3. Nucleons and Quarks

Advances and Challenges in Understanding Light Nuclei

An important ongoing research effort is devoted to measuring various properties of light nuclei having up to eight nucleons. These are the simplest of all nuclei, and the first quantitative comparisons between experimental and theoretical maps of their global and short-range structure have been made. These nuclei are ideal for probing the microscopic aspects of nuclear structure, especially those related to quarks and gluons. The light nuclei also have important roles in astrophysics, elementary particle physics, and energy production. For example, most of the matter in the visible universe is in the form of these light nuclei. The nuclear physics of the Big Bang and of conventional stars like our Sun is primarily governed by the reactions between light nuclei. Nuclear fusion reactors would use some of these reactions as their energy source.

Free neutrons are unstable to radioactive decay. Deuterium (2H) and helium-3 (3He) are the best available surrogates for neutron targets, needed for comparative measurements of the internal structure of neutrons versus protons. A detailed understanding of the structure of these nuclei is necessary for interpreting the results of such experiments.

A direct way to probe the structure of nuclei is again through electron scattering.

3. Nucleons and Quarks

Nuclear Forces and Simple Nuclei

Measuring various properties of nuclear forces and tracing their origins to the fundamental interactions between quarts and gluons has been one of the major recent goals of nuclear physics. The long-range part of the nuclear force is known to be mediated by pions, the lightest of the mesons. However, our knowledge of the short-range parts is still incomplete. When two nucleons are separated by subfemtometer distances, their internal quark-gluon structures overlap. In such cases, description in terms of the quark-gluon exchange becomes necessary.

The force between two nucleons has been studied extensively over the years by scattering one nucleon from another, and the data have been used to constrain parameters in models of the force. In the past decade, a few successful parameterizations of the low-energy nucleon-nucleon force have emerged; they offer descriptions that differ in their assumptions about short-range behavior. It is an important challenge to experiment and theory to find ways to better understand this aspect of the nuclear force, where the interface with QCD is the most critical. Such information is provided, for instance, in experiments measuring meson production in nucleon-nucleon collisions.

In reactions at threshold energies, the two colliding nucleons must come essentially to rest, giving up all of their kinetic energy to produce the meson’s mass. The rate of such reactions is sensitive to the strong, short-range parts of nuclear forces. New experiments aim to obtain additional information on pion production by using spin-polarized beams, and to search for the threshold production of heavier mesons. These experiments also probe meson-nucleon interactions at very low energies and provide crucial tests of QCD-based techniques for deriving the effective nucleon-nucleon interaction.

The bound nuclear systems are shown as a function of the proton number Z (vertical axis) and the neutron number N (horizontal axis). The black squares represent the nuclei that are stable, in the sense that they have survived long enough since their formation in stars to appear on Earth; these form the “valley of stability.” The yellow color indicates man-made nuclei that have been produced in laboratories and live a shorter time. By adding either protons or neutrons, one moves away from the valley of stability, finally reaching the drip lines where nuclear binding ends because the forces between neutrons and protons are no longer strong enough to hold these particles together. Many exotic nuclei with very small or very large N/Z ratios are yet to be made and explored: they are indicated by the green color. The proton drip line is established by experiments up to Z = 83. In contrast, the neutron drip line is considerably further from the valley of stability and harder to approach. Except for the lightest nuclei where it has been reached, the position of the neutron drip line is estimated on the basis of nuclear models; it is uncertain due to the large extrapolations involved. Green and purple lines indicate the paths along which nuclei are believed to form in stars; only some of the dominant processes are shown. While these processes often pass near the drip lines, the nuclei decay rapidly within the star into more stable ones. One important exception to this stability plot occurs in extremely massive and compact aggregations of neutrons, neutron stars, under the combined influences of the nuclear forces and gravity.Page 51Suggested Citation:“3 The Structure of Nuclei.” National Research Council. 1999. Nuclear Physics: The Core of Matter, The Fuel of Stars. Washington, DC: The National Academies Press. doi: 10.17226/6288.

Unique information on the strong force between hadrons can be obtained by comparing the forces between two nucleons and between a nucleon and a lambda particle in which one of the quarks is a heavier strange quark. Any difference between these forces is entirely due to the change in a single quark. The force between the lambda particle and the nucleon is being mapped with the improved experimental capabilities at CEBAF, as well as through the investigation of bound nuclear systems called hypernuclei, in which a nucleon is replaced by a lambda particle.

Even the best available parameterization of the nucleon-nucleon force cannot accurately explain nuclear binding. In order to reproduce the binding energies of the simplest light nuclei, it is essential to add three-body forces to the pairwise interactions determined from nucleon-nucleon scattering. Such three-nucleon forces are expected because the nucleons are themselves composite objects whose constituents can be distorted by an external force. A more familiar example of such a three-body force is known from the analysis of orbits of artificial satellites. In the Earth-moon satellite system, the tides induced by the moon in oceans in turn alter Earth’s pull on the satellite. The nuclear three-body forces are believed to be rather weak, and it has not been possible yet to measure their small effects on the scattering of three nucleons. For now, the strengths of three-body forces have been adjusted to reproduce the binding energies of light nuclei. However, a satisfactory microscopic picture of the three-body force between nucleons is still lacking.

3. Nucleons and Quarks

The Structure of Nuclei


The nucleus, the core and center of the atom, is a quantal many-body system governed by the strong interaction. Just as hadrons are composed of quarks and gluons, the nucleus is composed of the most stable of these hadrons—neutrons and protons. The question of how the strong force binds these nucleons together in nuclei is fundamental to the very existence of the universe. A few minutes after the Big Bang, the mutual interactions between nucleons led to the formation of light nuclei. These, and the subsequent nuclear process synthesizing heavier nuclei during stellar evolution and in violent events like supernovae, have been crucial in shaping the world we live in.

One of the central goals of nuclear physics is to come to a basic understanding of the structure and dynamics of nuclei. In approaching this goal, nuclear physicists address a broad range of questions, from the origin of the complex nuclear force to the origin of the elements. Among the key issues still to be resolved are the following:

  • How do the interactions between quarks and gluons generate the forces responsible for nuclear binding?
  • What is the microscopic structure of nuclei at length scales of the size of the nucleon? Is this structure best understood by including quarks and gluons explicitly in the treatment of nuclei?
  • How are the different approximate symmetries that are apparent in nuclear structure related to the underlying interaction and how can they be derived from many-body theory?

Page 48Suggested Citation:“3 The Structure of Nuclei.” National Research Council. 1999. Nuclear Physics: The Core of Matter, The Fuel of Stars. Washington, DC: The National Academies Press. doi: 10.17226/6288.

  • What are the limiting conditions under which nuclei can remain bound, and what new structure features emerge near these limits?
  • What is the origin of the naturally occurring elements of our world?

Quantitative answers to these questions are essential to our understanding of nuclei; they also have a potential impact far beyond nuclear structure physics. Probes of short-range structures in nuclei can illuminate the nature of quark confinement, by exposing the extent to which quarks either remain confined to their particular neutrons or protons within nuclear matter or are shared among nucleons as electrons are shared in molecules. As yet poorly understood properties of medium-mass nuclei and of very neutron-rich nuclei critically affect the collapse and explosion of supernovae. In creating the heaviest nuclei in the laboratory, nuclear physicists are extending the periodic table of the elements and revealing deviations from chemical periodicity. Among the new isotopes they have produced in approaching the limits of nuclear stability are ones whose radioactive decay will provide crucial new tests of fundamental symmetry principles.

Progress in all these areas relies on technical advances in theoretical and computational approaches, as well as in accelerator and detector design. For example, investigations of short-range structures in nuclei have been spurred by novel developments in proton accelerators and, especially, by the advent of continuous high-energy electron beams. The role of quarks and gluons in such structures is most likely to be revealed in the lightest nuclei, for which experimental maps can now be compared to essentially exact theoretical calculations based on the picture of interacting nucleons. These calculations have been made possible by adapting the latest quantum Monte Carlo computing methods to the unique aspects of nuclear forces.

On the other hand, it is well known in all branches of physics that a direct approach to the dynamics of complex many-body systems, based on the elementary interactions between their constituents, is not always useful. For example, many properties of heavier nuclei can be accurately described using simpler approximations that retain some, but not all, essential microscopic ingredients. Deep insight into the crucial features of nuclear structure can be gained from an understanding of why such approximations work well, and of where they break down. Particular challenges are to understand the variety of collective motions of nucleons in heavy nuclei, and the fascinating phenomenon of nuclear superconductivity. Significant progress in our understanding of heavy nuclei is expected to come from advances in experimental capabilities.

Another major advance is provided by facilities producing beams of short-lived nuclei. Current understanding of both nuclear structure and nucleosynthesis is largely based on what is known of the properties of stable and long-lived, near-stable nuclei. Between these nuclei and the drip lines, where nuclear binding comes to an end, lies an unexplored landscape containing more than 90Page 49Suggested Citation:“3 The Structure of Nuclei.” National Research Council. 1999. Nuclear Physics: The Core of Matter, The Fuel of Stars. Washington, DC: The National Academies Press. doi: 10.17226/6288.

percent of all expected bound nuclear systems, a region where many new nuclear phenomena are anticipated. As is evident from the map of the nuclear terrain in Figure, the limits of nuclear binding are poorly known at present; often, those limits are close to the regions where the processes that form the elements in stars must proceed.

In the 1996 Long Range Plan, a new experimental facility to explore nuclei near the limits of nuclear binding was identified as the choice for the next major construction project in nuclear science. Recommendation II of the present report is the construction of such a facility. Beams of short-lived nuclei will be produced and accelerated at this facility, and their reactions with target nuclei will be used to synthesize new nuclear species in uncharted territory. By elucidating the properties of these new exotic species, and enabling their use in reactions of astrophysical interest and in tests of fundamental symmetries, this new facility will provide answers to some of the most profound nuclear structure questions identified above.

3. Nucleons and Quarks


nucleon, either of the subatomic particles, the proton and the neutron, constituting atomic nuclei. Protons (positively charged) and neutrons (uncharged) behave identically under the influence of the short-range nuclear force, both in the way they are bound in nuclei and in the way they are scattered by each other. This strong interaction is independent of electric charge. Unstable subatomic particles heavier than nucleons (hyperons and baryon resonances) have a nucleon among their final decay products; the nucleon is thus the baryon ground state. The antinucleons include the antiproton and the antineutron.

3. Nucleons and Quarks

Binding forces and “massive” quarks

The binding forces carried by the gluons tend to be weak when quarks are close together. Within a proton (or other hadron), at distances of less than 10−15 metre, quarks behave as though they were nearly free. This condition is called asymptotic freedom. When one begins to draw the quarks apart, however, as when attempting to knock them out of a proton, the effect of the force grows stronger. This is because, as explained by QCD, gluons have the ability to create other gluons as they move between quarks. Thus, if a quark starts to speed away from its companions after being struck by an accelerated particle, the gluons utilize energy that they draw from the quark’s motion to produce more gluons. The larger the number of gluons exchanged among quarks, the stronger the effective binding forces become. Supplying additional energy to extract the quark only results in the conversion of that energy into new quarks and antiquarks with which the first quark combines. This phenomenon is observed at high-energy particle accelerators in the production of “jets” of new particles that can be associated with a single quark.

The discovery in the 1970s of the “charm” (c) and “bottom” (b) quarks and their associated antiquarks, achieved through the creation of mesons, strongly suggests that quarks occur in pairs. This speculation led to efforts to find a sixth type of quark called “top” (t), after its proposed flavour. According to theory, the top quark carries a charge of 2/3e; its partner, the bottom quark, has a charge of −1/3e. In 1995 two independent groups of scientists at the Fermi National Accelerator Laboratory reported that they had found the top quark. Their results give the top quark a mass of 173.8 ± 5.2 gigaelectron volts (GeV; 109 eV). (The next heaviest quark, the bottom, has a mass of about 4.2 GeV.) It has yet to be explained why the top quark is so much more massive than the other elementary particles, but its existence completes the Standard Model, the prevailing theoretical scheme of nature’s fundamental building blocks.

3. Nucleons and Quarks

Quark “colours”

The interpretation of quarks as actual physical entities initially posed two major problems. First, quarks had to have half-integer spin (intrinsic angular momentum) values for the model to work, but at the same time they seemed to violate the Pauli exclusion principle, which governs the behaviour of all particles (called fermions) having odd half-integer spin. In many of the baryon configurations constructed of quarks, sometimes two or even three identical quarks had to be set in the same quantum state—an arrangement prohibited by the exclusion principle. Second, quarks appeared to defy being freed from the particles they made up. Although the forces binding quarks were strong, it seemed improbable that they were powerful enough to withstand bombardment by high-energy particle beams from accelerators.

These problems were resolved by the introduction of the concept of colour, as formulated in quantum chromodynamics (QCD). In this theory of strong interactions, whose breakthrough ideas were published in 1973, colour has nothing to do with the colours of the everyday world but rather represents a property of quarks that is the source of the strong force. The colours red, green, and blue are ascribed to quarks, and their opposites, antired, antigreen, and antiblue, are ascribed to antiquarks. According to QCD, all combinations of quarks must contain mixtures of these imaginary colours that cancel out one another, with the resulting particle having no net colour. A baryon, for example, always consists of a combination of one red, one green, and one blue quark and so never violates the exclusion principle. The property of colour in the strong force plays a role analogous to that of electric charge in the electromagnetic force, and just as charge implies the exchange of photons between charged particles, so does colour involve the exchange of massless particles called gluons among quarks. Just as photons carry electromagnetic force, gluons transmit the forces that bind quarks together. Quarks change their colour as they emit and absorb gluons, and the exchange of gluons maintains proper quark colour distribution.

3. Nucleons and Quarks

Quark “flavours”

Throughout the 1960s theoretical physicists, trying to account for the ever-growing number of subatomic particles observed in experiments, considered the possibility that protons and neutrons were composed of smaller units of matter. In 1961 two physicists, Murray Gell-Mann of the United States and Yuval Neʾeman of Israel, proposed a particle classification scheme called the Eightfold Way, based on the mathematical symmetry group SU(3), which described strongly interacting particles in terms of building blocks. In 1964 Gell-Mann introduced the concept of quarks as a physical basis for the scheme, having adopted the fanciful term from a passage in James Joyce’s novel Finnegans Wake. (The American physicist George Zweig developed a similar theory independently that same year and called his fundamental particles “aces.”) Gell-Mann’s model provided a simple picture in which all mesons are shown as consisting of a quark and an antiquark and all baryons as composed of three quarks. It postulated the existence of three types of quarks, distinguished by unique “flavours.” These three quark types are now commonly designated as “up” (u), “down” (d), and “strange” (s). Each carries a fractional value of the electron charge (i.e., a charge less than that of the electron, e). The up quark (charge 2/3e) and down quark (charge −1/3e) make up protons and neutrons and are thus the ones observed in ordinary matter. Strange quarks (charge −1/3e) occur as components of K mesons and various other extremely short-lived subatomic particles that were first observed in cosmic rays but that play no part in ordinary matter.

3. Nucleons and Quarks


quark, any member of a group of elementary subatomic particles that interact by means of the strong force and are believed to be among the fundamental constituents of matter. Quarks associate with one another via the strong force to make up protons and neutrons, in much the same way that the latter particles combine in various proportions to make up atomic nuclei. There are six types, or flavours, of quarks that differ from one another in their mass and charge characteristics. These six quark flavours can be grouped in three pairs: up and down, charm and strange, and top and bottom. Quarks appear to be true elementary particles; that is, they have no apparent structure and cannot be resolved into something smaller. In addition, however, quarks always seem to occur in combination with other quarks or with antiquarks, their antiparticles, to form all hadrons—the so-called strongly interacting particles that encompass both baryons and mesons.

quark typebaryon numberchargestrangeness**charm**bottom**top**mass (MeV)
down (d)1/3−(1/3)e00005–15
up (u)1/3+(2/3)e00002–8
strange (s)1/3−(1/3)e−1000100–300
charm (c)1/3+(2/3)e01001,000–1,600
bottom (b)1/3−(1/3)e00−104,100–4,500
top (t)1/3+(2/3)e0001180,000
*Note that antiquarks exist for all flavours of quark and have opposite values for all the quantum numbers listed here.
**These are quantum numbers that must be assigned to the quarks to differentiate the various flavours.