Possible issue(s) with “inclusion of short-lived daughter radionuclides”

February 23rd, 2021
by Joseph Magill

Qu.) TvD, RIVM, Netherlands
Dear Nucleonica Team,
We are using Nucleonica and we have a question about the following App: Photon Dose Rate Constants++. This app offers the option to include short-lived daughter nuclides.
For Th-232, we get the following results:
Th-232 daughtersThis result occurs for the following two Data sets: 8th ToRI and the JEFF-3.1 (other data sets do not contain short-lived daughters). What is extremely puzzling is the BR product of 2.780E-12 for daughter products Tl-208, Hg-206 and Tl-206. If we look in the help section of this specific app, the following is mentioned under the inclusion of short-lived daughters:
+++
For the calculation of the dose rate constants, some nuclides are considered to be in equilibrium with daughter products. This is the case when a single radioactive decay chain in which radionuclides are present in their naturally occurring proportions, and in which no daughter nuclide has a half-life either longer than 10 days or longer than that of the parent nuclide, shall be considered as a single radionuclide. Such nuclides are denoted with an asterisk in the Nuclide Summary tab e.g. Cs-137*.
In the case of radioactive decay chains in which any daughter nuclide has a half-life either longer than 10 days or greater than that of the parent nuclide, the parent and such daughter nuclides shall be considered as mixtures of different nuclides.
+++

Our issues/questions are as follows:
Issue-1:
If the chain is assumed to be in secular equilibrium, the BR product for Tl-208 (we assume this stands for the product of branching ratios, i.e., the compound branching ratio) should actually amount to 0.36, or better: 0.3593.
Issue-2:
Why are other gamma-emitting nuclides missing, such as: Ra-228 (it has a half life of 5.75 y, but it should be taken into account as well due to the “either-or” formulation above), Ac-228, Th-228, Ra-224, Rn-220, Po-216, Pb-212, and Bi-212?
These are all preceding daughters (with photon emissions) in equilibrium as well.
Issue-3:
Under the same description for included daughters (see above, highlighted text in italics), why does U-238 not have any short-lived daughters? All nuclides could be included as no other daughters have a half life larger than that of the head-of-chain parent radionuclide U-238. Anyhow, I would at least expect the ‘actual’ short-lived nuclides to be included: Th-234 and Pa-234 and Pa-234m.
Issue-4:
What are Hg-206 and Tl-206 doing in this chain?

(Ans. Nucleonica Team)
We have now looked into your question in more detail.
Let’ start with …
Issue 4: Where does Hg-206 and Tl206 come from?
Hg206 and Tl206 come from cluster emission (CE) of the parent Th232. This is a very rare decay mode. They are included in the calculation for completeness although they have no effect on the results. If you look into the Datasheets (JEFF-3.1) for Th-232 you will see the cluster emission involves the emission of the nuclei Hg-206 and Hg-208. The nuclide Tl-208 arises through the decay of the cluster emitted Hg-208. (The Tl-208 is somewhat confusing since it arises both through cluster emission CE and from the Po-212 in the Th-232 decay chain. So the three nuclides shown in your table 1, Tl-208, Hg-206 and Tl206, all arise from CE and as such are not important.
Th-232 CE

Regarding the rules in italics…
– Th-232 (alpha) Ra-228: T/2(Ra-228) = 5.75 y > 10 d: not a short lived nuclide and thus no further short nuclides

– Th-232 (2ß) U-232: T/2(U-232) = 69.8 y > 10 d: not a short lived nuclide and thus no further short nuclides

– Th-232 (Ne-26) Hg-206: T/2(Hg-206) = 8.15 min < 10 d < T/2(Th-232) = 1.405e10 y: Hg-206 is a short lived nuclide,

Hg-206 (ß-) Tl-206: T/2(Tl-206) = 4.202 min < 10 d < T/2(Hg-206): Tl-206 is a short lived nuclide

Tl-206 (ß-) Pb-206 stable

– Th-232 (Ne-24) Hg-208: T/2(Hg-208) = 42 min < 10 d < T/2(Th-232): Hg-208 is a short lived nuclide, but has no radiations in JEFF-3.1;

Hg-208 (ß-) Tl-208: T/2(Tl-208) = 3.053 min < 10 d < T/2(Th-232): Tl-208 is a short lived nuclide

Tl-208 (ß-) Pb-208 stable

Issue-1: Here it is sufficient to say that the Th-232 is NOT in secular equilibrium with the (normal) daughters, only the CE daughters.

Issue-2: I think there is a misunderstanding of the rule in italics here. Ra-228 has a half-life of 5.75y and as such >10 days. So it should not be included in the calculation.

Additionally the italics text is not “either or”. The half-life must be less than 10 days AND less than the half-life of the parent nuclide. (this is the IAEA rule). In other words…In fact one follows the decay chains only as long as daughter nuclides having a half-life shorter than 10 days and shorter than that of the parent nuclide are found.

Issue-3: U-238 : the first daughter is Th-234 with a half-life 24.09 days.(i.e >10days). For this reason th228 and all daughters are not included.

I hope this manages to answer the questions you raise.

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