Nuclear Forces

Type of physical science: Nuclear physics

Field of study: Nuclei

Nuclear forces are part of the strong interaction. They bind the main constituents of nuclei, protons and neutrons, at the center of atoms. They are much stronger than the electromagnetic forces that hold the electrons in atoms, so that nuclei are more than ten thousand times smaller than atoms.

Overview

Ordinary matter consists of atoms that have a shell of electrons on the outside and a nucleus at the center. Protons and neutrons are the main components of nuclei and are held together by the nuclear forces, which are more than a hundred times stronger than the electromagnetic forces that bind electrons in atoms. The nuclear force is caused by the exchange of mesons, which are a family of strongly interacting particles. The π meson, or pion, is the lightest meson. Nuclei were discovered in 1911 by Ernest Rutherford in England. His team bombarded gold foils (and other target materials) with energetic helium ions (helium 4) emitted from a radioactive source of radium. Comparing the observed rate of helium ions scattered by the gold atoms with that expected from the electric forces between the two protons of the helium ion and the protons in the gold atoms, Rutherford noticed an unexpectedly large number of helium ions scattered at large angles (greater than 90 degrees). Since the incoming helium ions were much faster and more massive than the electrons in the gold target, these events, which resembled bullets ricocheting off a hard object, could only be interpreted as ions being reflected by a tiny and very dense nucleus at the center of each target atom. From this anomaly, the size (radius) of the nucleus can be measured to be a few fermi (1 fermi equals 1 x 10^-15 meter), which is more than ten thousand times smaller than an atom. In general, the masses of atoms are more than twice that of their protons; that of the electron shell is negligible because the proton mass is almost two thousand times that of the electron. As a result, Rutherford suspected that a neutral companion of the proton exists in nuclei. In 1932, this neutron was discovered at his laboratory--the Cavendish Laboratory at the University of Cambridge--by James Chadwick.

Since then, nuclei are known to be composed of protons and neutrons.

Nuclei are held together by forces that are much stronger than the electric forces which bind electrons in atoms. The strength of nuclear forces can be observed in the much higher energy released (from the nuclear forces) by an atomic bomb compared with that from an ordinary chemical explosion. As the distance over which the strong force acts increases, the force can hold together more nucleons and the nuclei will grow. Thus, the small size of nuclei indicates that the range of nuclear forces is short, about a few fermis. Strongly interacting nucleons behave almost like ballplayers. The lighter the ball, the farther they can throw it to a catcher. Thus, the range of a force is inversely proportional to the mass of the exchanged particle: The smaller the exchanged mass, the longer the distance over which the force can be felt.

In 1934, Enrico Fermi proposed a model for the weak forces governing the decay of the neutron (and many nuclei) that was similar to the electromagnetic forces, where the exchanged particle is a massless photon, Max Planck's quantum of light. Stimulated by this analogy, Hideki Yukawa suggested a year later that the forces between a neutron and a proton, two protons, or two neutrons, result from a similar exchange of a particle. Based on the short range of nuclear forces, the mass of this particle had to be between that of a proton and an electron--hence its name, meson, from the Greek word for middle. In 1947, the pion was discovered in cosmic rays, among energetic particles reaching the earth's atmosphere from outer space, with a mass about three hundred times that of an electron.

The pion is by far the lightest of all mesons and, therefore, pion exchange is the nuclear force of longest range; it dominates at distances beyond about 2 fermis. Since the 1940's the role of pion exchange gradually has been established in NN scattering experiments and in the properties of the deuteron, helium 2. This is the lightest nucleus consisting of a neutron and proton loosely bound at an average distance of about 4 fermis compared to less than the 2-fermi average distance between nucleons in heavier nuclei. Hence, pion exchange clearly dominates in the deuteron and explains many of its properties, such as its size. The pion has negative parity, which means that it would look different when viewed in a mirror. As a consequence, pion exchange between nucleons depends on their spin orientations; it has a part that is the same in all directions and another that tends to make the deuteron a bit cigar-shaped rather than disk-shaped.

Measurements of the shape agree with that prediction.

When two nucleons scatter off each other at distances larger than about 2 fermis, pion exchange dominates as well. In typical scattering experiments, all relative NN distances are sampled, but the contributions from large distances can be disentangled. Again, the observed interaction effects are in quantitative agreement with pion exchange.

When an electron scatters off a deuteron, while a charged pion is in flight between its proton and neutron, it is expected that the electron occasionally will hit the pion or at least deflect it, rather than the proton or neutron. This (pion exchange current) effect is the most exciting and compelling prediction from pion exchange, for which experimental evidence has increased since the 1970's. Normally the effect is small, but in special circumstances it can be magnified and clearly seen. When the electron scatters backward, the deuteron is given a strong kick but exactly enough energy to break the bond between the proton and neutron. The experiments agree beautifully with the predictions from pion exchange. They also can be done for helium 3, which contains two protons and one neutron, and for the triton, hydrogen 3, which has two neutrons and one proton. When the electron scatters backward from either one, the expected pion exchange current is observed.

In general, different spin orientations tend to average out, when many nucleons are involved, so that the one-pion exchange is practically eliminated in heavier nuclei, leaving the two-pion exchange. The latter provides most of the attraction that holds together all nuclei; thus, it is very important but is more difficult to disentangle. It competes with or exceeds the one-pion exchange at intermediate range between about 1 and 2 fermis. It contains contributions from two independent pions and strongly interacting (resonant) pions. The latter act as mesons, with the spin 0 and 1 of the two-pion system giving rise to scalar and vector-meson exchanges. The spin 1 force is of short range, as it corresponds to the exchange of a ρ meson; the unstable ρ meson is called a vector-meson because, as a result of its spin 1, it has a preferred direction in space like a vector. Its mass is about five times that of the pion, and it decays into two pions. At short distances, ρ exchange weakens the tendency of the one-pion exchange to deform nuclei.

Another even stronger force results from the exchange of an ω meson, another vector-meson of nearly the same mass as that of the ρ meson, which decays into three pions. It corresponds to the resonant part of the three-pion exchange and contributes to the important repulsion between nucleons at short distances. The strengths of these vector-meson exchanges are more uncertain than that of the one-pion exchange, which is known to within a few percent.

The general attraction of the nuclear forces is reflected in the systematics of nuclear binding energies. One of the most striking effects about nuclei is the approximate constancy of the nuclear density: The volume of a nucleus is proportional to the number of its protons and neutrons, exactly as a liquid, though of extremely high density. Indeed, the liquid drop model of the nucleus leads to an understanding of nuclear binding energies and is the precursor of collective models which describe the rotational and vibrational properties of nuclear spectra.

Moreover, nuclei have particularly stable configurations of high binding energy if the number of protons or neutrons (or both) is one of the so-called magic numbers 2, 8, 20, 28, 50, 82, 126. As in the case of atoms, such magic numbers indicate that shells exist in nuclei, although nuclei have no fixed center. The new feature in the nuclear shell model that explains the magic numbers is a strong correlation of the spin of a nucleon with its angular momentum from its motion. A consistent understanding of this spin-orbit force was derived from a relativistic treatment of the motion of neutrons and protons in nuclei that is in accord with Albert Einstein's special theory of relativity.

Nuclear forces are extremely complex. Despite all the evidence, the meson dynamics theory is not fundamental, since nucleons and mesons are not elementary particles. The first evidence for their internal structure resulted from high-energy electron scattering experiments, which measure nuclear sizes and the distribution of their internal charge and magnetism. Since the 1950's, such experiments at Stanford University have shown that the proton also has a definite size, about one ten-trillionth of a centimeter, or a hundred thousand times smaller than the atom. Thus, the nucleon itself is a composite system of even smaller particles, called quarks, whose properties were identified in the 1960's and confirmed in experiments in the 1970's.

Meson dynamics theory allows for the finite size of nucleons in order to build a consistent theory. As a result, meson exchange forces between two nucleons diminish as they approach and eventually overlap, and meson exchange dynamics is gradually replaced by nonmesonic quark dynamics. The rate at which this substitution occurs is a major source of uncertainty in terms of pion exchange and other meson exchanges at short distances between nucleons. Quarks interact according to the fundamental theory of the strong interaction, called quantum chromodynamics (QCD) since its structure resembles that of electrodynamics, whose quantum version is called quantum electrodynamics (QED). In QED, electric charges attract or repel each other, whereas in QCD quarks carry "strong" charges called colors. In contrast to QED, QCD is nonlinear and rather complicated. QCD remains unsolved at low energy and long distances, and it is not understood how meson dynamics emerges from quark dynamics, although there are several promising leads. In QCD, the number of quark colors, Nc, is three. If Nc is taken to be large, then a meson theory with many familiar features of meson dynamics can be obtained from QCD.

Nuclear forces determine the angular and energy distributions of the scattered particle in various reactions. Pion-nucleon and pion-nucleus scattering are other strong interaction processes that have provided complementary information on nuclear forces over the years. The usual pion interaction suggested by Yukawa's analogy with electrodynamics does not work at low energy, when applied naively. Instead, it contributes to a piN resonance (a pion strongly attracted by a nucleon for a moment, called Δ), the first excited state of the nucleon, which dominates pion-nucleon and pion-nucleus scattering at low and intermediate energies. Such excited states result from rearranging the quarks in the nucleon, requiring energy that is supplied by the incoming pion. A series of excited states usually is another indication that the system is a composite object.

Pion-nucleon collisions at low energy are actually governed by rho-meson exchange.

This fact is related to the special properties of the pion reflected in its relatively low mass and can be traced to the "chiral" (handed) symmetry of QCD when the quark masses are zero, which is almost the case for those quarks that compose the pion. When a massless quark reflects off another quark and changes its direction of motion, its spin will undergo the same change; thus, the quark's helicity or handedness is conserved. Whereas the equations of motion in QCD are chiral invariant, its lowest state--the vacuum--need not be so. The vacuum is suspected of having similarities with superconductivity, including condensed quark-antiquark pairs, which are known to break chiral symmetry. For QCD with massless quarks, the pion is the first excited state and has zero mass. When quarks are given a small mass, the pion acquires a small mass as well.

In the 1950's, several particles were found with the same spin and parity as the nucleon but were somewhat heavier. Called hyperons (denoted by L, Σ, and so on), these particles would be stable only if the strong interaction existed. They are partners of the nucleon and can replace a nucleon in a nucleus, thus forming a hypernucleus. These have been produced by various accelerators, and their study created a rich field of nuclear physics, where their structure is investigated along with LN, Σ N, and similar forces.

Applications

Nuclear reactions are the basis for understanding the energy production in the sun and other stars. No other source can provide sufficient energy to keep stars burning for billions of years. Fusing four hydrogen atoms into one helium atom, which is tightly bound and has a large binding energy, can release millions of times more energy than a chemical explosion. It is this awesome power that is set free in a hydrogen bomb.

Plasma and laser physicists in several industrialized countries are attempting to duplicate this fusion process under controlled conditions in the laboratory to harness the tremendous energy production. Temperatures of millions of degrees have been reached, but not sustained long enough to reach the break-even point, where as much energy is produced as is entered to squeeze and contain the hot deuteron-triton mixture. Although experts state that fusion power plants are economically feasible, such plants remain in the developmental stage.

In 1965, Arno A. Penzias and Robert W. Wilson discovered a background radiation in the sky with a wavelength in the centimeter range. This radiation, which looks the same in all directions, has provided evidence for the big bang theory of cosmology. According to this theory, the universe was created more than fifteen billion years ago from a primordial fireball. The radiation corresponds to about 2.7 degrees Celsius above absolute zero and is interpreted as leftover from the big bang. When the temperature dropped below about a billion degrees Celsius, deuterons that formed in the neutron capture reaction remained stable, because the energy of the surrounding radiation was no longer high enough to split them according to the inverse reaction.

Subsequently, helium was formed. This scenario describes the beginning of nucleosynthesis in the first four minutes of the universe.

The abundance of heavier elements cannot be explained by further neutron capture and big bang synthesis, because there are no stable nuclei with five and eight nucleons. To overcome this problem, the higher densities of stars are required; heavier elements are produced in stars and dispersed in supernova explosions of very massive stars. The remnants of such cataclysmic events form a neutron star (possibly a pulsar), or a black hole if the initial giant star had a mass greater than about four solar masses.

Neutron stars have a radius of about 10 kilometers and a crust containing iron nuclei, and are very dense. Their main interior has a density comparable to a nucleus, and their hadronic core may be even denser than the interior of a proton. The determination of their detailed structure requires input from many areas, including gravity, nuclear, particle, and condensed matter physics.

Beyond iron, the binding energy per nucleon decreases (at low pressure) because of the increasing electric repulsion between protons, and nuclear burning is no longer possible in ordinary stars such as the sun. This statement explains why elements appearing near iron in the periodic table are more abundant than others. Hence, if a heavy nucleus such as uranium breaks up into two nuclei of medium mass, there is a gain in binding energy. Such a fission process is fairly common in heavy nuclei, which usually are far from spherical, and is often initiated by slow neutron capture. Since neutrons are produced by fission, they can start a chain reaction.

This process is the key to the atomic bomb and to commercial energy generation. For commercial purposes, the chain reaction is slowed down and controlled in nuclear reactors by a moderator such as heavy water containing deuterons or graphite that capture neutrons.

Context

From the discovery of the nucleus in 1911 by Rutherford, it took more than twenty years for a realistic nuclear theory to be formulated with the discovery of the neutron in 1932. In the 1940's, nuclear physics was the high-energy frontier. In the 1950's, beginning with pion-nucleon scattering, the discovery of nucleon resonances, and their interpretation as excited states of the nucleon and of many other meson resonances, elementary particle physics gradually separated from nuclear physics. This development culminated with the establishment of the standard model comprising the (gauge field) theories for the unified electroweak and the strong interaction (QCD) in the 1970's. Since then, nuclear physics at intermediate energies and heavy-ion nuclear physics at high energy have joined again with particle physics to solve and understand QCD at low energies and long distances. Experimental nuclear physics is driven by various particle accelerators that provide electron, proton, heavy ion, and other beams at different energies.

Principal terms

ACCELERATOR: a machine that drives particles to high velocities, then slams them into one another or some other material in order to study their properties

HELICITY: the intrinsic rotation (spin) of a particle about its direction of motion

NEUTRON (N): the uncharged analogue of the proton and its companion in nuclei

NN POTENTIAL: a measurement of the energy of interaction between two nucleons, for example, pp, pn, or nn

NUCLEON (N): a doublet state that contains the proton and neutron, treating them as identical except for their charge (neglecting the 0.1 percent higher mass of the neutron)

PI-MESON: the lightest strongly interacting particle; the carrier of the nuclear force of longest range; has three charge states, positively charged π+, negatively charged π-, and neutral pi⁰; often called pion or pi

PROTON (P): positively charged nucleus of the hydrogen atom

RANGE OF FORCE: roughly the distance over which the force diminishes by about a factor of 3; inversely proportional to the mass of its carrier particle

Bibliography

Beyer, Robert T. SELECTED PAPERS IN FOUNDATIONS OF NUCLEAR PHYSICS. New York: Dover, 1949. A collection of pioneering papers in nuclear physics including those by Rutherford, Chadwick, Fermi, and Yukawa, followed by an extensive list of research papers until 1947.

Frauenfelder, Hans, and Ernest M. Henley. SUBATOMIC PHYSICS. Englewood Cliffs, N.J.: Prentice-Hall, 1974. A textbook on nuclear and particle physics for undergraduate students. The introductions to various chapters and numerous discussions are nontechnical.

Pagels, Heinz. THE COSMIC CODE. Toronto: Bantam, 1982. Describes the environment of modern nuclear and particle physics, including some historical context. For the general public.

Pais, Abraham. INWARD BOUND. Oxford, England: Clarendon Press, 1986. A fascinating historical account of the development of nuclear and particle physics in this century, including nuclear forces and some of its applications.

Reines, Frederick, ed. COSMOLOGY, FUSION AND OTHER MATTERS. Boulder: Colorado Associated University Press, 1972. Contains several articles on nucleosynthesis, fusion energy, and so on.

Segre, Emilio. FROM X-RAYS TO QUARKS. San Francisco: W. H. Freeman, 1976. Covers roughly the same period and material as Pais' book, but is easier to read and much less detailed.

Weinberg, Steven. THE FIRST THREE MINUTES. New York: Basic Books, 1977. A nontechnical description of big bang cosmology, including nucleosynthesis.

Models of the Atomic Nucleus

The Structure of the Atomic Nucleus

Fission and Thermonuclear Weapons

Nuclear Reactions and Scattering

Nuclear Synthesis in Stars

Quarks and the Strong Interaction

Thermonuclear Reactions in Stars