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The atomic nucleus is the small, dense region consisting of s and s at the center of an , discovered in 1911 by based on the 1909 . After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by and . An atom is composed of a positively-charged nucleus, with a cloud of negatively-charged s surrounding it, bound together by . Almost all of the of an atom is located in the nucleus, with a very small contribution from the . Protons and neutrons are bound together to form a nucleus by the . The diameter of the nucleus is in the range of () for (the diameter of a single proton) to about for . 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 ()) to about 60,250 ( is about ).26,634 derives from x / ; 60,250 derives from x / 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 .

# Introduction

## History

The nucleus was discovered in 1911, as a result of 's efforts to test Thomson's "" of the atom. The electron had already been discovered by . Knowing that atoms are electrically neutral, J.J.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 and with help of , that involved the deflection of s (helium nuclei) directed at a thin sheet of metal foil. He reasoned that if J.J 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.

## Etymology

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

## Nuclear makeup

The nucleus of an atom consists of neutrons and protons, which in turn are the manifestation of more elementary particles, called , that are held in association by the in certain stable combinations of s, called s. 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 an atom represents is determined by the number of s 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 . 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 s (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 s, with different values of the , so two protons and two neutrons can share the same space since they are not identical quantum entities. They are sometimes viewed as two different quantum states of the same particle, the '. Two fermions, such as two protons, or two neutrons, or a proton + neutron (the deuteron) can exhibit ic behavior when they become loosely bound in pairs, which have integer spin. In the rare case of a , a third called a , containing one or more 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. Nuclei can be spherical, rugby ball-shaped (prolate deformation), discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation) or pear-shaped.

# Forces

Nuclei are bound together by the residual strong force (). The residual strong force is a minor residuum of the 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 s 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 ); thus only nuclei smaller than a certain size can be completely stable. The largest known completely stable nucleus (i.e. stable to alpha, , and ) is 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, 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 s (fm); roughly one or two nucleon diameters) and causes an attraction between any pair of nucleons. For example, between s and s to form , 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 (also known as residual ) is represented by such as or , in which s, or other collections of neutrons, orbit at distances of about (roughly similar to the 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 s; for example, lithium-11 has a half-life of . 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 N, NNNor protons P, 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 ' 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 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 . This is due to two reasons: * In principle, the physics within a nucleus can be derived entirely from (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 that occurs between high-energy matter and low-energy ic matter, which renders unusable, making it difficult to construct an accurate QCD-derived model of the . Current approaches are limited to either phenomenological models such as the Argonne v18 potential or . * Even if the nuclear force is well constrained, a significant amount of computational power is required to accurately compute the properties of nuclei . Developments in 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. The (''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 (''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, :$R = r_0 A^ \,$ where ''A'' = Atomic (the number of protons ''Z'', plus the number of neutrons ''N'') and ''r''0 = 1.25 fm = 1.25 × 10−15 m. In this equation, the "constant" ''r''0 varies by 0.2 fm, depending on the nucleus in question, but this is less than 20% change from a constant. 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 ). Models of 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 as their size and composition changes (see ), 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: 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. Energy. The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy. Asymmetry energy (also called Energy). An energy associated with the . 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 s in 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 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 , 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, , with 3 nucleons, is very stable even with lack of a closed 1s orbital shell. Another nucleus with 3 nucleons, the triton is unstable and will decay into helium-3 when isolated. Weak nuclear stability with 2 nucleons in the 1s orbital is found in the deuteron , with only one nucleon in each of the proton and neutron potential wells. While each nucleon is a fermion, the deuteron is a boson and thus does not follow Pauli Exclusion for close packing within shells. 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 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 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 () and 61 (), 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 model of John Wheeler, of Linus Pauling and the of MacGregor.

## Consistency between models

As with the case of , 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 . The nucleons in atomic nuclei also exhibit a wave-like nature and lack standard fluid properties, such as friction. For nuclei made of s which are s, 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 's s.

# References

The Nucleus – a chapter from an online textbook

The LIVEChart of Nuclides – IAEA
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Accessed September 16, 2009.

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