First, we thank Dr. Leya for a comprehensive review of the paper. In general, the issues brought up in this review can be addressed with additional explanation. In the interests of brevity, we did not include detailed explanations of some of these issues in the main text, but we include them below in this response and we propose to make several additions to the paper, as enumerated below. The major issues fall into four categories: gas fractionation; the effects of gas loss during irradiation; the question of what exactly the “age” means; and questions about blank analyses. We address these in order below.

1. Fractionation:

Page 2, line 31: There is the problem with noble gas loss during operation. The authors mention thermally activated diffusion either out of the fuel element or into a bubble. In either way, this process will fractionate the gas. The light isotopes will diffuse faster and will therefore be lost more readily than the heavy isotopes. This process likely needs to be considered but at least should be discussed.

In addition there was no complete noble gas extraction. Usually, this also produces fractionation of the released but also of the remaining gas. Has this been tested? Are the noble gas isotope ratios released in the individual steps consistent? This needs a little more work.

[Line 30] Important question (I think), will these processes fractionate the gas?

[Line 135] Is this incomplete extraction causing any fractionation. I guess yes and this needs to be discussed.

[Line 221] Typical unfractionated losses would not [affect] the age at all, correct?’

The short answer to these questions is that we found that Xe and Kr are not diffusively fractionated during extraction by heating at relevant temperatures. Figure 1 shows the evolution of selected Xe and Kr isotope ratios during sequential heating steps for one of our samples (ATM-109-3-1, from the center of the fuel pellet). This sample experienced the greatest number of heating steps and, unlike the rest of the samples, was heated to complete gas exhaustion, so is the best example for this purpose. As shown in the figure, there is no significant variation in Xe and Kr isotope ratios throughout the heating schedule. Other samples, which were not heated to complete gas exhaustion (although probably to the ~95% range as suggested in the text), also show insignificant variation in isotope ratios through the heating schedule, with one exception. The exception is that some of the initial preheat steps at 600° C released gas that was isotopically distinct from that released in the remainder of the heating steps. As suggested in the text, this most likely results not from diffusive fractionation but instead from early release of gas segregated into bubbles that has a different age/residence time than matrix gas.

Figure 1. Evolution of selected Kr and Xe isotope ratios in sequential heating steps for sample ATM-109-3-1. Earlier and later heating steps with signals very close to background have very large uncertainties on the ratios, do not contribute significantly to the bulk composition, and are not shown.

Although all of the step-heating data are in the Supplement and therefore it would be possible to readers to also come to this conclusion by reference to the data, it is true that we did not specifically discuss this in the paper. We will add a short section of text discussing this.   

1. Gas loss:

Page 11: There is some point I cannot understand. First, how can gas loss affect the age? Assuming production is still in the linear range, i.e., short irradiation time, loss of noble gases would affect all isotopes simultaneously and would therefore have no effect on the age, right? This is true for any type of gas losses (location) but in my opinion also true for the time when the gas loss occurred (early or late in the irradiation). The same is true with a change in production rates. If the change is the same of all isotopes, you won’t see it in your procedure. For a long irradiation, when the increase of 85Kr is lower than linear due to saturation effects. One still loses the same amount of 83Kr, 84Kr, and 85Kr in that hypothetical loss event but now one loses relatively more 83Kr and 84Kr relative to 85Kr.

[Line 195] still, not completely true. here you discuss isotope ratios, losses should affect all isotopes similarly.

[Line 198] Actually, I don't understand this. You show here that neutron fluence in lower at the edges than at the center. I follow this. But I don't see how this translates into gas losses?

It appears we were unclear as to how gas loss during the irradiation can affect the isotope ratios. The reviewer interprets ‘gas loss’ as the situation in which there is a single inventory of gas, and part of it is lost by diffusion. In this situation, it is true (as shown by the discussion above of fractionation during heating) that the isotopic composition of the gas that is lost is the same as that of the gas that is retained, and in this case gas loss cannot affect the apparent gas age. The reviewer correctly points this out.

However, this is not the situation that we are describing. Gas is continuously produced during an irradiation. Gas inventories produced at different times during the irradiation can be produced with a different initial composition, and also experience different residence times/irradiation durations. Thus, at the end of the irradiation, if it were possible to separately consider the gas inventory produced at the beginning of the irradiation and the gas inventory produced at the end of the irradiation, they would be isotopically distinct. The gas produced at the beginning of the irradiation would, for example, have lower ⁸⁵Kr/(⁸³Kr+⁸⁴Kr) (because it was produced a longer time ago), and would have higher ⁸⁴Kr/⁸³Kr (because it has experienced a longer duration of irradiation and therefore a greater neutron fluence).

Of course, these gas inventories are mixed so that it is not possible to analyze them separately. If all the gas produced during the irradiation is retained, a measurement of the gas composition after the irradiation yields an average isotopic composition for gas produced at all times during the irradiation.

However, if gas loss occurs during the irradiation, this is no longer true. Suppose, for example, that recrystallization of the fuel near the pellet edge 75% of the way through the irradiation results in loss of much of the fission gas produced up to that point. Then, at the end of the irradiation, the isotopic composition of the gas in a sample from the pellet edge would not be an average of the gas produced throughout the entire irradiation, but only of the gas produced during the final 25% of the irradiation. The apparent Kr-85 age of this gas would be within the last quarter of the irradiation rather than in the middle of the entire irradiation, and the fluence-sensitive isotope ratios (e.g., 84/83) would show a low fluence in relation to samples that had not experienced gas loss.

To summarize, the effect of gas loss during irradiation is not that the process of loss causes fractionation, but instead that loss of gas produced early in the irradiation means that the measured gas contains information only about the end of the irradiation, not about the entire irradiation. We will add some explanatory information to the text to make this more clear.

1. What is the “age” exactly?

Page 5 , sample acquisition.

• Both samples are not perfect for determining the age, right? For sample BR3, there was 2 years of irradiation, the one year pause and another year of irradiation. In this one year time gap, some of the ⁸⁵Kr decays already. In such a scenario, what exactly are you dating? Is the decay during the gap included. If you know the irradiation conditions, time dependent flux, you can correct for this. I think this should be discussed.
• Sample ATM-109 is, in my opinion, even worse. With the long irradiation time, you start seeing saturation effects in ⁸⁵ How are they included. My understanding was, that this procedure holds for short irradiation times, i.e., when the increase for stable and radioactive isotopes are more or less linear but that saturation eKects are not included. For example, in Fig. 2, the ratio ⁸⁵Kr / (⁸³Kr + ⁸⁴Kr) starts decreasing for long irradiation times. How is this treated?

[Line 204, regarding fluence estimates] This is only true if the neutron flux was more or less the same for all irradiation periods. If, for example, the last irradiation period has a much higher flux, the end of irradiation would be at the irradiation. I mean, with the temporal information of the flux density, you can properly calculate ⁸⁵Kr at the end or irradiation.

[Figure 6] I see a problem here: you had a break in the irradiation, right, therefore, some ⁸⁵Kr decayed between the irradiation and some is then reformed. In addition, for ⁸⁵Kr in ATM , irradiation was about 1 half-live long, therefore saturation effects might become important.

Basically, what the reviewer is pointing out here is that the fuel samples we analyzed were irradiated for a time that is fairly long in relation to the ⁸⁵Kr half-life, so a significant fraction of the ⁸⁵Kr produced during the irradiation decayed before the irradiation ended. The result of this is that the apparent ⁸⁵Kr age of the gas does not represent a specific point-like event, for example the beginning or the end of the irradiation. This is correct and is an inherent property of the situation in which the duration of  an event is similar in magnitude to the half-life of the isotope used to date it.

It is possible to relate the apparent ⁸⁵Kr age with a specific point in the irradiation if one makes several additional assumptions, specifically that (i) there is one period of irradiation; (ii) all gas produced in the irradiation is retained until the time of measurement; and (iii) the production rate of fissiogenic Kr is constant throughout the irradiation. We allude to this on p. 11 of the paper, but, as the reviewer points out, don’t go into detail. However, these assumptions would still allow one to date the middle of the irradiation, not the beginning or end.

Thus, the reviewer is correct in pointing out that the apparent ⁸⁵Kr age does not date a specific point in time. Instead, it is only constrained to lie somewhere within the irradiation duration of the fuel. This information is, however, valuable for the purposes of this work, which are mainly to (i) determine the approximate age of the material; (ii) confirm or exclude proposed origins for fuel samples, and (iii) group together disparate samples that were irradiated together. An apparent gas age that falls somewhere within the irradiation is useful for these purposes, especially for more typical nuclear fuels that are irradiated for 1-2 years (in contrast to the studied fuels that were irradiated for excessively long periods for research purposes).

It should also be noted that the concept of an ‘apparent age’ that does not correspond to a point-like event is often used in geochronology and Earth sciences; one common example is the concept of “cooling age” in which a single numerical age is used to represent a point in a continuous cooling process that may extend over a long period of time.

Thus, to address this comment, we will add material to the text to:

• Clearly define the concept of an “apparent” ⁸⁵Kr age that does not represent a point-like event
• Include additional detail in the section on expected ages on p. 11 of the submitted version
• Highlight in the conclusions the utility of an apparent age for the desired purposes.

1. Blanks:

Item 3: I am not too happy with the blank treatment. From our experience, the blank in a cold environment, i.e., not shooting the laser is typically much lower than the blank in a hot environment, i.e., shooting the laser. This has something to do with production and condensation of hot gas and is actually understandable, heating something up produces gas and some material condenses somewhere and thereby produces blank.

Also: near line 145: “Why not heating empty packets. This would be a blank much closer to the samples.”

It appears our explanation of this in the paper was too concise. In fact, we quantified blank contributions in two ways, which follow common practice in noble gas analysis as suggested by the reviewer.

First, as (very briefly) described in the paper, during the period of the analyses, we measured “cold” blanks between heating steps. Typically a cold blank was measured after every sample heating step, although the frequency was reduced to every 2 or 3 sample heating steps when small signals were expected. The signal that is captured in the cold blanks is generally associated with mass spectrometer and extraction line “memory” effects, in which small amounts of adsorbed Kr and Xe are not fully pumped out of the system between analyses. Cold blanks are typically on the order of counts per second for the minor isotopes and tens of counts per second for the major isotopes, are small in relation to signals in sample analyses, and vary somewhat with the amounts and isotope compositions of Xe and Kr in the adjacent samples. All sample analyses are therefore corrected using the cold blank measured immediately before the sample.

Second, we also made offline (“offline” meaning in a completely separate loading of the sample chamber when no samples were present) “hot” blank measurements in which we heated empty Ta packets. Hot blanks yielded small (i.e., slightly above cold blank values) amounts of Kr and Xe that had a composition indistinguishable from atmosphere. This is unsurprising, as any included Xe and Kr in manufactured metal components is expected to be atmosphere-derived. The measurements of fissiogenic Kr and Xe in the samples already include a correction for atmospheric Xe and Kr. Thus, the fact that the gas released from empty Ta packets was indistinguishable from atmosphere means that correction for any hot blank is already included in the atmospheric correction. Therefore we did not make a separate correction for hot blanks.

We will add additional text to make this procedure more clear.

1. Technical corrections and clarifications. Finally, the review included a number of technical corrections and requests for clarification. We will correct these in the revised text.
2. Summary. To summarize, our proposed revisions to the text are as follows:

1. Add text briefly describing the fact that we did not observe diffusive fractionation during heating.
2. Add discussion to clarify the process by which gas loss affects Kr and Xe isotope ratios. Specifically, we will clearly distinguish the concept of potential fractionation of gas during diffusive loss from the concept of preferential retention of gas produced later in the irradiation.
3. Add discussion to clearly define the concept of an “apparent age” that falls within a period of irradiation, but does not correspond to a specific event.
4. Expand the description of blank corrections as noted above.
5. Make various technical corrections and clarify certain areas noted by the reviewer.

First, we thank the reviewer for their comments on this paper. We address them below.

However, the manuscript is an excellent publication of a method, the main problem is that it does not fit to the scope of Geochronology.

While the subject matter of the paper may lie slightly outside the category of 'geochronology strictly defined, we think that the paper is of interest to readers of Geochronology for several reasons, as follows:

• Noble gas geochemistry and radioisotope decay systems are both core areas of practice and research in geochronology. This paper presents a novel application of both tools, which, although not in itself a geoscience application, is directly analogous to many geoscience applications. Thus, we expect this paper will be easily understandable, intellectually engaging, and of substantial interest to many geochronologists.
• The application of principles of isotope geochronology to a field outside geoscience strictly defined will likely be of great interest to students and early career scientists exploring potential careers outside of academia. We would argue that an outward-looking attitude of this sort is critical to sustaining the field of geochronology.
• Geochronology of recent (e.g., post-WWII) sedimentary records commonly relies on stratigraphic markers formed by easily detectable radioisotopes released by atmospheric nuclear testing and unplanned releases of nuclear materials. Particles of irradiated material like those described in this paper have been in the past, and could be in future, accidentally released from nuclear facilities, transported by Earth surface processes, and incorporated in sedimentary archives. Thus, direct geochronology applications in dating post-1950's sediments could arise from this work.

Thus, we disagree with the reviewer’s assessment of relevance, and we strongly encourage the Geochronology editors to take our view.

The abstract is far too short (only one sentence), it does not make a concise summary of the manuscript.

We disagree that the abstract does not make a concise summary of the manuscript. The main point of the paper is, in fact, extremely simple: we show that the radioisotope krypton-85 can be used to date spent nuclear fuel. The abstract clearly and concisely communicates this simple point.

However, based on the comments of this reviewer and reviewer 3, it appears it would be valuable to add material to the abstract explaining the overall context and applicability of this work. We will pursue this.

Please provide examples, how the dating of spent fuel can contribute to forensic investigations. Is it possible that the lifeway of spent fuel is not reported. Can it be lost or stolen? Are there examples?

The general subject of nuclear forensics applications of radiochronometry is quite large. In addition, much of this information is not publicly available. Thus, we have not attempted to give either a complete overview of the subject, or specific examples, in this paper (instead we cite some reviews, which are quite comprehensive). The general idea, which we allude to in the introduction, is that if nuclear fuel were found in the environment, or anywhere outside of its expected location in a nuclear facility, it would clearly be important to identify its source. Determining the age of the material would obviously be valuable in, for example, establishing whether the material was inadvertently lost from an active nuclear facility (perhaps an accident scenario) or was taken from some long-term storage location (perhaps an intentional dispersal scenario). Overall, we think it is fairly self-evident that if irradiated material is found in the environment it is important to find out where it came from. We can highlight this reasoning a bit more in the introduction, but we do not propose to add significant amounts of background material that are well covered in review papers and books.

-line 279: where does ²⁴¹Am come from?

-line 285: what are the three successive neutron capture reactions?

During irradiation of nuclear fuel in a reactor, neutron capture on ²³⁸U yields ²³⁹U, which decays to ²³⁹Np with a 23-minute half-life; neutron capture on ²³⁹Np yields ²⁴⁰Np, which decays to ²⁴⁰Pu with a 1-hour half-life; and neutron capture on ²⁴⁰Pu yields ²⁴¹Pu, which decays to ²⁴¹Am with a 14-year half-life. ²⁴¹Am then has a 400-year half-life. Thus, the comparable radiochronometer to ⁸⁵Kr is the ²⁴¹Pu-²⁴¹Am pair. 

To summarize, in response to this review we propose to add a modest amount of additional context to the discussion of nuclear forensic applications in the abstract and introduction.

We thank Dr. Popov for taking the time to write an unsolicited comment and we appreciate his interest in the paper.

I found this manuscript interesting to read, however I currently work on UO2 and thus am unsure if this is representative. I suppose it may be interesting for geochronologists to learn more about the subject, but I would say that the manuscript would need to provide more background information to be useful for that. I had many questions after reading it (one relating to the loss argument). I think that I have found answers for most of these after re-reading a few times and spending a fair bit of time on the internet search. However, is this how it should be?

As the reviewer knows, it is never possible to put all possible needed background information in a single paper. We tried to put in enough that the general concept, but maybe not all of the details, are understandable to a person with knowledge of geochronology applications of radioactive decay systems. From the reviewer’s remarks, it sounds like we did not do a terrible job, because at least the paper was interesting. However, it would probably be useful to add a little bit more background information in certain areas that geochronologists were probably only briefly exposed to in an isotope geochemistry course, for example fission yields and neutron capture reactions. We can try to add some additional background without making the paper too complicated.

1) There are many references to Cassata et al. (2023) with only lean explanations of what the reader is supposed to find there. I don’t know if that is just my bad lack, but this article turned out to be in a journal for which there is no subscription at my place of work.

This is unfortunately beyond our control, although we can send Dr. Popov a copy of the paper. Basically, what is in the Cassata paper is a general discussion of the systematics of Xe and Kr isotopes in spent fuel. It’s interesting and useful background reading, but it’s not necessary for understanding the present paper. Mainly the reason the Cassata study is cited so much is that it is the original source of the noble gas data from the BR-3 fuel.

2) In addition to the brevity of all the explanations, which require extra effort on the side of the reader, the manuscript lacks equations to do the calculations therein described. I find this odd for a method description. This also makes it too demanding for a casual reader to verify if the author’s arguments have been understood correctly.

The equation for the apparent ⁸⁵Kr age is just the simple radioactive decay equation R_m = R_i * exp(-lt), where R_mis the measured ⁸⁵Kr(⁸³Kr+⁸⁴Kr) ratio, R_i is the initial ratio at the time of fission production, l is the decay constant (yr^-1), and we are solving for the age t (yr). This is very commonly used and our thinking was that most readers of Geochronology have seen this equation too many times already.

However, the part that is less obvious, which we probably should have put in the text, is how you estimate R_i from the fission yields. We can add both equations to the text.

3) It would be nice if readers were not left to guess what kind of electron microscopy images appear in Figs 3 and 4. It would also be nice to see some comments on the microtexture, including on whether you avoided to sample from the jog/fci layer. Finally, it would be nice to see sources for the bits of information that are certainly new for most of the audience of this journal such as that in lines 205-6.

Assuming that the reviewer is asking for details on the type of microscope used and the general imaging method, we can add this to the text. Although the microtextures are certainly interesting and possibly relevant to the issue of gas loss, they are not particularly relevant to the main point of the paper, which is the dating method. There is also quite a large literature already on microstructure of UO₂ fuels and its relation to their thermal and mechanical properties (for example, see the Clark, 2020, Buck, 2015, and Pellegrini, 2019 references for very detailed discussion of the microstructure of ATM-109), and we are not really contributing anything new to this field. Thus, we intentionally minimized discussion of this subject.

To summarize, proposed changes in response to this review are:

• Try to add additional background information on various nuclear processes that are not commonly used in geochronology
• Include equations for initial ratio and age
• Add collection details for images