Introduction

We consider two types of nuclear transformation: (spontaneous) radioactive decay, in which a nucleus emits ``radiation'', thereby being transformed into another nucleus (or to a less excited nucleus), and nuclear reactions, in which nuclei collide and rearrange their energy and their constituents.

These decay and reaction processes can all be treated as transitions between different quantum states. The final states that are accessible are governed by the conservation laws. In particular, conservation of energy, momentum, charge, and baryon and lepton numbers determine whether a transition between two configurations is possible. Transitions between particular states are also determined by angular momentum and parity conservation -- these define selection rules in addition to the general conservation laws. (As long as we are not dealing with beta decays, the number of protons and neutrons in a reaction are also separately conserved).

One of the first observations of nuclear physics was the spontaneous transformation of one element into another by what became known as radioactive decay. This was observed initially in heavy elements in the region of the periodic table above lead. It was soon observed that these transformations were accompanied by various radiations. Three basic types of transformation form the basis of our study of nuclear decay -- these are alpha, beta and gamma decay:

alpha decay

A nucleus emits an alpha particle (a nucleus) and reduces its atomic number by 2 and its mass number by 4.

beta decay

A nucleus emits a beta particle (an electron) (and an antineutrino) and changes its atomic number by 1. The mass number is unchanged, and so beta decays occur amongst isobars. Later, positron decay was observed, and we can speak of ``beta plus" and ``beta minus" decays.

gamma decay

A nucleus emits a photon in making a transition between excited states. (In natural radioactive decay, this follows one of the above two decay processes, which leaves the final nucleus in an excited state.)

These three, together with fission, can be regarded as natural decay mechanisms in that they are observed in naturally occurring nuclei. They also represent mechanisms that proceed via the different forces: the nuclear force (trivially), the weak force and the electromagnetic interaction respectively. By creating nuclei in accelerator experiments in highly excited states or far from the stability line, other forms of emission have been observed, such as proton or neutron emission. In fact, any type of cluster emission (from proton emission to fission) shares many features with alpha decay and can be treated in a similar fashion. Hence a study of these classic decay mechanisms enlightens our study of general reaction mechanisms.

The natural decay processes are important because they give us a means of dating various things by knowledge of the characteristic decay times of different nuclei.

Much of our present knowledge of nuclear physics comes from the study of nuclear reactions. Binary reactions with a two-body final state may generally be denoted as

where a is a projectile, A a target nucleus, b an ejectile and B a residual nucleus. This is usually represented as

Many important reactions are of this type. Some examples (note also the notation) are

Elastic scattering

-- no change in the internal energy of the constituents.

Inelastic scattering

-- there is a change in the internal energy of the , and hence in the energy of the outgoing alpha (hence the prime).

Pickup reaction

. A proton is ``picked up'' from the target nucleus. This is a typical rearrangement collision.