Nuclear force

This article is about the force sometimes called the residual strong force. For the "strong nuclear force" see strong interaction; for the "weak nuclear force", see weak interaction.

The nuclear force (or nucleon-nucleon interaction or residual strong force) is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. To a large extent, this force can be understood in terms of the exchange of light mesons, such as the pions.

Sometimes the nuclear force is called the residual strong force, in contrast to the strong interactions which are now understood to arise from quantum chromodynamics (QCD). This phrasing was forced during the 1970s due to a change in paradigm. Before that time, the strong nuclear force referred to the inter-nucleon potential. After the introduction of the quark model, strong interaction came to mean QCD. Since nucleons have no color charge, the nuclear force does not directly involve the force carriers of quantum chromodynamics, the gluons.

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 (NN) forces.

In 1935, 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 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.

Historically, it turned out to be a formidable task to describe the nuclear force just phenomenologically, and it took a quarter of a century to come up with the first semi-empirical quantitative models in the mid-1950s. Ever since, there has been substantial progress in experiment and theory related to the nuclear force. Most basic questions were settled in the 1960s and 1970s. 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.

Basic properties of the nuclear force

The nuclear force is only felt among hadrons.
At typical nucleon separation (1.3 fm) it is a very strong attractive force (104 newtons).
At much smaller separations between nucleons the force is very powerfully repulsive, which keeps the nucleons at a certain average separation.
Beyond about 1.3 fm separation, the force exponentially dies off to zero.
At short distances, the nuclear force is stronger than the Coulomb force; it can overcome the Coulomb repulsion of protons inside the nucleus. However, the Coulomb force between protons has a much larger range and becomes the only significant force between protons when their separation exceeds about 2.5 fm.
The NN force is nearly independent of whether the nucleons are neutrons or protons. This property is called charge independence.
The NN force depends on whether the spins of the nucleons are parallel or antiparallel.
The NN force has a noncentral or tensor component. This part of the force does not conserve orbital angular momentum, which is a constant of motion under central forces.

Nucleon-nucleon potentials

Two-nucleon systems such as the deuteron 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, 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.

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 non-trivial and require powerful computation techniques.
There is evidence that, in systems of more than two nucleons, three-nucleon forces (and maybe also four-nucleon forces, five-nucleon forces, etc.) play some significant role. Thus, three-nucleon potentials (at least) must be included into the model.

However, thanks to the ongoing advances in computational resources, microscopic calculations directly producing nuclear shell structure from two- and three-nucleon potentials have become feasible and have been attempted for nuclear masses up to A=12.

A novel and promising approach is to develop effective field theories for a consistent description of nucleon-nucleon and three-nucleon forces. In particular, chiral symmetry breaking can be analysed 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.

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.

References

Gerald Edward Brown and A. D. Jackson, The Nucleon-Nucleon Interaction, (1976) North-Holland Publishing, Amsterdam ISBN 0-7204-0335-9
R. Machleidt and I. Slaus, "The nucleon-nucleon interaction", J. Phys. G 27 (2001) R69 (topical review).
Kenneth S. Krane, "Introductory Nuclear Physics", (1988) Wiley & Sons.
P. Navrátil and W.E. Ormand, "Ab initio shell model with a genuine three-nucleon force for the p-shell nuclei", Phys. Rev. C 68, 034305 (2003).

Nuclear physics | Quantum chromodynamics

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