Nucleons

The nucleus is made up of protons and neutrons, collectively known as nucleons. These are fermions (spin-half particles) of almost the same mass (in fact it is often useful to think of them as two different states of the same particle, distinguished by different values of quantum number, isospin). Basic properties are given in Table 1.

Nucleons interact with one another via a strong nuclear force (the protons also interact via the electromagnetic force). The origins of this force lie in the interactions between quarks, and the ``force law'' is only approximately known. At the level of nuclear physics, it can be viewed as resulting from the interchange of various mesons between the nucleons. The most important of these are the pi mesons (pions: ).

The force is strongly spin-dependent, i.e. the force depends on the orientations of the intrinsic spins of the two nucleons. An important component is the tensor force, similar in structure to the force between magnet dipoles (or bar magnets). In addition the force is momentum-dependent; as a result it displays spin-orbit coupling.

The spin-independent central part of the force is illustrated schematically in the figure. Note that it has a strongly damped attractive tail, and a strongly repulsive (``hard'') core.

Points to note about the nuclear force:

• The force is charge symmetric: the n-n and the p-p forces are the same.
• The force is essentially charge independent: the n-p force is similar in strength to the p-p and n-n forces.

  In the above, comparisons must be made for pairs in the same quantum states. Thus as far as the nuclear force is concerned, the neutron and proton are simply two aspects of the same particle. This symmetry is exploited by introducing isospin.

• The force is short-ranged, with an exponential cut-off determined by the pion mass. This range of the force essentially determines the size of a nucleus; nuclear effects are not expected to be important at greater distances.
• The force is repulsive at short distances. There is thus an equilibrium separation of nucleons in a nucleus, and a nucleus is not very compressible.
• The central force has a similar shape to that of the van der Waals force between molecules (but the underlying physics is different\!). We can thus naively expect a nucleus to behave somewhat like a liquid drop.

Even in the absence of an interaction, the behaviour of nucleons is not intuitive (i.e. don't think they behave like little billiard balls). Nucleons are fermions, and the one of the simplest models of a nucleus is to consider it as a Fermi gas. The properties are non-classical.