Nuclear force
The nuclear force is a force that acts between hadrons, most commonly observed between 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 electrostatic force. The nuclear force binds nucleons into atomic nuclei.
The nuclear force is powerfully attractive between nucleons at distances of about 0.8 femtometre, 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 repulsion is responsible for the size of nuclei, since nucleons can come no closer than the force allows. The nuclear force is not simple, though, as it depends on the nucleon spins, has a tensor component, and may depend on the relative momentum of the nucleons.
The nuclear force has an essential role in storing energy that is used in nuclear power and nuclear weapons. Work 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 internucleon 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. 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. Pions, fulfilling the prediction, 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 neighbouring nucleons, is a multiparticle interaction, the collective effect of strong force on the underlining structure of the nucleons.
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 the force becomes repulsive, which keeps the nucleons at a certain average separation. For identical nucleons this repulsion arises from the Pauli exclusion force. A Pauli repulsion also occurs between quarks of the same flavour from different nucleons.Field strength
At distances larger than 0.7 fm the force becomes attractive between spin-aligned nucleons, becoming maximal at a centre–centre 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, 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.
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 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, 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, 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 isospin transformations, just as other interactions between particles are invariant under SU transformations of intrinsic spin. In other words, both isospin and intrinsic spin transformations are isomorphic to the SU 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.
File:pn scatter pi0.svg|thumb|300px|A simplified Feynman diagram of a strong proton–neutron interaction mediated by a virtual neutral pion. Time proceeds from left to right. 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, 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 processes such 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.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 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 mediate the interaction between two nucleons. In light of quantum chromodynamics —and, by extension, the Standard Model—meson theory is no longer perceived as fundamental. But the meson-exchange concept continues to represent the best working model for a quantitative NN potential. The Yukawa potential is a potential of the form
where g is a magnitude scaling constant, i.e., the amplitude of potential, 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 r between particles, 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. 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
where and where the potential is given in units of MeV. 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.