Essentials of Nuclear Medicine Physics, Instrumentation, and Radiation Biology. Rachel A. Powsner

are found naturally as a mix of isotopic forms that are all radioactive.

For those nuclei with a stable state there is an optimal ratio of neutrons to protons. For the lighter elements this ratio is approximately 1:1; for increasing atomic weights, stability is more likely when the number of neutrons exceeds the number of protons. A plot depicting the number of neutrons as a function of the number of protons is called the line of stability (Figure 1.12).

      Stability

      Strictly speaking, stability is a relative term. We call a nuclide stable when its half‐life is so long as to be practically immeasurable—say greater than 100 years. An isotope of potassium, 40K for example, which makes up about 1% of the potassium found in nature is considered stable but actually has a half‐life of 10⁹ years.

Figure 1.12 Combinations of neutrons and protons that can coexist in a stable nuclear configuration all lie within the gray shaded regions.

Radioactivity

      The unstable nucleus and radioactive decay

      A nucleus which is not in its stable state will adjust itself until it is more stable either by ejecting portions of its nucleus or by emitting energy in the form of photons (gamma rays). This process is referred to as radioactive decay. The type of decay depends on which of the following rules for nuclear stability is violated.

       Excessive nuclear mass

       Alpha decay:

Very large unstable atoms, atoms with high atomic mass, may split into nuclear fragments. The smallest stable nuclear fragment that is emitted is the particle consisting of two neutrons and two protons, equivalent to the nucleus of a helium atom. Because it was one of the first types of radiation discovered, the emission of a helium nucleus is called alpha radiation, and the emitted helium nucleus an alpha particle (Figure 1.13).

       Fission:

Under some circumstances, the nucleus of the unstable atom may break into larger fragments, a process usually referred to as nuclear fission. During fission two or three neutrons are emitted (Figure 1.14).

       Unstable Neutron–Proton Ratio

       Too many neutrons—beta decay:

Nuclei with excess neutrons can achieve stability by a process that amounts to the conversion of a neutron into a proton and an electron. The proton remains in the nucleus, but the electron is emitted. This is called beta radiation, and the electron itself a beta particle (Figure 1.15). The process and the emitted electron were given these names to contrast with the alpha particle before the physical nature of either was discovered. The beta particle generated in this decay will become a free electron until it finds a vacancy in an electron shell either in the atom of its origin or in another atom.

Figure 1.13 Alpha decay.

Figure 1.14 Fission of a ²³⁵U nucleus.

Figure 1.15 β ^– (negatron) decay.

      Careful study of beta decay suggested to physicists that the conversion of neutron to proton involved more than the emission of a beta particle (electron). Beta emission satisfied the rule for conservation of charge in that the neutral neutron yielded one positive proton and one negative electron; however, it did not appear to satisfy the equally important rule for conservation of energy. Measurements showed that most of the emitted electrons simply did not have all the energy expected. To explain this apparent discrepancy, the emission of a second particle was postulated and that particle was later identified experimentally. Called an antineutrino (neutrino for small and neutral), it carries the “missing” energy of the reaction.

       Too many protons—positron decay and electron capture:

      In a manner analogous to that for excess neutrons, an unstable nucleus with too many protons can undergo a decay that has the effect of converting a proton into a neutron. There are two ways this can occur: positron decay and electron capture. In general, these proton rich nuclei decay by a combination of these two processes.

      Positron decay:

A proton can be converted into a neutron and a positron, which is an electron with a positive, instead of negative, charge (Figure 1.16). The positron is also referred to as a positive beta particle or positive electron or anti‐electron. In positron decay, a neutrino is also emitted. In many ways, positron decay is the mirror image of beta decay: positive electron instead of negative electron, neutrino instead of antineutrino. Unlike the negative electron, the positron itself survives only briefly. It quickly encounters an electron (electrons are plentiful in matter), and both are annihilated (see Chapter 8, Figure 8.1). This is why it is considered an anti‐electron. Generally speaking, antiparticles react with the corresponding particle to annihilate both. During the annihilation reaction, the combined mass of the positron and electron is converted into two photons of energy equivalent to the mass destroyed, each with an energy of 511 keV or a total of 1.022 MeV. Following ejection of a positron from a nucleus the atom must also shed an orbital electron to keep the overall charge of the atom neutral. So, in essence, the atom is losing the mass equivalent of two electrons (remember positrons are basically positively charged electrons). Positron emission will only occur when the difference in mass between the parent (original) and daughter atoms is at minimum the mass of two electrons, which, as we will see in Chapter 2, Figure 2.12 is equal to 1.02 MeV of energy.

Figure 1.16 β ⁺ (positron) decay.