reagan and Gorbachev ratified it on 1 June 1988.The INF Treaty eliminated all of the two nations' land-based ballistic missiles, cruise missiles, and missile launchers with ranges of 500–1,000 kilometers (310–620 mi) (short medium-range) and 1,000–5,500 km (620–3,420 mi) (intermediate-range). The treaty did not apply to air- or sea-launched missiles. By May 1991, the nations had eliminated 2,692 missiles, followed by 10 years of on-site verification inspections.President Donald Trump announced on 20 October 2018 that he was withdrawing the U.S. from the treaty, accusing Russia of non-compliance. The U.S. formally suspended the treaty on 1 February 2019, and Russia did so on the following day in response to the U.S. withdrawal.


In particle physics, mesons ( or ) are hadronic subatomic particles composed of one quark and one antiquark, bound together by strong interactions. Because mesons are composed of quack subparticles, they have physical size, notably a diameter of roughly one femtometer, which is about 1.2 times the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Charged mesons decay (sometimes through mediating particles) to form electrons and neutrinos. Uncharged mesons may decay to photons. Both of these decays imply that color is no longer a property of the byproducts.

Outside the nucleus, mesons appear in nature only as short-lived products of very high-energy collisions between particles made of quarks, such as cosmic rays (high-energy protons and neutrons) and ordinary matter. Mesons are also frequently produced artificially in cyclotron in the collisions of protons, antiprotons, or other particles.

Mesons are the associated quantum-field particles that transmit the nuclear force between hadrons that pull those together into a nucleus. Their effect is analogous to photons that are the force carriers that transmit the electromagnetic force of attraction between oppositely charged protons and electrons that allow individual atoms to exist, and further, to pull atoms together into molecules. Higher energy (more massive) mesons were created momentarily in the Big Bang, but are not thought to play a role in nature today. However, such heavy mesons are regularly created in particle accelerator experiments, in order to understand the nature of the heavier types of quark that compose the heavier mesons.

Mesons are part of the hadron particle family, and are defined simply as particles composed of an even number of quarks. The other members of the hadron family are the baryons: subatomic particles composed of odd numbers of valence quarks (at least 3), and some experiments show evidence of exotic mesons, which do not have the conventional valence quark content of two quarks (one quark and one antiquark), but 4 or more.

Because quarks have a spin of ​1⁄2, the difference in quark number between mesons and baryons results in conventional two-quark mesons being bosons, whereas baryons are fermions.

Each type of meson has a corresponding antiparticle (antimeson) in which quacks are replaced by their corresponding antiquarks and vice versa. For example, a positive pion (π+) is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion (π−), is made of one up antiquark and one down quark.

Because mesons are composed of quarks, they participate in both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction. Mesons are classified according to their quark content, total angular momentum, parity and various other properties, such as C-parity and G-parity. Although no meson is stable, those of lower mass are nonetheless more stable than the more massive, and hence are easier to observe and study in particle accelerators or in cosmic ray experiments. Mesons are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher-energy phenomena more readily than do baryons. For example, the charm quark was first seen in the J/Psi meson (J/ψ) in 1974, and the bottom quark in the upsilon meson (ϒ) in 1977.


The neutron is a subatomic particle, symbol n or n0, with no net electric charge and a mass slightly larger than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave similarly within the nucleus, and each has a mass of approximately one atomic mass unit, they are both referred to as nucleons. Their properties and interactions are described by nuclear physics.

The chemical and nuclear properties of the nucleus are determined by the number of protons, called the atomic number, and the number of neutrons, called the neutron number. The atomic mass number is the total number of nucleons. For example, carbon has atomic number 6, and its abundant carbon-12 isotope has 6 neutrons, whereas its rare carbon-13 isotope has 7 neutrons. Some elements occur in nature with only one stable isotope, such as fluorine. Other elements occur with many stable isotopes, such as tin with ten stable isotopes.

Within the nucleus, protons and neutrons are bound together through the nuclear force. Neutrons are required for the stability of nuclei, with the exception of the single-proton hydrogen atom. Neutrons are produced copiously in nuclear fission and fusion. They are a primary contributor to the nucleosynthesis of chemical elements within stars through fission, fusion, and neutron capture processes.

The neutron is essential to the production of nuclear power. In the decade after the neutron was discovered by James Chadwick in 1932, neutrons were used to induce many different types of nuclear transmutations. With the discovery of nuclear fission in 1938, it was quickly realized that, if a fission event produced neutrons, each of these neutrons might cause further fission events, etc., in a cascade known as a nuclear chain reaction. These events and findings led to the first self-sustaining nuclear reactor (Chicago Pile-1, 1942) and the first nuclear weapon (Trinity, 1945).

Free neutrons, while not directly ionizing atoms, cause ionizing radiation. As such they can be a biological hazard, depending upon dose. A small natural "neutron background" flux of free neutrons exists on Earth, caused by cosmic ray showers, and by the natural radioactivity of spontaneously fissionable elements in the Earth's crust. Dedicated neutron sources like neutron generators, research reactors and spallation sources produce free neutrons for use in irradiation and in neutron scattering experiments.

Neutron emission

Neutron emission is a mode of radioactive decay in which one or more neutrons are ejected from a nucleus. It occurs in the most neutron-rich/proton-deficient nucleides, and also from excited states of other nucleides as in photoneutron emission and beta-delayed neutron emission. As only a neutron is lost by this process the number of protons remains unchanged, and an atom does not become an atom of a different element, but a different isotope of the same element.

Neutrons are also produced in the spontaneous and induced fission of certain heavy nucleides.

Neutron–proton ratio

The neutron–proton ratio (N/P ratio or nuclear ratio) of an atomic nucleus is the ratio of its number of neutrons to its number of protons. Among stable nuclei and naturally occurring nuclei, this ratio generally increases with increasing atomic number. This is because electrical repulsive forces between protons scale with distance differently than strong nuclear force attractions. In particular, most pairs of protons in large nuclei are not far enough apart, such that electrical repulsion dominates over the strong nuclear force, and thus proton density in stable larger nuclei must be lower than in stable smaller nuclei where more pairs of protons have appreciable short-range nuclear force attractions.

For each element with atomic number Z small enough to occupy only the first three nuclear shells, that is up to that of calcium (Z = 20), there exists a stable isotope with N/Z ratio of one, with the exception of beryllium (N/Z = 1.25) and every element with odd atomic number between 9 and 19 inclusive (N = Z+1). Hydrogen-1 (N/Z ratio = 0) and helium-3 (N/Z ratio = 0.5) are the only stable isotopes with neutron–proton ratio under one. Uranium-238 and plutonium-244 have the highest N/Z ratios of any primordial nuclide at 1.587 and 1.596, respectively, while lead-208 has the highest N/Z ratio of any known stable isotope at 1.537. Radioactive decay generally proceeds so as to change the N/Z ratio to increase stability. If the N/Z ratio is greater than 1, alpha decay increases the N/Z ratio, and hence provides a common pathway towards stability for decays involving large nuclei with too few neutrons. Positron emission and electron capture also increase the ratio, while beta decay will decrease the ratio.

Nuclear waste exists mainly because nuclear fuel has a higher stable N/Z ratio than the parts into which it is fissioned.

No. 15 Squadron RAF

No. 15 Squadron sometimes written as XV Squadron of the Royal Air Force operated the Panavia Tornado GR4 from RAF Lossiemouth. XV (Reserve) Squadron was the RAF's Operational Conversion Unit for the Tornado GR4 which taught pilots how to fly the aircraft and what tactics to use to best exploit the performance of their aircraft and its weapons.

Non-contact force

A non-contact force is a force which acts on an object without coming physically in contact with it. The most familiar example of a non-contact force is a gravity, which confers weight. In contrast a contact force is a force applied to a body by another body that is in contact with it.

Nuclear binding energy

Nuclear binding energy is the minimum energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are collectively called nucleons. The binding is always a positive number, as we need to spend energy in moving these nucleons, attracted to each other by the strong nuclear force, away from each other. The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons, according to Einstein's equation E=mc2. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.

The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse (nuclear fusion), or when heavy nuclei split (nuclear fission), either process can result in release of this binding energy. This energy may be made available as nuclear energy and can be used to produce electricity, as in nuclear power, or in a nuclear weapon. When a large nucleus splits into pieces, excess energy is emitted as photon (gamma rays) and as the kinetic energy of a number of different ejected particles (nuclear fission products).

These nuclear binding energies and forces are on the order of a million times greater than the electron binding energies of light atoms like hydrogen.The mass defect of a nucleus represents the amount of mass equivalent to the

binding energy of the nucleus (E=mc2), which is the difference between the mass of a nucleus and the sum of the individual masses of the nucleons of which it is composed.


In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: π) is any of three subatomic particles: π0, π+, and π−. Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more generally, the lightest hadrons. They are unstable, with the charged pions π+ and π− decaying with a mean lifetime of 26.033 nanoseconds (2.6033×10−8 seconds), and the neutral pion π0 decaying with a much shorter lifetime of 8.4×10−17 seconds. Charged pions most often decay into muons and muon neutrinos, while neutral pions generally decay into gamma rays.

The exchange of virtual pions, along with the vector, rho and omega mesons, provides an explanation for the residual strong force between nucleons. Pions are not produced in radioactive decay, but are commonly produced in high energy accelerators in collisions between hadrons. All types of pions are also produced in natural processes when high energy cosmic ray protons and other hadronic cosmic ray components interact with matter in the Earth's atmosphere. Recently, the detection of characteristic gamma rays originating from the decay of neutral pions in two supernova remnants has shown that pions are produced copiously after supernovas, most probably in conjunction with production of high energy protons that are detected on Earth as cosmic rays.The concept of mesons as the carrier particles of the nuclear force was first proposed in 1935 by Hideki Yukawa. While the muon was first proposed to be this particle after its discovery in 1936, later work found that it did not participate in the strong nuclear interaction. The pions, which turned out to be examples of Yukawa's proposed mesons, were discovered later: the charged pions in 1947, and the neutral pion in 1950.

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 system of baryons and mesons". Quantum hadrodynamics is closely related and partly derived from quantum chromodynamics, which is the theory of interactions between quarks and gluons that bind them together to form hadrons, via the strong force.

An important phenomenon in quantum hadrodynamics is the nuclear force, or residual strong force. It is the force operating between those hadrons which are nucleons – protons and neutrons – as it binds them together to form the atomic nucleus. The bosons which mediate the nuclear force are three types of mesons: pions, rho mesons and omega mesons. Since mesons are themselves hadrons, quantum hadrodynamics also deals with the interaction between the carriers of the nuclear force itself, alongside the nucleons bound by it. The hadrodynamic force keeps nuclei bound, against the electrodynamic force which operates to break them apart (due to the mutual repulsion between protons in the nucleus).

Quantum hadrodynamics, dealing with the nuclear force and its mediating mesons, can be compared to other quantum field theories which describe fundamental forces and their associated bosons: quantum chromodynamics, dealing with the strong interaction and gluons; quantum electrodynamics, dealing with electromagnetism and photons; quantum flavordynamics, dealing with the weak interaction and W and Z bosons.

Rho meson

In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as ρ+, ρ0 and ρ−. Along with pions and omega mesons, the rho meson carries the nuclear force within the atomic nucleus. After the pions and kaons, the rho mesons are the lightest strongly interacting particle, with a mass of 775.45±0.04 MeV (roughly 770 MeV) for all three states.The rho mesons have a very short lifetime and their decay width is about 145 MeV with the peculiar feature that the decay widths are not described by a Breit–Wigner form. The principal decay route of the rho mesons is to a pair of pions with a branching rate of 99.9%.

Second strike

In nuclear strategy, a second-strike capability is a country's assured ability to respond to a nuclear attack with powerful nuclear retaliation against the attacker. To have such an ability (and to convince an opponent of its viability) is considered vital in nuclear deterrence, as otherwise the other side might attempt to try to win a nuclear war in one massive first strike against its opponent's own nuclear forces.

Strong interaction

In particle physics, the strong interaction is the mechanism responsible for the strong nuclear force (also called the strong force, nuclear strong force, or colour force), and is one of the four known fundamental interactions, with the others being electromagnetism, the weak interaction, and gravitation. At the range of 10−15 m (1 femtometer), the strong force is approximately 137 times as strong as electromagnetism, a million times as strong as the weak interaction, and 1038 times as strong as gravitation. The strong nuclear force holds most ordinary matter together because it confines quarks into hadron particles such as the proton and neutron. In addition, the strong force binds neutrons and protons to create atomic nuclei. Most of the mass of a common proton or neutron is the result of the strong force field energy; the individual quarks provide only about 1% of the mass of a proton.

The strong interaction is observable at two ranges and mediated by two force carriers. On a larger scale (about 1 to 3 fm), it is the force (carried by mesons) that binds protons and neutrons (nucleons) together to form the nucleus of an atom. On the smaller scale (less than about 0.8 fm, the radius of a nucleon), it is the force (carried by gluons) that holds quarks together to form protons, neutrons, and other hadron particles. In the latter context, it is often known as the color force. The strong force inherently has such a high strength that hadrons bound by the strong force can produce new massive particles. Thus, if hadrons are struck by high-energy particles, they give rise to new hadrons instead of emitting freely moving radiation (gluons). This property of the strong force is called color confinement, and it prevents the free "emission" of the strong force: instead, in practice, jets of massive particles are produced.

In the context of atomic nuclei, the same strong interaction force (that binds quarks within a nucleon) also binds protons and neutrons together to form a nucleus. In this capacity it is called the nuclear force (or residual strong force). So the residuum from the strong interaction within protons and neutrons also binds nuclei together. As such, the residual strong interaction obeys a quite different distance-dependent behavior between nucleons, from when it is acting to bind quarks within nucleons. Differences in the binding energy of the nuclear force between different nuclei power nuclear fusion and nuclear fission. Nuclear fusion accounts for most energy production in the Sun and other stars. Nuclear fission allows for decay of radioactive elements and isotopes, although it is often mediated by the weak interaction. Artificially, the energy associated with the nuclear force is partially released in nuclear power and nuclear weapons, both in uranium or plutonium-based fission weapons and in fusion weapons like the hydrogen bomb.The strong interaction is mediated by the exchange of massless particles called gluons that act between quarks, antiquarks, and other gluons. Gluons are thought to interact with quarks and other gluons by way of a type of charge called color charge. Color charge is analogous to electromagnetic charge, but it comes in three types (±red, ±green, ±blue) rather than one, which results in a different type of force, with different rules of behavior. These rules are detailed in the theory of quantum chromodynamics (QCD), which is the theory of quark-gluon interactions.

W and Z bosons

The W and Z bosons are together known as the weak or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are W+, W−, and Z. The W bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. The Z boson is electrically neutral and is its own antiparticle. The three particles have a spin of 1. The W bosons have a magnetic moment, but the Z has none. All three of these particles are very short-lived, with a half-life of about 3×10−25 s. Their experimental discovery was a triumph for what is now known as the Standard Model of particle physics.

The W bosons are named after the weak force. The physicist Steven Weinberg named the additional particle the "Z particle", and later gave the explanation that it was the last additional particle needed by the model. The W bosons had already been named, and the Z bosons have zero electric charge.The two W bosons are verified mediators of neutrino absorption and emission. During these processes, the W boson charge induces electron or positron emission or absorption, thus causing nuclear transmutation. The Z boson is not involved in the absorption or emission of electrons and positrons.

The Z boson mediates the transfer of momentum, spin and energy when neutrinos scatter elastically from matter (a process which conserves charge). Such behavior is almost as common as inelastic neutrino interactions and may be observed in bubble chambers upon irradiation with neutrino beams. Whenever an electron is observed as a new free particle suddenly moving with kinetic energy, it is inferred to be a result of a neutrino interacting directly with the electron, since this behavior happens more often when the neutrino beam is present. In this process, the neutrino simply strikes the electron and then scatters away from it, transferring some of the neutrino's momentum to the electron.

Because neutrinos are neither affected by the strong force nor the electromagnetic force, and because the gravitational force between subatomic particles is negligible, such an interaction can only happen via the weak force. Since such an electron is not created from a nucleon, and is unchanged except for the new force impulse imparted by the neutrino, this weak force interaction between the neutrino and the electron must be mediated by an electromagnetically neutral, weak-force boson particle. Thus, this interaction requires a Z boson.

Weak interaction

In particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms. The weak interaction serves an essential role in nuclear fission, and the theory regarding it in terms of both its behavior and effects is sometimes called quantum flavordynamics (QFD). However, the term QFD is rarely used because the weak force is better understood in terms of electroweak theory (EWT). In addition to this, QFD is related to quantum chromodynamics (QCD), which deals with the strong interaction, and quantum electrodynamics (QED), which deals with the electromagnetic force.

The effective range of the weak force is limited to subatomic distances, and is less than the diameter of a proton. It is one of the four known force-related fundamental interactions of nature, alongside the strong interaction, electromagnetism, and gravitation.

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