Answer to Question #7434 Submitted to "Ask the Experts"

Kindly tell me the difference between branching fraction and adundance of a radionuclide. How can abundance or branching fraction be more than 100% as in ¹¹¹In, ¹¹C, and other radionuclides?

In addition to radionuclide abundance and branching fraction that you mention, we should also consider the concept of radiation yield since I believe it is the latter that you are probably confused about.

The abundance of a particular species refers to the atom fraction of that nuclide that is found in nature. The term is used only in reference to stable nuclides and radionuclides that have sufficiently long half-lives that they are still present on earth. For example, the fractional atom abundances of the two important uranium isotopes, ²³⁸U (half-life of 4.5 x 10⁹ years) and ²³⁵U (half-life of 7.0 x 10⁸ years), are 0.992745 and 0.0072. A third natural isotope of uranium, ²³⁴U, has an atom abundance of 0.000055; note that the ²³⁴U has a half-life of only 2.5 x 10⁵ years, not long enough to ensure its survival since the beginning of the earth, but it is produced as part of the decay chain of ²³⁸U and is continually produced as the ²³⁸U decays. The abundance of any atomic species, including naturally occurring radionuclides, cannot exceed 1.0.

The concept of branching fraction, as applied to decay of a radionuclide, means that the radionuclide decays by more than one possible mode. For example, a number of radionuclides that contain an excess number of protons in their nuclei may decay by both electron capture and by positron emission; both decay events result in reduction of the proton number by one. The branching fraction refers to the fraction of the time the decay occurs by the respective route. For example, the radionuclide ⁵⁸Co decays by both electron capture and positron emission with respective branching fractions of 0.85 and 0.15. The sum of branching fractions cannot exceed 1.0. A value of 1.0 for a branching fraction implies that the nuclide decays by only a single mode.

This brings us to the notion of radiation yield, which is also sometimes referred to as radiation abundance (but not radionuclide abundance). This refers to the fractional yield (number of that type of radiation emitted per disintegration of the nucleus) of a particular radiation emitted during the decay process. The major decay processes are beta minus (or negatron) decay, beta plus (or positron) decay, electron capture decay, and alpha decay. These are associated, respectively with the emission of beta minus particles, positrons, x rays, and alpha particles. As noted above, if branch decay is possible, the sum of the branching fractions for a particular radionuclide cannot exceed 1.0; therefore, the sum of the yields of the major particulate radiations (beta particles or alpha particles) that result from decay of that radionuclide also cannot exceed 1.0. In addition to the major decay radiations, however, gamma radiation is often present as a result of deexcitation of the nucleus following the decay event. It is possible for the sum of the gamma ray yields to exceed 1.0 because deexcitation may occur through sequential emissions from different nuclear excited states. One of the most common examples of this process occurs in the case of ⁶⁰Co. This radionuclide decays by beta minus emission to an excited nuclear state of ⁶⁰Ni, which immediately deexcites by emitting a 1.17 MeV gamma ray that leads to a second lower excited state, and this state deexcites with the emission of a second gamma ray of 1.33 MeV. Each of these gamma rays occurs every time a ⁶⁰Co nucleus decays by beta minus emission, which it does 100% of the time; therefore, the total gamma yield (or gamma abundance) is 2.0 (2 gamma rays per disintegration). In the case of the ¹¹¹In that you mention, the nucleus decays100% of the time by electron capture, which leads to an excited state of ¹¹¹Cd. This excited state deexcites 90.5%t of the time with the emission of a 0.171 MeV gamma ray (in the other 10.5% of the deexcitations a conversion electron is emitted rather than a gamma ray); similarly to the ⁶⁰Co case, this initial deexcitation leads to a lower excited state that deexcites with the emission of a second gamma ray with a yield of 0.940 and an energy of 0.245 MeV. The sum of the two gamma ray yields for this decay is then 1.845.

In the case of a radionuclide that decays by positron emission, there is another factor that adds more photons to the process; these are the annihilation photons that result when the positron that is emitted slows down and encounters an electron. The two antibodies annihilate, and two annihilation photons, each of 0.511 MeV, are produced. These are often shown when you look up decay scheme data, frequently being presented as if they were gamma rays, although they are actually not since they do not originate in the nucleus. At any rate, since there are two such photons produced per positron emitted, a radionuclide that decays 100% of the time by positron emission will exhibit an annihilation photon yield of 2.0. This is more-or-less the case for the¹¹C that you cite, since it decays almost 100% (99.8%) of the time by positron emission.

I hope this discussion resolves most of your confusion about the concepts of nuclide abundance, branching fraction, and radiation yield.

George Chabot, PhD, CHP