In this chapter we present some of the theory of β-decay and ℽ-decay. In both cases, a fuller treatment requires more quantum mechanics than is usually contained in an undergraduate course, but we shall see that much of the experimental phenomena can be understood qualitatively without the complete relativistic theory.

12.1 What must a theory of β -decay explain?

In β d-decay, introduced in §3.5, the charge of a nucleus changes while A remains fixed. This occurs either by the simultaneous emission of an electron and an anti-neutrino, or a positron and a neutrino, or by the capture of an atomic electron with the emission of a neutrino. The appropriate stability conditions were discussed in §4.6. Several nuclei, for example 64Cu, can decay by any of these processes (Fig. 4.5). In electron capture, the neutrino energy and the recoil energy of the nucleus are sharply defined. In the other processes, the electron (or positron) can take any energy between zero and the maximum allowed by energy conservation. Figure 12.1 shows the experimentally determined energy spectra for electron emission and for positron emission from 6429Cu. It was the observation of continuous energy distributions such as these that led Pauli to infer the existence of the neutrino in 1931: given that the energy levels of a nucleus are discrete, the electron and nuclear recoil energies in the centre-of-mass frame would by energy and momentum conservation be likewise discrete, unless some third particle (the neutrino) were present to share energy and momentum.