# Atomic Nucleus Photo by: Petr Vaclavek

The atomic nucleus is a tiny massive entity at the center of an atom. Occupying a volume whose radius is 1/100,000 the size of the atom, the nucleus contains most (99.9%) of the mass of the atom. In describing the nucleus, we shall describe its composition, size, density, and the forces that hold it together. After describing the structure of the nucleus, we shall go on to describe some of the limits of nuclear stability.

The nucleus is composed of protons (charge = +1; mass = 1.007 atomic mass units ([μ]) and neutrons. The number of protons in the nucleus is called the atomic number Z and defines which chemical element the nucleus represents. The number of neutrons in the nucleus is called the neutron number N, whereas the total number of neutrons and protons in the nucleus is referred to as the mass number A, where A = N + Z. The neutrons and protons are referred to collectively as nucleons. A nucleus with a given N and Z is referred to as a nuclide. Nuclides with the same atomic number are isotopes , such as 12 C and 14 C, whereas nuclides with the same N, such as 14 C and 16 O, are called isotones. Nuclei such as 14 N and 14 C, which have the same mass number, are isobars. Nuclides are designated by a shorthand notation in which one writes , that is, for a nucleus with 6 protons and 8 neutrons, one writes , or, , or just 14 C. The size of a nucleus is approximately 1 to 10 × 10 −15 m, with the nuclear radius being represented more precisely as 1.2 × A 1/3 × 10 −15 m. We can roughly approximate the nucleus as a sphere and thus we can calculate its density

where 1.66 × 10 −27 kg is the mass of the nucleon. Thus the nuclear density is about 200,000 tonnes/mm 3 and is independent of A. Imagine a cube that is 1 mm on a side. If filled with nuclear matter, it would have a mass of about 200,000 tonnes. This calculation demonstrates the enormous matter/energy density of nuclei and gives some idea as to why nuclear phenomena lead to large energy releases.

Of the 6,000 species of nuclei that can exist in the universe, about 2,700 are known, but only 270 of these are stable. The rest are radioactive, that is, they spontaneously decay. The driving force behind all radioactive decay is the ability to produce products of greater stability than one had initially. In other words, radioactive decay releases energy and because of the high energy density of nuclei, that energy release is substantial. Qualitatively we describe radioactive decay as occurring in three general ways: α -, β -, and γ -decay. Alpha-decay occurs in the heavy elements, and consists of the emission of a 4 He nucleus. Beta-decay occurs in nuclei whose N/Z ratio is different from that of a stable nucleus and consists of a transformation of neutrons into protons or vice versa to make the nucleus more stable. Gamma-decay occurs when excited nuclei get rid of some or all of their excitation energy via the emission of electromagnetic radiation, or via the radiationless transfer of energy to orbital electrons.

The force responsible for holding the neutrons and protons together within the very small nuclear volume must be unusually strong. The nuclear force, or strong interaction, is one of the four fundamental forces of nature (namely, the gravitational, electromagnetic, strong, and weak forces). The nuclear force is charge-independent, meaning that the nuclear force between two protons, or two neutrons, or a neutron and a proton, is the same. The nuclear force is short-ranged, meaning it acts over a distance of 10 −15 to 10 −14 m, that is, the size of nuclei. Of course the nuclear force is attractive, as it binds the nucleons in a nucleus. But some experiments have shown the nuclear force has a "repulsive core," meaning that at very short distances, the force switches from attractive to repulsive, preventing the nucleus from collapsing in on itself. The nuclear force is an "exchange" force, resulting from the virtual exchange of pions (short-lived particles with integral spin, produced normally in nuclear reactions) between interacting nucleons. More recently we have come to understand the nuclear force using a theory called quantum chromodynamics (QCD), which describes protons and neutrons as being made up of quarks. In particular, the proton is thought of as a combination of two up quarks (uu) and a down quark (d), whereas the neutron is thought to consist of one up quark (u) and two down quarks (dd). The up and down quarks are small particles with charges of +2/3 and −1/3, respectively. The quarks account for approximately 2 percent of the mass of the proton. The rest of the mass consists of gluons, which are the particles exchanged between the quarks to bind them together. The force acting between the quarks has the unusual property of being small when they are close together, and increasing as the distance between them grows. Because of this, no isolated quarks have been observed in nature.

In close analogy to atomic structure, we speak of the structure of various nuclei. Many nuclear properties can be described using a nuclear shell model in which the nucleons are placed in orbitals like electrons in atoms. These orbitals and their properties are predicted by applying quantum mechanics to the problem of defining the states of the nucleons, which move under the influence of the average force in the nucleus. Like atoms, there are certain configurations of nucleons that have special stability, for example, the so-called magic numbers akin to the inert gas structures in chemistry. In addition to those nuclear properties that are best described in terms of a shell model, there are other properties that seem to be best explained by the large-scale collective motion of a number of nucleons. These motions lead to nuclear rotations and vibrations, which are described by a nuclear collective model.

Current research on nuclei, their properties, and the forces that hold them together focuses on studying nuclei at the limits of stability. The basic idea is that when one studies nuclei under extreme conditions, one then has a unique ability to test theories and models that were designed to describe the "normal" properties of nuclei. One limit of nuclear stability is that of high Z, that is, as the atomic number of the nucleus increases, the repulsion between the nuclear protons becomes so large as to cause the nucleus to spontaneously fission . The competition between this repulsive Coulomb force and the cohesive nuclear force is what defines the size of the Periodic Table and the number of chemical elements. At present there are 112 known chemical elements, and evidence for the successful synthesis of elements having the atomic numbers 114 and 116 has been presented.

Another limit of nuclear stability is the extreme of the neutron to proton ratio, N/Z. For certain very neutron-rich nuclei, such as 11 Li, an unusual halo structure has been observed. In halo nuclei, a "core" of nucleons is surrounded by a "misty cloud, a halo" of valence nucleons that are weakly bound and extend out to great distances, analogous to electrons surrounding the nucleus in an atom. Halo nuclei are fragile objects, are relatively large, and interact easily with other nuclei (have enhanced reaction cross sections). The halo nucleus 11 Li, which has a 9 Li core surrounded by a two-neutron halo is shown in Figure 1. 11 Li is as large as 208 Pb. 11 Li and other Figure 1. Schematic views of the nuclear halo nuclei 11 Li and 19 C that compares them to 208 Pb and the Borromean rings of medieval times. (Source: http://www.phy.anl.gov/ria/index)

two-neutron halo nuclei are three-body systems (2 neutrons and a 9 Li core), which pose a special challenge to nuclear theorists. They are also examples of Borromean systems, in which the nucleus is no longer bound if any one of the three components is removed. (The name derives from the heraldic emblem of medieval princes of Borromeo, which has three rings interlocked in such a way that removal of any one ring will make the others fall apart.)

Walter Loveland

## Bibliography

Heyde, Kris (1999). Basic Ideas and Concepts in Nuclear Physics: An Introductory Approach , 2nd edition. Philadelphia: Institute of Physics Publishers.

Krane, Kenneth S. (1987). Introductory Nuclear Physics. New York: Wiley.

Seaborg, Glenn T., and Loveland, Walter D. (1990). The Elements beyond Uranium. New York: Wiley.