General Properties of Nuclei

Nuclei are studied and their nature and properties revealed in essentially three ways. First, they can be bombarded by other particles to see how these particles are scattered or how the nucleus disintegrates. We speak of the latter process as a nuclear reaction. The nuclear behaviour in such processes is dependent on its structure and careful analysis of this behaviour can reveal a great deal of information about the structure. Second, many nuclei are radioactive and the nature of this radioactivity again depends on the structure of the nuclei involved. Third, the fine details of atomic spectra or the behaviour of nuclei in applied electromagnetic fields gives information about their electric and magnetic properties. In subsequent sections these different investigative processes will be discussed in more detail. In this section the focus of the discussion will be simply on the general properties of nuclei which emerge from such studies.

Shape and Size. Nuclei are frequently spherical but sometimes have shapes rather like a lemon or a squashed orange. Their radii vary from around l0^-I5m for the lightest through to around l0^-I4m for the heaviest and their volumes turn out to be simply proportional to the value of A, i.e. proportional to the number of particles they contain. They are, of course, very dense since virtually all the mass of an atom is concentrated in their very small volumes. This density is some 10¹⁴ times greater than that of ordinary matter one cubic inch of nuclear matter would weigh around 4,000,000,000 tons. Finally, the edge of a nucleus is not sharp like a billiard ball but is somewhat ‘fuzzy’.

Binding Energy. As has already been mentioned there must be a strong attractive force between nucleons which holds them tightly together in the nucleus. Given such a force means that if a nucleon is to be extracted or knocked out of a nucleus then work has to be done against this retaining force energy has to be provided. Of course, the amount needed varies, roughly speaking, according to whether the nucleon being extracted is hovering near the nuclear surface or is buried deep in the interior. It obviously varies from nucleon to nucleon but will have an average value. This average value is simply the energy needed to completely knock a nucleus to pieces so that all the nucleons are well separated from each other, divided by the total number of nucleons (i.e. A). The energy needed to disintegrate the nucleus in this way is referred to as its binding energy (denoted by B) since it is the energy binding the nucleus together. In turn, it follows that if we brought all the component nucleons together from a large distance an amount of energy equal to B would be released. This means, because of the equivalence between mass and energy and since energy has been released in assembling the nucleus, that its mass is less than the mass of the component nucleons by B/c². This is why nuclear masses, as mentioned earlier, are only approximately equal to the total mass of their component nucleons. It is interesting to plot the binding energy per nucleon (B/A) as a function of A. The energy is measured in MeV (millions of electron volts). The electron volt is a unit of energy widely used in physics and which is defined in the Glossary. We shall see later on that the shape of this curve has implications for the nature of the nuclear force and also for the processes of fission and fusion.

Nuclear Energy levels. As with the electrons in an atom so the motions of nucleons in a nucleus must satisfy the laws of quantum mechanics. In turn, only certain energies are allowed for the nucleus and each nucleus is characterized by a series of possible excitation energies it can have its energy levels. The lowest of these is referred to as the ground state and the remainder as excited states. Each state, as well as having a definite energy, also has a definite angular momentum and that of the ground state is

Figure 1.1: Binding energy per nucleon (B/A) as a function of mass number A.

known as the nuclear spin. It is found that those nuclei for which A is even always have states with angular momentum equal to an integer multiple of h, and those with an odd value of A have angular momentum equal to 1/2, 3/2, 5/2,..., etc times h. This latter observation has the implication that nucleons (protons and neutrons), like electrons, must have spin ½. Being identical spin ½ particles, protons obey the Pauli exclusion principle  and so, similarly, do neutrons.

Electromagnetic Properties. It is to be expected that since nuclei contain charged protons which are moving about in the nucleus, like electrons in an atom, then the resultant electric currents lead to the nucleus behaving like a magnet. Such magnetic properties have been measured for the ground and some of the excited states of many nuclei. It is found that all nuclei having non-zero spin behave as magnets but the strength of this magnetism can only be understood if the protons and neutrons themselves, like electrons, also behave as miniscule magnets. The fact that nuclei with zero spin do not behave as magnets is easy to understand since, with no spin, the nucleus has no spatial direction associated with it whereas a magnet (think of a bar magnet) is highly directional. In addition, those nuclei which are non-spherical in shape produce a rather complicated electric field due to the associated non-spherical distribution of charge carried by the protons. These distorted charge distributions have been measured carefully and we shall that where the distortion is large it has an important effect on the nuclear energy levels. Having briefly described some nuclear properties we now consider their implications for the nature of the nuclear force.