1.3 Radioactive decay

Nuclear stability and decay are best understood in the context of the chart of nuclides. It has already been noted that naturally occurring nuclides define a path in the chart of the nuclides, corresponding to the greatest stability of proton/neutron ratio. For nuclides of low atomic mass, the greatest stability is achieved when the number of neutrons and protons are approximately equal (N = Z) but as atomic mass increases, the stable neutron/proton ratio increases until N/Z = 1.5. Theoretical stability limits are illustrated on a plot of N/Z against mass number (A) in Fig. 1.9 (Hanna, 1959).

The path of stability is in fact an energy ‘valley’ into which the surrounding unstable nuclides tend to fall, emitting particles and energy. This constitutes the process of radioactive decay. The nature of particles emitted depends on the location of the unstable nuclide relative to the energy valley. Unstable nuclides on either side of the valley usually decay by ‘isobaric’ processes. That is, a nuclear proton is converted to a neutron, or vice-versa, but the mass of the nuclide does not change significantly (except for the ‘mass defect’ consumed as nuclear binding energy). In contrast, unstable nuclides at the high end of the energy valley often decay by emission of a heavy particle (e.g. an " particle), thus reducing the overall mass of the nuclide.

Fig. 1.9. Theoretical stability limits of nuclides illustrated on a plot of N/Z against mass number (A). Lower limits for " emission are shown for " energies of 0, 2 and 4 MeV. Stability limits against spontaneous fission are shown for half-lives of 10¹⁰ yr and zero (instantaneous fission). After Hanna (1959).

1.3.1 Isobaric decay

Different decay processes indicated in Fig. 1.9 can best be understood by looking at example sections of the chart of nuclides. Figure 1.10 shows a part of the chart around the element potassium. The diagonal lines indicate isobars (nuclides of equal mass) which are displayed on energy sections in Fig. 1.11 and Fig 1.12.

Fig. 1.10. Part of the chart of the nuclides, in coordinates of atomic number (Z) against neutron number (N) in the region of potassium. Stable nuclides are shaded; the long-lived unstable nuclide ⁴⁰K is hatched. Diagonal lines are isobars (lines of constant mass number, A).

Nuclides deficient in protons decay by transformation of a neutron into a proton and an electron. The latter is then expelled from the nucleus as a negative ‘$’ particle ($^!), along with an anti-neutrino (<). The energy released by the transformation is divided between the $ particle and the anti-neutrino as kinetic energy (Fermi, 1934). The observed consequence is that the $ particles emitted have a continuous energy distribution from nearly zero to the maximum decay energy. Low-energy $ particles are very difficult to separate from background noise in a detector, making the $ decay constant of nuclides such as ⁸⁷Rb very difficult to determine accurately by direct counting (section 3.1).

Fig. 1.11. A simple energy section through the chart of nuclides along the isobar A = 38 showing nuclides and isomers. Data from Lederer and Shirley (1978).

In many cases the nuclide produced by $ decay is left in an excited state which subsequently decays to the ground state nuclide by a release of energy. This may either be lost as a ( ray of discrete energy, or may be transferred from the nucleus to an orbital electron, which is then expelled from the atom. In the latter case, nuclear energy emission in excess of the binding energy of the electron is transferred to the electron as kinetic energy, which is superimposed as a line spectrum on the continuous spectrum of the $ particles. The meta-stable states, or ‘isomers’ of the product nuclide are denoted by the superfix ‘m’, and have half-lives from less than a picosecond up to 241 years (in the case of ^192mIr). Many $ emitters have complex energy spectra involving a ground state product and more than one short-lived isomer, as shown in Fig. 1.11. The decay of ⁴⁰Cl can yield 35 different isomers of ⁴⁰Ar (Lederer and Shirley, 1978), but these are omitted from Fig. 1.12 for the sake of clarity.

Nuclides deficient in neutrons, e.g. ³⁸K (Fig. 1.11), may decay by two different processes: positron emission and electron capture. Both processes yield a product nuclide which is an isobar of the parent, by transformation of a proton to a neutron. In positron emission a positively charged electron ($⁺) is emitted from the nucleus along with a neutrino. As with $^! emission, the decay energy is shared between the kinetic energy of the two particles. After having been slowed down by collision with atoms, the positron interacts with an orbital electron, whereby both are annihilated, yielding two 0.511 MeV ( rays. (This forms part of the decay energy of the nuclear transformation).

In electron capture decay (E.C.) a nuclear proton is transformed into a neutron by capture of an orbital electron, usually from one of the inner shells, but possibly from an outer shell. A neutrino is emitted from the nucleus, and an outer orbital electron falls into the vacancy produced by electron capture, emitting a characteristic X-ray. The product nucleus may be left in an excited state, in which case it decays to the ground state by ( emission.

When the transition energy of a decay route is less than the energy equivalent of the positron mass (2m_eC²= 1.022 MeV), decay is entirely by electron capture. Thereafter, the ratio $⁺/E.C. increases rapidly with increasing transition energy (Fig. 1.12), but a small amount of electron capture always accompanies positron emission even at high transition energies.

Fig. 1.12. Energy section through the chart of nuclides along isobar A = 40. Isomers are omitted for simplicity. For nuclides with more than one decay mechanism the percentage of transitions by different decay routes is indicated. Data from Lederer and Shirley (1978).

It is empirically observed (Mattauch, 1934) that adjacent isobars cannot be stable. Since ⁴⁰Ar and ⁴⁰Ca are both stable species (Fig. 1.10), ⁴⁰K must be unstable, and exhibits a branched decay to the isobars on either side (Fig. 1.12).

1.3.2 Alpha and Heavy Particle Decay

Heavy atoms above bismuth in the chart of nuclides often decay by emission of an " particle, consisting of two protons and two neutrons (He²⁺). The daughter product is not an isobar of the parent, and has an atomic mass reduced by four. The product nuclide may be in the ground state, or remain in an excited state and subsequently decay by ( emission. The decay energy is shared between kinetic energy of the " particle and recoil energy of the product nuclide.

The U and Th decay series are shown in Fig. 12.2. Because the energy valley of stable proton/neutron ratios in this part of the chart of the nuclides has a slope of less than unity, " decays tend to drive the products off to the neutron-rich side of the energy valley, where they undergo $ decay. In fact $ decay may occur before the corresponding " decay.

At intermediate masses in the chart of the nuclides, " decay may occasionally be an alternative to positron or electron capture decay for proton-rich species such as ¹⁴⁷Sm. However, " decays do not occur at low atomic numbers because the path of nuclear stability has a Z/N slope close to unity in this region (Fig. 1.1). Any such decays would simply drive unstable species along (parallel to) the energy valley.

An exotic mode of radioactive decay was discovered in the ²³⁵U to ²⁰⁷Pb decay series (Rose and Jones, 1984), whereby ²²³Ra decays by emission of ¹⁴C directly to ²⁰⁹Pb with a decay energy of 13.8 MeV. However this mode of decay occurs with a frequency of less than 10^!9 of the " decay of ²²³Ra.

1.3.3 Nuclear Fission and the Oklo natural reactor

The nuclide ²³⁸U (atomic no. 92) undergoes spontaneous fission into two product nuclei of different atomic number, typically ca. 38 and 53 (Sr and I), along with various other particles and a large amount of energy. Because the heavy parent nuclide has a high neutron/proton ratio, the daughter products have an excess of neutrons and undergo isobaric decay by $ emission. Although the frequency of spontaneous fission of ²³⁸U is less than 2 H 10^!6 that of " decay, in heavier transuranium elements spontaneous fission is the principal mode of decay. Other nuclides, such as ²³⁵U, may undergo fission if they are struck by a neutron. Furthermore, since fission releases neutrons which promote further fission reactions, a chain reaction may be established. If the concentration of fissile nuclides is high enough, this leads to a thermonuclear explosion, as in a supernova or atomic bomb.

In special cases where an intermediate heavy-element concentration is maintained, a self-sustaining but non-explosive chain reaction may be possible. This depends largely on the presence of a ‘moderator’. Energetic ‘fast’ neutrons produced by fission undergo multiple elastic collisions with atoms of the moderator. They are decelerated into ‘thermal’ neutrons, having velocities characteristic of the thermal vibration of the medium, the optimum velocity for promoting fission reactions in the surrounding heavy atoms. One natural case of such an occurrence is known, termed the Oklo natural reactor (Cowan, 1976; Naudet, 1976).

In May 1972, ²³⁵U depletions were found in uranium ore entering a French processing plant and traced to an ore deposit at Oklo in the Gabon republic of central Africa. Despite its apparent improbability, there is overwhelming geological evidence that the ²³⁵U depletions were caused by the operation of a natural fission reactor ca. 1.8 Byr ago. It appears that in the Early Proterozoic, conditions were such that the series of coincidences needed to create a natural fission reactor were achieved more easily than at the present day.

This probably began when uranium dispersed in granitic basement was eroded and concentrated in stream-bed placer deposits. It was immobilised in this environment as the insoluble reduced form due to the nature of prevailing atmospheric conditions. With the appearance of blue-green algae, the first organisms capable of photosynthesis, the oxygen content of the atmosphere, and hence river water, probably rose, converting some reduced uranium into more soluble oxidised forms. These were carried down-stream in solution. When the soluble uranium reached a river delta it must have encountered sediments rich in organic ooze, creating an oxygen deficiency which again reduced and immobilised uranium, but now at a much higher concentration (up to 0.5% uranium by weight).

After burial and compaction of the deposit, it was subsequently uplifted, folded and fractured, allowing oxygenated ground-waters to re-mobilise and concentrate the ores into veins over 1 m wide of almost pure uranium oxide. Hence the special oxygen fugacity conditions obtaining in the Proterozoic helped to produce a particularly concentrated deposit. However, its operation as a reactor depended on the greater ²³⁵U abundance (3%) at that time, compared with the present day level of 0.72%, reduced by "-decay in the intervening time (half-life = 700 Myr).

In the case of Oklo, light water (H₂O), must have acted as a moderator, and the nuclear reaction was controlled by a balance between hot water loss (by convective heating or boiling) and replacement by cold ground-water influx. In this way the estimated total energy output (15 000 mega-watt years, representing the consumption of six tons of ²³⁵U) was probably maintained at an average of only 20 kilowatts for about 0.8 Myr.

Geochemical evidence for the occurrence of fission is derived firstly from the characteristic elemental abundances of fission products. For example, excess concentrations of rare earths and other immobile elements such as Zr are observed. Alkali metal and alkali earths were probably also enriched, but have subsequently been removed by leaching. Secondly, the characteristic isotope abundances of some elements can only be explained by fission (Raffenach et al., 1976).

The Nd isotope composition of the Oklo ore is very distinctive (Fig. 1.13). ¹⁴²Nd is shielded from isobaric decay of the neutron-rich fission products (Fig. 1.8) so that its abundance indicates the level of normal Nd. After correction for an enhanced abundance of ¹⁴⁴Nd and ¹⁴⁶Nd due to neutron capture by the large cross-section nuclides ¹⁴³Nd and ¹⁴⁵Nd, Oklo Nd has an isotopic composition closely resembling that of normal reactor fission product waste (Fig. 1.13).

Fig. 1.13. Bar charts of the isotope composition in normal Nd, Oklo ore, and reactor fission product waste. Data from Cowan (1976).

Evidence for a significant neutron flux is also demonstrated by the isotope signatures of actinide elements. For example, the abundant isotope of uranium (²³⁸U) readily captures fast neutrons to yield an appreciable amount of ²³⁹U, which decays by $ emission to ²³⁹Np and then ²³⁹Pu (Fig. 1.14). The latter decays by " emission with a half-life of 24 400 yr to yield more ²³⁵U, contributing an extra 50% to the ‘burnable’ fuel, as in a ‘fast’ breeder reactor (‘fast’ refers to the speed of the neutrons involved). Because the fission products of ²³⁹Pu and ²³⁵U have distinct isotopic signatures, it is determined that very little ²³⁹Pu underwent neutron-induced fission before decaying to ²³⁵U. Hence, the low flux and prolonged lifetime of the natural reactor are deduced.

Fig. 1.14. Nuclear reactions leading to ‘breeding’ of transuranium element fuel in the Oklo natural reactor.

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