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Unstable Nuclei and Radioactive Decay 61

(e) The total angular momentum PI of the system must be conserved, i.e.

(PI)1 + (1191)2 --" (/91)3 + (PI)4 (4.8)

Since there exist two types of angular momentum, one caused by orbital movement of the
individual nucleons and the other due to the intrinsic spin of the nucleons (internal angular
momentum), a more practical formulation of (4.8) is

AI=I 3 +14-I1-I 2 (4.9)

where I is the (total) nuclear spin quantum number. The quantum rule is

AI = 0, 1, 2, 3, ... (4.10)

i.e. the change of nuclear spin in a reaction must have an integral value.
The three first laws are general in classical physics; the last two refer particularly to
nuclear reactions. In Ch. 10 and 1 1 other conservation laws are discussed for nuclear
reactions, but these are less important in radioactive decay.

4.3. Alpha decay

4.3.1. Detection

Alpha particles cause extensive ionization in matter. If the particles are allowed to pass
into a gas, the electrons released by the ionization can be collected on a positive electrode
to produce a pulse or current. Ionization chambers and proportional counters are
instruments of this kind, which permit the individual counting of each t~-particle emitted
by a sample. Alpha particles interacting with matter may also cause molecular excitation,
which can result in fluorescence. This fluorescence - or scintillation - allowed the first
observation of individual nuclear particles. The ionization in semiconductors caused by t~-
particles is now the most common means of detection, see Ch. 8.

4.3.2. Decay energy

Alpha decay is observed for the elements heavier than lead and for a few nuclei as light
as the lanthanide elements. It can be written symbolically as

~X --, z_2XA-4 + ~He (4.11)

We use X to indicate any element defined by its nuclear charge, Z and Z-2 in this
equation. Examples are given in Ch. 1, and can be found e.g. in the natural radioactive
decay series, see next chapter.
The decay energy can be calculated from the known atomic masses, because the binding
energy released (spontaneous decay processes must be exoergic) corresponds to a