The nuclear force (or nucleon–nucleon interaction
or residual strong force) is a force that
acts between the protons and neutrons of atoms.
Neutrons and protons, both nucleons, are affected
by the nuclear force almost identically. Since
protons have charge +1 e, they experience
an electric force that tends to push them
apart, but at short range the attractive nuclear
force is strong enough to overcome the electromagnetic
force. The nuclear force binds nucleons into
atomic nuclei.
The nuclear force is powerfully attractive
between nucleons at distances of about 1 femtometre
(fm, or 1.0 × 10−15 metres), but it rapidly
decreases to insignificance at distances beyond
about 2.5 fm. At distances less than 0.7 fm,
the nuclear force becomes repulsive. This
repulsive component is responsible for the
physical size of nuclei, since the nucleons
can come no closer than the force allows.
By comparison, the size of an atom, measured
in angstroms (Å, or 1.0 × 10−10 m), is
five orders of magnitude larger. The nuclear
force is not simple, however, since it depends
on the nucleon spins, has a tensor component,
and may depend on the relative momentum of
the nucleons. The strong nuclear force is
one of the fundamental forces of nature.
The nuclear force plays an essential role
in storing energy that is used in nuclear
power and nuclear weapons. Work (energy) is
required to bring charged protons together
against their electric repulsion. This energy
is stored when the protons and neutrons are
bound together by the nuclear force to form
a nucleus. The mass of a nucleus is less than
the sum total of the individual masses of
the protons and neutrons. The difference in
masses is known as the mass defect, which
can be expressed as an energy equivalent.
Energy is released when a heavy nucleus breaks
apart into two or more lighter nuclei. This
energy is the electromagnetic potential energy
that is released when the nuclear force no
longer holds the charged nuclear fragments
together.A quantitative description of the
nuclear force relies on equations that are
partly empirical. These equations model the
internucleon potential energies, or potentials.
(Generally, forces within a system of particles
can be more simply modeled by describing the
system's potential energy; the negative gradient
of a potential is equal to the vector force.)
The constants for the equations are phenomenological,
that is, determined by fitting the equations
to experimental data. The internucleon potentials
attempt to describe the properties of nucleon–nucleon
interaction. Once determined, any given potential
can be used in, e.g., the Schrödinger equation
to determine the quantum mechanical properties
of the nucleon system.
The discovery of the neutron in 1932 revealed
that atomic nuclei were made of protons and
neutrons, held together by an attractive force.
By 1935 the nuclear force was conceived to
be transmitted by particles called mesons.
This theoretical development included a description
of the Yukawa potential, an early example
of a nuclear potential. Mesons, predicted
by theory, were discovered experimentally
in 1947. By the 1970s, the quark model had
been developed, by which the mesons and nucleons
were viewed as composed of quarks and gluons.
By this new model, the nuclear force, resulting
from the exchange of mesons between neighboring
nucleons, is a residual effect of the strong
force.
== Description ==
While the nuclear force is usually associated
with nucleons, more generally this force is
felt between hadrons, or particles composed
of quarks. At small separations between nucleons
(less than ~ 0.7 fm between their centers,
depending upon spin alignment) the force becomes
repulsive, which keeps the nucleons at a certain
average separation, even if they are of different
types. This repulsion arises from the Pauli
exclusion force for identical nucleons (such
as two neutrons or two protons). A Pauli exclusion
force also occurs between quarks of the same
type within nucleons, when the nucleons are
different (a proton and a neutron, for example).
=== Field strength ===
At distances larger than 0.7 fm the force
becomes attractive between spin-aligned nucleons,
becoming maximal at a center–center distance
of about 0.9 fm. Beyond this distance the
force drops exponentially, until beyond about
2.0 fm separation, the force is negligible.
Nucleons have a radius of about 0.8 fm.At
short distances (less than 1.7 fm or so),
the attractive nuclear force is stronger than
the repulsive Coulomb force between protons;
it thus overcomes the repulsion of protons
within the nucleus. However, the Coulomb force
between protons has a much greater range as
it varies as the inverse square of the charge
separation, and Coulomb repulsion thus becomes
the only significant force between protons
when their separation exceeds about 2 to 2.5
fm.
The nuclear force has a spin-dependent component.
The force is stronger for particles with their
spins aligned than for those with their spins
anti-aligned. If two particles are the same,
such as two neutrons or two protons, the force
is not enough to bind the particles, since
the spin vectors of two particles of the same
type must point in opposite directions when
the particles are near each other and are
(save for spin) in the same quantum state.
This requirement for fermions stems from the
Pauli exclusion principle. For fermion particles
of different types, such as a proton and neutron,
particles may be close to each other and have
aligned spins without violating the Pauli
exclusion principle, and the nuclear force
may bind them (in this case, into a deuteron),
since the nuclear force is much stronger for
spin-aligned particles. But if the particles'
spins are anti-aligned the nuclear force is
too weak to bind them, even if they are of
different types.
The nuclear force also has a tensor component
which depends on the interaction between the
nucleon spins and the angular momentum of
the nucleons, leading to deformation from
a simple spherical shape.
=== Nuclear Binding ===
To disassemble a nucleus into unbound protons
and neutrons requires work against the nuclear
force. Conversely, energy is released when
a nucleus is created from free nucleons or
other nuclei: the nuclear binding energy.
Because of mass–energy equivalence (i.e.
Einstein's famous formula E = mc2), releasing
this energy causes the mass of the nucleus
to be lower than the total mass of the individual
nucleons, leading to the so-called "mass defect".The
nuclear force is nearly independent of whether
the nucleons are neutrons or protons. This
property is called charge independence. The
force depends on whether the spins of the
nucleons are parallel or antiparallel, as
it has a non-central or tensor component.
This part of the force does not conserve orbital
angular momentum, which under the action of
central forces is conserved.
The symmetry resulting in the strong force,
proposed by Werner Heisenberg, is that protons
and neutrons are identical in every respect,
other than their charge. This is not completely
true, because neutrons are a tiny bit heavier,
but it is an approximate symmetry. Protons
and neutrons are therefore viewed as the same
particle, but with different isospin quantum
numbers; conventionally, the proton is isospin
up, while the neutron is isospin down. The
strong force is invariant under SU(2) isospin
transformations, just as other interactions
between particles are invariant under SU(2)
transformations of intrinsic spin. In other
words, both isospin and intrinsic spin transformations
are isomorphic to the SU(2) symmetry group.
There are only strong attractions when the
total isospin of the set of interacting particles
is 0, which is confirmed by experiment.Our
understanding of the nuclear force is obtained
by scattering experiments and the binding
energy of light nuclei.
The nuclear force occurs by the exchange of
virtual light mesons, such as the virtual
pions, as well as two types of virtual mesons
with spin (vector mesons), the rho mesons
and the omega mesons. The vector mesons account
for the spin-dependence of the nuclear force
in this "virtual meson" picture.
The nuclear force is distinct from what historically
was known as the weak nuclear force. The weak
interaction is one of the four fundamental
interactions, and plays a role in such processes
as beta decay. The weak force plays no role
in the interaction of nucleons, though it
is responsible for the decay of neutrons to
protons and vice versa.
== History ==
The nuclear force has been at the heart of
nuclear physics ever since the field was born
in 1932 with the discovery of the neutron
by James Chadwick. The traditional goal of
nuclear physics is to understand the properties
of atomic nuclei in terms of the 'bare' interaction
between pairs of nucleons, or nucleon–nucleon
forces (NN forces).
Within months after the discovery of the neutron,
Werner Heisenberg and Dmitri Ivanenko had
proposed proton–neutron models for the nucleus.
Heisenberg approached the description of protons
and neutrons in the nucleus through quantum
mechanics, an approach that was not at all
obvious at the time. Heisenberg's theory for
protons and neutrons in the nucleus was a
"major step toward understanding the nucleus
as a quantum mechanical system." Heisenberg
introduced the first theory of nuclear exchange
forces that bind the nucleons. He considered
protons and neutrons to be different quantum
states of the same particle, i.e., nucleons
distinguished by the value of their nuclear
isospin quantum numbers.
One of the earliest models for the nucleus
was the liquid drop model developed in the
1930s. One property of nuclei is that the
average binding energy per nucleon is approximately
the same for all stable nuclei, which is similar
to a liquid drop. The liquid drop model treated
the nucleus as a drop of incompressible nuclear
fluid, with nucleons behaving like molecules
in a liquid. The model was first proposed
by George Gamow and then developed by Niels
Bohr, Werner Heisenberg and Carl Friedrich
von Weizsäcker. This crude model did not
explain all the properties of the nucleus,
but it did explain the spherical shape of
most nuclei. The model also gave good predictions
for the nuclear binding energy of nuclei.
In 1934, Hideki Yukawa made the earliest attempt
to explain the nature of the nuclear force.
According to his theory, massive bosons (mesons)
mediate the interaction between two nucleons.
Although, in light of quantum chromodynamics
(QCD), meson theory is no longer perceived
as fundamental, the meson-exchange concept
(where hadrons are treated as elementary particles)
continues to represent the best working model
for a quantitative NN potential. The Yukawa
potential (also called a screened Coulomb
potential) is a potential of the form
V
Yukawa
(
r
)
=
−
g
2
e
−
μ
r
r
,
{\displaystyle V_{\text{Yukawa}}(r)=-g^{2}{\frac
{e^{-\mu r}}{r}},}
where g is a magnitude scaling constant, i.e.,
the amplitude of potential,
μ
{\displaystyle \mu }
is the Yukawa particle mass, r is the radial
distance to the particle. The potential is
monotone increasing, implying that the force
is always attractive. The constants are determined
empirically. The Yukawa potential depends
only on the distance between particles, r,
hence it models a central force.
Throughout the 1930s a group at Columbia University
led by I. I. Rabi developed magnetic resonance
techniques to determine the magnetic moments
of nuclei. These measurements led to the discovery
in 1939 that the deuteron also possessed an
electric quadrupole moment. This electrical
property of the deuteron had been interfering
with the measurements by the Rabi group. The
deuteron, composed of a proton and a neutron,
is one of the simplest nuclear systems. The
discovery meant that the physical shape of
the deuteron was not symmetric, which provided
valuable insight into the nature of the nuclear
force binding nucleons. In particular, the
result showed that the nuclear force was not
a central force, but had a tensor character.
Hans Bethe identified the discovery of the
deuteron's quadrupole moment as one of the
important events during the formative years
of nuclear physics.Historically, the task
of describing the nuclear force phenomenologically
was formidable. The first semi-empirical quantitative
models came in the mid-1950s, such as the
Woods–Saxon potential (1954). There was
substantial progress in experiment and theory
related to the nuclear force in the 1960s
and 1970s. One influential model was the Reid
potential (1968).
V
Reid
(
r
)
=
−
10.463
e
−
μ
r
μ
r
−
1650.6
e
−
4
μ
r
μ
r
+
6484.2
e
−
7
μ
r
μ
r
{\displaystyle V_{\text{Reid}}(r)=-10.463{\frac
{e^{-\mu r}}{\mu r}}-1650.6{\frac {e^{-4\mu
r}}{\mu r}}+6484.2{\frac {e^{-7\mu r}}{\mu
r}}}
In recent years, experimenters have concentrated
on the subtleties of the nuclear force, such
as its charge dependence, the precise value
of the πNN coupling constant, improved phase
shift analysis, high-precision NN data, high-precision
NN potentials, NN scattering at intermediate
and high energies, and attempts to derive
the nuclear force from QCD.
== The nuclear force as a residual of the
strong force ==
The nuclear force is a residual effect of
the more fundamental strong force, or strong
interaction. The strong interaction is the
attractive force that binds the elementary
particles called quarks together to form the
nucleons (protons and neutrons) themselves.
This more powerful force is mediated by particles
called gluons. Gluons hold quarks together
with a force like that of electric charge,
but of far greater strength. Quarks, gluons
and their dynamics are mostly confined within
nucleons, but residual influences extend slightly
beyond nucleon boundaries to give rise to
the nuclear force.
The nuclear forces arising between nucleons
are analogous to the forces in chemistry between
neutral atoms or molecules called London forces.
Such forces between atoms are much weaker
than the attractive electrical forces that
hold the atoms themselves together (i.e.,
that bind electrons to the nucleus), and their
range between atoms is shorter, because they
arise from small separation of charges inside
the neutral atom. Similarly, even though nucleons
are made of quarks in combinations which cancel
most gluon forces (they are "color neutral"),
some combinations of quarks and gluons nevertheless
leak away from nucleons, in the form of short-range
nuclear force fields that extend from one
nucleon to another nearby nucleon. These nuclear
forces are very weak compared to direct gluon
forces ("color forces" or strong forces) inside
nucleons, and the nuclear forces extend only
over a few nuclear diameters, falling exponentially
with distance. Nevertheless, they are strong
enough to bind neutrons and protons over short
distances, and overcome the electrical repulsion
between protons in the nucleus.
Sometimes, the nuclear force is called the
residual strong force, in contrast to the
strong interactions which arise from QCD.
This phrasing arose during the 1970s when
QCD was being established. Before that time,
the strong nuclear force referred to the inter-nucleon
potential. After the verification of the quark
model, strong interaction has come to mean
QCD.
== Nucleon–nucleon potentials ==
Two-nucleon systems such as the deuteron,
the nucleus of a deuterium atom, as well as
proton–proton or neutron–proton scattering
are ideal for studying the NN force. Such
systems can be described by attributing a
potential (such as the Yukawa potential) to
the nucleons and using the potentials in a
Schrödinger equation. The form of the potential
is derived phenomenologically (by measurement),
although for the long-range interaction, meson-exchange
theories help to construct the potential.
The parameters of the potential are determined
by fitting to experimental data such as the
deuteron binding energy or NN elastic scattering
cross sections (or, equivalently in this context,
so-called NN phase shifts).
The most widely used NN potentials are the
Paris potential, the Argonne AV18 potential
, the CD-Bonn potential and the Nijmegen potentials.
A more recent approach is to develop effective
field theories for a consistent description
of nucleon–nucleon and three-nucleon forces.
Quantum hadrodynamics is an effective field
theory of the nuclear force, comparable to
QCD for color interactions and QED for electromagnetic
interactions. Additionally, chiral symmetry
breaking can be analyzed in terms of an effective
field theory (called chiral perturbation theory)
which allows perturbative calculations of
the interactions between nucleons with pions
as exchange particles.
=== From nucleons to nuclei ===
The ultimate goal of nuclear physics would
be to describe all nuclear interactions from
the basic interactions between nucleons. This
is called the microscopic or ab initio approach
of nuclear physics. There are two major obstacles
to overcome before this dream can become reality:
Calculations in many-body systems are difficult
and require advanced computation techniques.
There is evidence that three-nucleon forces
(and possibly higher multi-particle interactions)
play a significant role. This means that three-nucleon
potentials must be included into the model.This
is an active area of research with ongoing
advances in computational techniques leading
to better first-principles calculations of
the nuclear shell structure. Two- and three-nucleon
potentials have been implemented for nuclides
up to A = 12.
=== Nuclear potentials ===
A successful way of describing nuclear interactions
is to construct one potential for the whole
nucleus instead of considering all its nucleon
components. This is called the macroscopic
approach. For example, scattering of neutrons
from nuclei can be described by considering
a plane wave in the potential of the nucleus,
which comprises a real part and an imaginary
part. This model is often called the optical
model since it resembles the case of light
scattered by an opaque glass sphere.
Nuclear potentials can be local or global:
local potentials are limited to a narrow energy
range and/or a narrow nuclear mass range,
while global potentials, which have more parameters
and are usually less accurate, are functions
of the energy and the nuclear mass and can
therefore be used in a wider range of applications.
== See also ==
Strong interaction
Standard Model
