6.1 Energy release in a-decay

We saw at the end of Chapter 4 that the binding energy per nucleon curve of the yd-stable nuclei has a maximum in the neighbourhood of iron (Fig. 4.7), and that the heavier elements may be unstable to spontaneous disintegration. The principal mode of break-up is by emission of a 4 2He nucleus. Historically, the particles emitted in the decays of naturally occurring a-unstable nuclei were called a-particles before they were identified by Rutherford in 1908 as 4 2He nuclei, and the name has stayed.

The kinetic energy release Q(A, Z) in an a-decay of a nucleus (A, Z) is given in terms of the binding energies of the parent and daughter nuclei by

Q(A, Z) = B(A - 4, Z - 2) + 28.3 MeV - B(A, Z), (6.1)

(where 28.3 MeV is the experimental binding energy of the 4 2He nucleus). If the nucleus is assumed to lie on the β-stability curve, given approximately by equation (4.14), then Q may be calculated as a function of Z (or of A) from the semi-empirical mass formula, using equation (4.5). Neglecting the pairing energy term, the effects of which are small, the resulting smooth Q(Z) is plotted in Fig. 6.1 for Z > 50. Negative values of Q imply absolute stability against α-decay. Also shown are Q values calculated from the experimentally measured masses of d-stable nuclei and their corresponding daughter nuclei. The trend of the experimental points is given correctly by the semi-empirical formula.