atomic nucleus

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The atomic nucleus is the small, dense region consisting of
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s and
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
s at the center of an
atom Every atom is composed of a atomic nucleus, nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, l ...
, discovered in 1911 by
Ernest Rutherford Ernest Rutherford, 1st Baron Rutherford of Nelson, (30 August 1871 – 19 October 1937) was a New Zealand physicist who came to be known as the father of nuclear physics. ''Encyclopædia Britannica'' considers him to be the greatest ...
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 Dmitri Dmitrievich Ivanenko (russian: Дми́трий Дми́триевич Иване́нко; July 29, 1904 – December 30, 1994) was a Ukraine, Ukrainian Theoretical physics, theoretical physicist who made great contributions to the physical ...
and
Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics ...
. An atom is composed of a positively charged nucleus, with a cloud of negatively charged
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
s surrounding it, bound together by
electrostatic force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that quantifies the amount of force between two stationary, electric charge, electrically charged particles. The electric force between char ...
. Almost all of the
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
of an atom is located in the nucleus, with a very small contribution from the
electron cloud In atomic theory and quantum mechanics, an atomic orbital is a Function (mathematics), function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electr ...
. Protons and neutrons are bound together to form a nucleus by the
nuclear force The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nucle ...
. The diameter of the nucleus is in the range of () for
hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the chemical ...
(the diameter of a single proton) to about for
uranium Uranium is a chemical element with the Symbol (chemistry), symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. ...
. 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 ( hydrogen atomic radius 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 that bind it together, is called
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the ...
.

Introduction

History

The nucleus was discovered in 1911, as a result of
Ernest Rutherford Ernest Rutherford, 1st Baron Rutherford of Nelson, (30 August 1871 – 19 October 1937) was a New Zealand physicist who came to be known as the father of nuclear physics. ''Encyclopædia Britannica'' considers him to be the greatest ...
's efforts to test Thomson's "
plum pudding model The plum pudding model is one of several historical scientific modelling, scientific models of the atom. First proposed by J. J. Thomson in 1904 soon after the discovery of the electron, but before the discovery of the atomic nucleus, the model t ...
" of the atom. The electron had already been discovered by J.J. Thomson. 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
Hans Geiger Johannes Wilhelm "Hans" Geiger (; ; 30 September 1882 – 24 September 1945) was a German physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all leng ...
and with help of Ernest Marsden, that involved the deflection of
alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than tha ...
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 , a diminutive of ('nut'), meaning 'the kernel' (i.e., the 'small nut') inside a watery type of fruit (like a
peach The peach (''Prunus persica'') is a deciduous tree first domesticated and Agriculture, cultivated in Zhejiang, Zhejiang province of East China, Eastern China. It bears edible juicy fruits with various characteristics, most called peaches and o ...
). In 1844,
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, ...
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, 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.''" Similarly, the term ''kern'' meaning kernel is used for nucleus in German and Dutch.

Nuclear makeup

The nucleus of an atom consists of neutrons and protons, which in turn are the manifestation of more elementary particles, called
quarks A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
, that are held in association by the nuclear strong force in certain stable combinations of
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite particle, composite subatomic particle made of two or more quarks bound state, held together by the strong interaction. They are analogous to molecules tha ...
s, called
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron list of particles, family of particles; hadrons are composed o ...
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
chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
an atom represents is determined by the number of
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
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 nuclei 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
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbe ...
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
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks ...
s, with different values of the strong isospin
quantum number In Quantum mechanics, quantum physics and chemistry, quantum numbers describe values of conserved quantity, conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of Operator (quantum mechanics), ope ...
, so two protons and two neutrons can share the same space
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex number, complex-valued probability amplitude, and the probabilities for the possible results of ...
since they are not identical quantum entities. They are sometimes viewed as two different quantum states of the same particle, the ''
nucleon In physics and chemistry, 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 the atom's mass number, mass number (nucleon number). Until the 1960s, n ...
''. Two fermions, such as two protons, or two neutrons, or a proton + neutron (the deuteron) can exhibit
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer ...
ic behavior when they become loosely bound in pairs, which have integer spin. In the rare case of a hypernucleus, a third
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron list of particles, family of particles; hadrons are composed o ...
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. 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 (
nuclear force The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nucle ...
). The residual strong force is a minor residuum of the
strong interaction The strong interaction or strong force is a fundamental interaction that confines Quark, quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is calle ...
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 force In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic bond, ionic or covalent bonds, these attractions do not result from a Chemical bond, chemical electronic bond; they are c ...
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 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 Beta (, ; uppercase , lowercase , or cursive Greek, cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents th ...
, 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 Bismuth-209 (209Bi) is the isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that ...
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
femtometre file:Helium atom QM.svg, The helium atom and perspective Magnitude (mathematics), magnitudes The femtometre (American spelling femtometer) symbol fm derived from the Danish language, Danish and Norwegian language, Norwegian word 'fifteen', grc ...
s (fm); roughly one or two nucleon diameters) and causes an attraction between any pair of nucleons. For example, between
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s and
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
s to form P
deuteron Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
, 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 The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nucle ...
(also known as residual
strong force The strong interaction or strong force is a fundamental interaction that confines Quark, quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is calle ...
) 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 (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
millisecond A millisecond (from ''milli-'' and second; symbol: ms) is a unit of time in the International System of Units (SI) equal to one thousandth (0.001 or 10−3 or 1/1000) of a second and to 1000 microseconds. A unit of 10 milliseconds may be called ...
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 '' 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 The Standard Model of particle physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles ...
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 Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standa ...
. This is due to two reasons: * In principle, the physics within a nucleus can be derived entirely from
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type o ...
(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 In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of ...
that occurs between high-energy
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
matter and low-energy
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite particle, composite subatomic particle made of two or more quarks bound state, held together by the strong interaction. They are analogous to molecules tha ...
ic 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. * 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. 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 The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive e ...
(''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
mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive e ...
(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 prolate). 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 In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
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: 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 The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In 2019 redefinition of the SI base units, the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant curre ...
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 In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spin (physics), spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This 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 orbital In atomic theory and quantum mechanics, an atomic orbital is a Function (mathematics), function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electr ...
s in
atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
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 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...
, 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 Helium-3 (3He see also helion (chemistry), helion) is a light, stable isotope of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than Isotopes of hydrogen#Hydrog ...
, 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 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 deuteron is a boson and thus does not follow Pauli Exclusion for close packing within shells.
Lithium-6 Naturally occurring lithium Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the Symbol (chemistry), symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard temperature and ...
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 Tin is a chemical element with the Chemical symbol, symbol Sn (from la, :la:Stannum, stannum) and atomic number 50. Tin is a silvery-coloured metal. Tin is soft enough to be cut with little force and a bar of tin can be bent by hand wit ...
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 Technetium is a chemical element with the Symbol (chemistry), symbol Tc and atomic number 43. It is the lightest element whose isotopes are all radioactive. All available technetium is produced as a synthetic element. Naturally occurring techneti ...
) and 61 (
promethium Promethium is a chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemic ...
), 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.

Consistency between models

As with the case of
superfluid Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortex, vortices that continue to rotate indefinitely. Superfluidity occurs ...
liquid helium Liquid helium is a physical state of helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol (chemistry), symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert gas, inert, mo ...
, 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
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite particle, composite subatomic particle made of two or more quarks bound state, held together by the strong interaction. They are analogous to molecules tha ...
s which are
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks ...
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 Erwin Schrödinger's quantum orbitals.

References

The Nucleus – a chapter from an online textbook

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

{{DEFAULTSORT:Atomic Nucleus Atoms Nuclear chemistry Nuclear physics Subatomic particles Radiochemistry Proton Electron