The atomic nucleus is the small, dense region
consisting of protons and neutrons at the
center of an atom, discovered in 1911 by Ernest
Rutherford based on the 1909 Geiger–Marsden
gold foil experiment.
After the discovery of the neutron in 1932,
models for a nucleus composed of protons and
neutrons were quickly developed by Dmitri
Ivanenko and Werner Heisenberg.
An atom is composed of a positively-charged
nucleus, with a cloud of negatively-charged
electrons surrounding it, bound together by
electrostatic force.
Almost all of the mass of an atom is located
in the nucleus, with a very small contribution
from the electron cloud.
Protons and neutrons are bound together to
form a nucleus by the nuclear force.
The diameter of the nucleus is in the range
of 1.7566 fm (1.7566×10−15 m) for hydrogen
(the diameter of a single proton) to about
11.7142 fm for the heaviest atom uranium.
These dimensions are much smaller than the
diameter of the atom itself (nucleus + electron
cloud), by a factor of about 26,634 (uranium
atomic radius is about 156 pm (156×10−12
m)) to about 60,250 (hydrogen atomic radius
is about 52.92 pm).The branch of physics concerned
with the study and understanding of the atomic
nucleus, including its composition and the
forces which bind it together, is called nuclear
physics.
== Introduction ==
=== 
History ===
The nucleus was discovered in 1911, as a result
of Ernest Rutherford's efforts to test Thomson's
"plum pudding model" of the atom.
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.
=== Etymology ===
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.
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"
=== Nuclear makeup ===
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.
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.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 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 strong force range limits
==
The effective absolute limit of the range
of the 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.
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 (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
1
/
3
{\displaystyle R=r_{0}A^{1/3}\,}
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.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 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 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.
=== 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 ==
== Notes
