Atomic nucleus

The discovery of the atomic nucleus played a significant role in science.

Nucleus drawing
A model of the atomic nucleus showing it as a compact bundle of the two types of nucleons: protons (red) and neutrons (blue). In this diagram, protons and neutrons look like little balls stuck together, but an actual nucleus (as understood by modern nuclear physics) cannot be explained like this, but only by using quantum mechanics. In a nucleus which occupies a certain energy level (for example, the ground state), each nucleon can be said to occupy a range of locations.

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[1] and Werner Heisenberg.[2][3][4][5][6] 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.[7] 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))[8] to about 60,250 (hydrogen atomic radius is about 52.92 pm).[a]

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.



The nucleus was discovered in 1911, as a result of Ernest Rutherford's efforts to test Thomson's "plum pudding model" of the atom.[9] The electron had already been discovered earlier by J.J. Thomson himself. Knowing that atoms are electrically neutral, Thomson postulated that there must be a positive charge as well. In his plum pudding model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge. Ernest Rutherford later devised an experiment with his research partner Hans Geiger and with help of Ernest Marsden, that involved the deflection of alpha particles (helium nuclei) directed at a thin sheet of metal foil. He reasoned that if Thomson's model were correct, the positively charged alpha particles would easily pass through the foil with very little deviation in their paths, as the foil should act as electrically neutral if the negative and positive charges are so intimately mixed as to make it appear neutral. To his surprise, many of the particles were deflected at very large angles. Because the mass of an alpha particle is about 8000 times that of an electron, it became apparent that a very strong force must be present if it could deflect the massive and fast moving alpha particles. He realized that the plum pudding model could not be accurate and that the deflections of the alpha particles could only be explained if the positive and negative charges were separated from each other and that the mass of the atom was a concentrated point of positive charge. This justified the idea of a nuclear atom with a dense center of positive charge and mass.


The term nucleus is from the Latin word nucleus, a diminutive of nux ("nut"), meaning the kernel (i.e., the "small nut") inside a watery type of fruit (like a peach). In 1844, Michael Faraday used the term to refer to the "central point of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912.[10] The adoption of the term "nucleus" to atomic theory, however, was not immediate. In 1916, for example, Gilbert N. Lewis stated, in his famous article The Atom and the Molecule, that "the atom is composed of the kernel and an outer atom or shell"[11]

Nuclear makeup

Helium atom QM
A figurative depiction of the helium-4 atom with the electron cloud in shades of gray. In the nucleus, the two protons and two neutrons are depicted in red and blue. This depiction shows the particles as separate, whereas in an actual helium atom, the protons are superimposed in space and most likely found at the very center of the nucleus, and the same is true of the two neutrons. Thus, all four particles are most likely found in exactly the same space, at the central point. Classical images of separate particles fail to model known charge distributions in very small nuclei. A more accurate image is that the spatial distribution of nucleons in a helium nucleus is much closer to the helium electron cloud shown here, although on a far smaller scale, than to the fanciful nucleus image.

The nucleus of an atom consists of neutrons and protons, which in turn are the manifestation of more elementary particles, called quarks, that are held in association by the nuclear strong force in certain stable combinations of hadrons, called baryons. The nuclear strong force extends far enough from each baryon so as to bind the neutrons and protons together against the repulsive electrical force between the positively charged protons. The nuclear strong force has a very short range, and essentially drops to zero just beyond the edge of the nucleus. The collective action of the positively charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations and numbers of electrons that make their orbits stable. Which chemical element an atom represents is determined by the number of protons in the nucleus; the neutral atom will have an equal number of electrons orbiting that nucleus. Individual chemical elements can create more stable electron configurations by combining to share their electrons. It is that sharing of electrons to create stable electronic orbits about the nucleus that appears to us as the chemistry of our macro world.

Protons define the entire charge of a nucleus, and hence its chemical identity. Neutrons are electrically neutral, but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons can explain the phenomenon of isotopes (same atomic number with different atomic mass.) The main role of neutrons is to reduce electrostatic repulsion inside the nucleus.

Composition and shape

Protons and neutrons are fermions, with different values of the strong isospin quantum number, so two protons and two neutrons can share the same space wave function since they are not identical quantum entities. They are sometimes viewed as two different quantum states of the same particle, the nucleon.[12][13] Two fermions, such as two protons, or two neutrons, or a proton + neutron (the deuteron) can exhibit bosonic behavior when they become loosely bound in pairs, which have integer spin.

In the rare case of a hypernucleus, a third baryon called a hyperon, containing one or more strange quarks and/or other unusual quark(s), can also share the wave function. However, this type of nucleus is extremely unstable and not found on Earth except in high energy physics experiments.

The neutron has a positively charged core of radius ≈ 0.3 fm surrounded by a compensating negative charge of radius between 0.3 fm and 2 fm. The proton has an approximately exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm.[14]

Nuclei can be spherical, rugby ball-shaped (prolate deformation), discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation) or pear-shaped.[15][16]


Nuclei are bound together by the residual strong force (nuclear force). The residual strong force is a minor residuum of the strong interaction which binds quarks together to form protons and neutrons. This force is much weaker between neutrons and protons because it is mostly neutralized within them, in the same way that electromagnetic forces between neutral atoms (such as van der Waals forces that act between two inert gas atoms) are much weaker than the electromagnetic forces that hold the parts of the atoms together internally (for example, the forces that hold the electrons in an inert gas atom bound to its nucleus).

The nuclear force is highly attractive at the distance of typical nucleon separation, and this overwhelms the repulsion between protons due to the electromagnetic force, thus allowing nuclei to exist. However, the residual strong force has a limited range because it decays quickly with distance (see Yukawa potential); thus only nuclei smaller than a certain size can be completely stable. The largest known completely stable nucleus (i.e. stable to alpha, beta, and gamma decay) is lead-208 which contains a total of 208 nucleons (126 neutrons and 82 protons). Nuclei larger than this maximum are unstable and tend to be increasingly short-lived with larger numbers of nucleons. However, bismuth-209 is also stable to beta decay and has the longest half-life to alpha decay of any known isotope, estimated at a billion times longer than the age of the universe.

The residual strong force is effective over a very short range (usually only a few femtometres (fm); roughly one or two nucleon diameters) and causes an attraction between any pair of nucleons. For example, between protons and neutrons to form [NP] deuteron, and also between protons and protons, and neutrons and neutrons.

Halo nuclei and nuclear force range limits

The effective absolute limit of the range of the nuclear force (also known as residual strong force) is represented by halo nuclei such as lithium-11 or boron-14, in which dineutrons, or other collections of neutrons, orbit at distances of about 10 fm (roughly similar to the 8 fm radius of the nucleus of uranium-238). These nuclei are not maximally dense. Halo nuclei form at the extreme edges of the chart of the nuclides—the neutron drip line and proton drip line—and are all unstable with short half-lives, measured in milliseconds; for example, lithium-11 has a half-life of 8.8 ms.

Halos in effect represent an excited state with nucleons in an outer quantum shell which has unfilled energy levels "below" it (both in terms of radius and energy). The halo may be made of either neutrons [NN, NNN] or protons [PP, PPP]. Nuclei which have a single neutron halo include 11Be and 19C. A two-neutron halo is exhibited by 6He, 11Li, 17B, 19B and 22C. Two-neutron halo nuclei break into three fragments, never two, and are called Borromean nuclei because of this behavior (referring to a system of three interlocked rings in which breaking any ring frees both of the others). 8He and 14Be both exhibit a four-neutron halo. Nuclei which have a proton halo include 8B and 26P. A two-proton halo is exhibited by 17Ne and 27S. Proton halos are expected to be more rare and unstable than the neutron examples, because of the repulsive electromagnetic forces of the excess proton(s).

Nuclear models

Although the standard model of physics is widely believed to completely describe the composition and behavior of the nucleus, generating predictions from theory is much more difficult than for most other areas of particle physics. This is due to two reasons:

  • In principle, the physics within a nucleus can be derived entirely from quantum chromodynamics (QCD). In practice however, current computational and mathematical approaches for solving QCD in low-energy systems such as the nuclei are extremely limited. This is due to the phase transition that occurs between high-energy quark matter and low-energy hadronic matter, which renders perturbative techniques unusable, making it difficult to construct an accurate QCD-derived model of the forces between nucleons. Current approaches are limited to either phenomenological models such as the Argonne v18 potential or chiral effective field theory.[17]
  • Even if the nuclear force is well constrained, a significant amount of computational power is required to accurately compute the properties of nuclei ab initio. Developments in many-body theory have made this possible for many low mass and relatively stable nuclei, but further improvements in both computational power and mathematical approaches are required before heavy nuclei or highly unstable nuclei can be tackled.

Historically, experiments have been compared to relatively crude models that are necessarily imperfect. None of these models can completely explain experimental data on nuclear structure.[18]

The nuclear radius (R) is considered to be one of the basic quantities that any model must predict. For stable nuclei (not halo nuclei or other unstable distorted nuclei) the nuclear radius is roughly proportional to the cube root of the mass number (A) of the nucleus, and particularly in nuclei containing many nucleons, as they arrange in more spherical configurations:

The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula,

where A = Atomic mass number (the number of protons Z, plus the number of neutrons N) and r0 = 1.25 fm = 1.25 × 10−15 m. In this equation, the "constant" r0 varies by 0.2 fm, depending on the nucleus in question, but this is less than 20% change from a constant.[19]

In other words, packing protons and neutrons in the nucleus gives approximately the same total size result as packing hard spheres of a constant size (like marbles) into a tight spherical or almost spherical bag (some stable nuclei are not quite spherical, but are known to be prolate).[20]

Models of nuclear structure include :

Liquid drop model

Early models of the nucleus viewed the nucleus as a rotating liquid drop. In this model, the trade-off of long-range electromagnetic forces and relatively short-range nuclear forces, together cause behavior which resembled surface tension forces in liquid drops of different sizes. This formula is successful at explaining many important phenomena of nuclei, such as their changing amounts of binding energy as their size and composition changes (see semi-empirical mass formula), but it does not explain the special stability which occurs when nuclei have special "magic numbers" of protons or neutrons.

The terms in the semi-empirical mass formula, which can be used to approximate the binding energy of many nuclei, are considered as the sum of five types of energies (see below). Then the picture of a nucleus as a drop of incompressible liquid roughly accounts for the observed variation of binding energy of the nucleus:

Liquid drop model

Liquid drop model

Volume energy. When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. So, this nuclear energy is proportional to the volume.

Surface energy. A nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.

Coulomb Energy. The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy.

Asymmetry energy (also called Pauli Energy). An energy associated with the Pauli exclusion principle. Were it not for the Coulomb energy, the most stable form of nuclear matter would have the same number of neutrons as protons, since unequal numbers of neutrons and protons imply filling higher energy levels for one type of particle, while leaving lower energy levels vacant for the other type.

Pairing energy. An energy which is a correction term that arises from the tendency of proton pairs and neutron pairs to occur. An even number of particles is more stable than an odd number.

Shell models and other quantum models

A number of models for the nucleus have also been proposed in which nucleons occupy orbitals, much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons to be either sizeless point particles in potential wells, or else probability waves as in the "optical model", frictionlessly orbiting at high speed in potential wells.

In the above models, the nucleons may occupy orbitals in pairs, due to being fermions, which allows explanation of even/odd Z and N effects well-known from experiments. The exact nature and capacity of nuclear shells differs from those of electrons in atomic orbitals, primarily because the potential well in which the nucleons move (especially in larger nuclei) is quite different from the central electromagnetic potential well which binds electrons in atoms. Some resemblance to atomic orbital models may be seen in a small atomic nucleus like that of helium-4, in which the two protons and two neutrons separately occupy 1s orbitals analogous to the 1s orbital for the two electrons in the helium atom, and achieve unusual stability for the same reason. Nuclei with 5 nucleons are all extremely unstable and short-lived, yet, helium-3, with 3 nucleons, is very stable even with lack of a closed 1s orbital shell. Another nucleus with 3 nucleons, the triton hydrogen-3 is unstable and will decay into helium-3 when isolated. Weak nuclear stability with 2 nucleons {NP} in the 1s orbital is found in the deuteron hydrogen-2, with only one nucleon in each of the proton and neutron potential wells. While each nucleon is a fermion, the {NP} deuteron is a boson and thus does not follow Pauli Exclusion for close packing within shells. Lithium-6 with 6 nucleons is highly stable without a closed second 1p shell orbital. For light nuclei with total nucleon numbers 1 to 6 only those with 5 do not show some evidence of stability. Observations of beta-stability of light nuclei outside closed shells indicate that nuclear stability is much more complex than simple closure of shell orbitals with magic numbers of protons and neutrons.

For larger nuclei, the shells occupied by nucleons begin to differ significantly from electron shells, but nevertheless, present nuclear theory does predict the magic numbers of filled nuclear shells for both protons and neutrons. The closure of the stable shells predicts unusually stable configurations, analogous to the noble group of nearly-inert gases in chemistry. An example is the stability of the closed shell of 50 protons, which allows tin to have 10 stable isotopes, more than any other element. Similarly, the distance from shell-closure explains the unusual instability of isotopes which have far from stable numbers of these particles, such as the radioactive elements 43 (technetium) and 61 (promethium), each of which is preceded and followed by 17 or more stable elements.

There are however problems with the shell model when an attempt is made to account for nuclear properties well away from closed shells. This has led to complex post hoc distortions of the shape of the potential well to fit experimental data, but the question remains whether these mathematical manipulations actually correspond to the spatial deformations in real nuclei. Problems with the shell model have led some to propose realistic two-body and three-body nuclear force effects involving nucleon clusters and then build the nucleus on this basis. Three such cluster models are the 1936 Resonating Group Structure model of John Wheeler, Close-Packed Spheron Model of Linus Pauling and the 2D Ising Model of MacGregor.[18]

Consistency between models

As with the case of superfluid liquid helium, atomic nuclei are an example of a state in which both (1) "ordinary" particle physical rules for volume and (2) non-intuitive quantum mechanical rules for a wave-like nature apply. In superfluid helium, the helium atoms have volume, and essentially "touch" each other, yet at the same time exhibit strange bulk properties, consistent with a Bose–Einstein condensation. The nucleons in atomic nuclei also exhibit a wave-like nature and lack standard fluid properties, such as friction. For nuclei made of hadrons which are fermions, Bose-Einstein condensation does not occur, yet nevertheless, many nuclear properties can only be explained similarly by a combination of properties of particles with volume, in addition to the frictionless motion characteristic of the wave-like behavior of objects trapped in Erwin Schrödinger's quantum orbitals.

See also


  1. ^ 26,634 derives from 2 x 156 pm / 11.7142 fm; 60,250 derives from 2 x 52.92 pm / 1.7166 fm


  1. ^ Iwanenko, D.D. (1932). "The neutron hypothesis". Nature. 129 (3265): 798. Bibcode:1932Natur.129..798I. doi:10.1038/129798d0.
  2. ^ Heisenberg, W. (1932). "Über den Bau der Atomkerne. I". Z. Phys. 77: 1–11. Bibcode:1932ZPhy...77....1H. doi:10.1007/BF01342433.
  3. ^ Heisenberg, W. (1932). "Über den Bau der Atomkerne. II". Z. Phys. 78 (3–4): 156–164. Bibcode:1932ZPhy...78..156H. doi:10.1007/BF01337585.
  4. ^ Heisenberg, W. (1933). "Über den Bau der Atomkerne. III". Z. Phys. 80 (9–10): 587–596. Bibcode:1933ZPhy...80..587H. doi:10.1007/BF01335696.
  5. ^ Miller A. I. Early Quantum Electrodynamics: A Sourcebook, Cambridge University Press, Cambridge, 1995, ISBN 0521568919, pp. 84–88.
  6. ^ Fernandez, Bernard & Ripka, Georges (2012). "Nuclear Theory After the Discovery of the Neutron". Unravelling the Mystery of the Atomic Nucleus: A Sixty Year Journey 1896 — 1956. Springer. p. 263. ISBN 9781461441809.
  7. ^ Angeli, I., Marinova, K.P. (January 10, 2013). "Table of experimental nuclear ground state charge radii: An update". Atomic Data and Nuclear Data Tables. 99: 69–95. Bibcode:2013ADNDT..99...69A. doi:10.1016/j.adt.2011.12.006.CS1 maint: Multiple names: authors list (link)
  8. ^ "Uranium" IDC Technologies.
  9. ^ "The Rutherford Experiment". Rutgers University. Archived from the original on November 14, 2001. Retrieved February 26, 2013.
  10. ^ Harper, D. "Nucleus". Online Etymology Dictionary. Retrieved 2010-03-06.
  11. ^ Lewis, G.N. (1916). "The Atom and the Molecule". Journal of the American Chemical Society. 38 (4): 4. doi:10.1021/ja02261a002.
  12. ^ Sitenko, A.G. & Tartakovskiĭ, V.K. (1997). Theory of Nucleus: Nuclear Structure and Nuclear Interaction. Kluwer Academic. p. 3. ISBN 978-0-7923-4423-0.
  13. ^ Srednicki, M.A. (2007). Quantum Field Theory. Cambridge University Press. pp. 522–523. ISBN 978-0-521-86449-7.
  14. ^ Basdevant, J.-L.; Rich, J. & Spiro, M. (2005). Fundamentals in Nuclear Physics. Springer. p. 155. ISBN 978-0-387-01672-6.
  15. ^ Battersby, Stephen (2013). "Pear-shaped nucleus boosts search for new physics". Nature. doi:10.1038/nature.2013.12952. Retrieved 23 November 2017.
  16. ^ Gaffney, L. P.; Butler, P A; Scheck, M; Hayes, A B; Wenander, F; et al. (2013). "Studies of pear-shaped nuclei using accelerated radioactive beams" (PDF). Nature. 497 (7448): 199–204. Bibcode:2013Natur.497..199G. doi:10.1038/nature12073. ISSN 0028-0836. Archived (PDF) from the original on May 9, 2013.
  17. ^ Machleidt, R.; Entem, D.R. (2011). "Chiral effective field theory and nuclear forces". Physics Reports. 503 (1): 1–75. arXiv:1105.2919. Bibcode:2011PhR...503....1M. doi:10.1016/j.physrep.2011.02.001.
  18. ^ a b Cook, N.D. (2010). Models of the Atomic Nucleus (2nd ed.). Springer. p. 57 ff. ISBN 978-3-642-14736-4.
  19. ^ Krane, K.S. (1987). Introductory Nuclear Physics. Wiley-VCH. ISBN 978-0-471-80553-3.
  20. ^ Serway, Raymond; Vuille, Chris; Faughn, Jerry (2009). College Physics (8th ed.). Belmont, CA: Brooks/Cole, Cengage Learning. p. 915. ISBN 9780495386933.

External links

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.

Atomic energy

Atomic energy is energy carried by atoms. The term originated in 1903 when Ernest Rutherford began to speak of the possibility of atomic energy. The term was popularized by H. G. Wells in the phrase, "splitting the atom", devised at a time prior to the discovery of the nucleus. Atomic energy may include:

Nuclear binding energy, the energy required to split a nucleus of an atom.

Nuclear potential energy, the potential energy of the particles inside an atomic nucleus.

Nuclear reaction, a process in which nuclei or nuclear particles interact, resulting in products different from the initial ones; see also nuclear fission and nuclear fusion.

Radioactive decay, the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles.

The energy of inter-atomic or chemical bonds, which holds atoms together in compounds.Atomic energy is the source of nuclear power, which uses sustained nuclear fission to generate heat and electricity.

Atomic mass unit

The unified atomic mass unit or dalton (SI symbols: u, or Da; Deprecated/colloquial symbol: amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest, and has a value of 1.66053906660(50)×10−27 kg, or approximately 1.66 yoctograms. The CIPM has categorised it as a non-SI unit accepted for use with the SI, and whose value in SI units must be obtained experimentally.The atomic mass unit (amu) without the "unified" prefix is technically an obsolete unit based on oxygen, which was replaced in 1961. However, some nontechnical and preparatory sources continue to occasionally use the term amu but now define it in the same way as u (i.e., based on carbon-12). In this sense, most uses of the terms atomic mass units and amu, today, actually refer to unified atomic mass unit. For standardization, a specific atomic nucleus (carbon-12 vs. oxygen-16) had to be chosen because the average mass of a nucleon depends on the count of the nucleons in the atomic nucleus due to mass defect. This is also why the mass of a proton or neutron by itself is more than (and not equal to) 1 u.

The atomic mass unit is not the unit of mass in the atomic units system, which is rather the electron rest mass (me).

Until the 2019 redefinition of SI base units, the number of daltons in a gram is exactly the Avogadro number by definition, or equivalently, a dalton is exactly equivalent to 1 gram/mol. Thereafter, these relationships will no longer be exact, but they will still be extremely accurate approximations.

Charged particle

In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, which are all believed to have the same charge (except antimatter). Another charged particle may be an atomic nucleus devoid of electrons, such as an alpha particle.

A plasma is a collection of charged particles, atomic nuclei and separated electrons, but can also be a gas containing a significant proportion of charged particles.

Decay energy

The decay energy is the energy released by a radioactive decay. Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide.


In particle physics, a hadron (listen) (Greek: ἁδρός, hadrós; "stout, thick") is a composite particle made of two or more quarks held together by the strong force in a similar way as molecules are held together by the electromagnetic force. Most of the mass of ordinary matter comes from two hadrons, the proton and the neutron.

Hadrons are categorized into two families: baryons, made of an odd number of quarks – usually three quarks – and mesons, made of an even number of quarks—usually one quark and one antiquark. Protons and neutrons are examples of baryons; pions are an example of a meson. "Exotic" hadrons, containing more than three valence quarks, have been discovered in recent years. A tetraquark state (an exotic meson), named the Z(4430)−, was discovered in 2007 by the Belle Collaboration and confirmed as a resonance in 2014 by the LHCb collaboration. Two pentaquark states (exotic baryons), named P+c(4380) and P+c(4450), were discovered in 2015 by the LHCb collaboration. There are several more exotic hadron candidates, and other colour-singlet quark combinations that may also exist.

Almost all "free" hadrons and antihadrons (meaning, in isolation and not bound within an atomic nucleus) are believed to be unstable and eventually decay (break down) into other particles. The only known exception relates to free protons, which are possibly stable, or at least, take immense amounts of time to decay (order of 1034+ years). Free neutrons are unstable and decay with a half-life of about 611 seconds. Their respective antiparticles are expected to follow the same pattern, but they are difficult to capture and study, because they immediately annihilate on contact with ordinary matter. "Bound" protons and neutrons, contained within an atomic nucleus, are generally considered stable. Experimentally, hadron physics is studied by colliding protons or nuclei of heavy elements such as lead or gold, and detecting the debris in the produced particle showers. In the environment, mesons such as pions are produced by the collisions of cosmic rays with the atmosphere.

Halo nucleus

In nuclear physics, an atomic nucleus is called a halo nucleus or is said to have a nuclear halo when it has a core nucleus surrounded by a "halo" of orbiting protons or neutrons, which makes the radius of the nucleus appreciably larger than that predicted by the liquid drop model. Halo nuclei form at the extreme edges of the table of nuclides — the neutron drip line and proton drip line — and have short half-lives, measured in milliseconds. These nuclei are studied shortly after their formation in an ion beam.

Typically, an atomic nucleus is a tightly bound group of protons and neutrons. However, in some nuclides, there is an overabundance of one species of nucleon. In some of these cases, a nuclear core and a halo will form.

Often, this property may be detected in scattering experiments, which show the nucleus to be much larger than the otherwise expected value. Normally, the cross-section (corresponding to the classical radius) of the nucleus is proportional to the cube root of its mass, as would be the case for a sphere of constant density. Specifically, for a nucleus of mass number A, the radius r is (approximately)

where is 1.2 fm.

One example of a halo nucleus is 11Li, which has a half-life of 8.6 ms. It contains a core of 3 protons and 6 neutrons, and a halo of two independent and loosely bound neutrons. It decays into 11Be by the emission of an antineutrino and an electron. Its mass radius of 3.16 fm is close to that of 32S or, even more impressively, of 208Pb, both much heavier nuclei.

Experimental confirmation of nuclear halos is recent and ongoing. Additional candidates are suspected. Several nuclides including 9B, 13N, and 15N are calculated to have a halo in the excited state but not in the ground state.

Hydron (chemistry)

In chemistry, a hydron is the general name for a cationic form of atomic hydrogen, represented with the symbol H+. However, this term is avoided and instead "proton" is used, which strictly speaking refers to the cation of protium, the most common isotope of hydrogen. The term "hydron" includes cations of hydrogen regardless of their isotopic composition: thus it refers collectively to protons (1H+) for the protium isotope, deuterons (2H+ or D+) for the deuterium isotope, and tritons (3H+ or T+) for the tritium isotope. Unlike most other ions, the hydron consists only of a bare atomic nucleus.

The negatively charged counterpart of the hydron is the hydride anion, H−.

Mass number

The mass number (symbol A, from the German word Atomgewicht (atomic weight), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It determines the atomic mass of atoms. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion. The mass number is different for each different isotope of a chemical element. This is not the same as the atomic number (Z) which denotes the number of protons in a nucleus, and thus uniquely identifies an element. Hence, the difference between the mass number and the atomic number gives the number of neutrons (N) in a given nucleus: .

The mass number is written either after the element name or as a superscript to the left of an element's symbol. For example, the most common isotope of carbon is carbon-12, or 12
, which has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (Z) as a subscript to the left of the element symbol directly below the mass number: 12
. This is technically redundant, as each element is defined by its atomic number, so it is often omitted.

NGC 7252

NGC 7252 is a peculiar galaxy resulting from an interaction between two galaxies that started a billion years ago. It is located 220 million light years away in the constellation Aquarius. It is also called Atoms for Peace Galaxy, a nickname which comes from its loop-like structure, made of stars, that resembles a diagram of an electron orbiting an atomic nucleus.

Neutron capture

Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, which are repelled electrostatically.Neutron capture plays an important role in the cosmic nucleosynthesis of heavy elements. In stars it can proceed in two ways: as a rapid (r-process) or a slow process (s-process). Nuclei of masses greater than 56 cannot be formed by thermonuclear reactions (i.e. by nuclear fusion), but can be formed by neutron capture.

Neutron capture on protons yields a line at 2.223 MeV predicted and commonly observed in solar flares.

Nuclear shell model

In nuclear 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 model was proposed by Dmitry Ivanenko (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by several physicists, most notably Eugene Paul Wigner, Maria Goeppert Mayer and J. Hans D. Jensen, who shared the 1963 Nobel Prize in Physics for their contributions.

The shell model is partly analogous to the atomic shell model which describes the arrangement of electrons in an atom, in that a filled shell results in greater stability. When adding nucleons (protons or neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. This observation, that there are certain magic numbers of nucleons: 2, 8, 20, 28, 50, 82, 126 which are more tightly bound than the next higher number, is the origin of the shell model.

The shells for protons and for neutrons are independent of each other. Therefore, "magic nuclei" exist in which one nucleon type or the other is at a magic number, and "doubly magic nuclei", where both are. Due to some variations in orbital filling, the upper magic numbers are 126 and, speculatively, 184 for neutrons but only 114 for protons, playing a role in the search for the so-called island of stability. Some semimagic numbers have been found, notably Z=40 giving nuclear shell filling for the various elements; 16 may also be a magic number.In order to get these numbers, the nuclear shell model starts from an average potential with a shape something between the square well and the harmonic oscillator. To this potential a spin orbit term is added. Even so, the total perturbation does not coincide with experiment, and an empirical spin orbit coupling must be added with at least two or three different values of its coupling constant, depending on the nuclei being studied.

Nevertheless, the magic numbers of nucleons, as well as other properties, can be arrived at by approximating the model with a three-dimensional harmonic oscillator plus a spin-orbit interaction. A more realistic but also complicated potential is known as Woods–Saxon potential.

Nuclear structure

Understanding the structure of the atomic nucleus is one of the central challenges in nuclear physics.


In chemistry and physics, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines an isotope's mass number (nucleon number).

Until the 1960s, nucleons were thought to be elementary particles, not made up of smaller parts. Now they are known to be composite particles, made of three quarks bound together by the so-called strong interaction. The interaction between two or more nucleons is called internucleon interaction or nuclear force, which is also ultimately caused by the strong interaction. (Before the discovery of quarks, the term "strong interaction" referred to just internucleon interactions.)

Nucleons sit at the boundary where particle physics and nuclear physics overlap. Particle physics, particularly quantum chromodynamics, provides the fundamental equations that explain the properties of quarks and of the strong interaction. These equations explain quantitatively how quarks can bind together into protons and neutrons (and all the other hadrons). However, when multiple nucleons are assembled into an atomic nucleus (nuclide), these fundamental equations become too difficult to solve directly (see lattice QCD). Instead, nuclides are studied within nuclear physics, which studies nucleons and their interactions by approximations and models, such as the nuclear shell model. These models can successfully explain nuclide properties, as for example, whether or not a particular nuclide undergoes radioactive decay.

The proton and neutron are both fermions, hadrons and baryons. The proton carries a positive net charge and the neutron carries a zero net charge; the proton's mass is only about 0.13% less than the neutron's. Thus, they can be viewed as two states of the same nucleon, and together form an isospin doublet (I = ​1⁄2). In isospin space, neutrons can be transformed into protons via SU(2) symmetries, and vice versa. These nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space. According to the Noether theorem, isospin is conserved with respect to the strong interaction.


Photodisintegration (also called phototransmutation) is a nuclear process in which an atomic nucleus absorbs a high-energy gamma ray, enters an excited state, and immediately decays by emitting a subatomic particle. The incoming gamma ray effectively knocks one or more neutrons, protons, or an alpha particle out of the nucleus. The reactions are called (γ,n), (γ,p), and (γ,α).

Photodisintegration is endothermic (energy absorbing) for atomic nuclei lighter than iron and sometimes exothermic (energy releasing) for atomic nuclei heavier than iron. Photodisintegration is responsible for the nucleosynthesis of at least some heavy, proton-rich elements via the p-process in supernovae.

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%.

Robert James Moon

Robert James Moon (February 14, 1911 – November 1, 1989) was an American physicist, chemist and engineer. An important figure in 20th century nuclear science, he was involved in America's wartime Manhattan Project. He pioneered work on the fundamental structure of the atomic nucleus based on Platonic solids.

Semi-empirical mass formula

In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called Weizsäcker's formula, or the Bethe–Weizsäcker formula, or the Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass and various other properties of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory and partly on empirical measurements. The theory is based on the liquid drop model proposed by George Gamow, which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker, and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today.The SEMF gives a good approximation for atomic masses and several other effects, but does not explain the appearance of magic numbers of protons and neutrons, and the extra binding-energy and measure of stability that are associated with these numbers of nucleons.

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