Experimental validation of inventory simulations on molybdenum and its isotopes for fusion applications

For tungsten, the predicted radiological response is not too severe at long decay times (decades and beyond), although impurities introduced during the manufacture of industrial W, such as cobalt (Co) and potassium (K) at concentrations of around 0.001 weight % [11], could create a waste problem [12]. At short times (weeks, months, or even several years), W-based components of a fusion reactor (particularly the divertor) will require active cooling even after operation as significant residual decay heat will be generated by β-emitting radionuclides: ¹⁸⁵W (T_1/2≈ 75 days) and ¹⁸⁷W (∼ 24 hours) [11, 13].

Short-term activity is less of an issue for Mo; decay-heat and activity from Mo is predicted to be lower than in W after a typical fusion first wall exposure and around two-orders of magnitude lower after a year [14], which is confirmed by the calculations below (see figure 1). However, at longer timescales—decades and beyond—several problematic radionuclides are predicted to remain in naturally occurring Mo at levels sufficient to exceed regulatory limits for low-level waste (LLW) disposal. This makes it difficult to justify pure Mo for fusion applications where the goal is to avoid the generation of intermediate-level waste (ILW) requiring long-term deep geological disposal [12].

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For example, if Mo were used instead of W for divertor PFCs (armour), or in the tritium-breeder-blanket first wall armour, of a recent conceptual design [15] for a European demonstration power plant (DEMO) then, after typical operating scenarios for that device, 'natural' Mo is predicted to exceed the 12 MBq kg⁻¹ β+γ emissions limit [16] for disposal in the UK's low-level, near-surface waste repositories for more than 1000 years. Here natural refers to Mo composed of its stable isotopes in their naturally occurring concentrations (⁹²Mo: 14.65%, ⁹⁴Mo: 9.19%, ⁹⁵Mo: 15.87%, ⁹⁶Mo: 16.67%, ⁹⁷Mo: 9.58%, ⁹⁸Mo: 24.29%, ¹⁰⁰Mo: 9.74%). This prediction is based on the results in figure 1(a), which shows the time-evolution in activation of irradiated Mo after the expected operational lifetime of divertor and blanket components in DEMO.

For this calculation, spectra of neutron fluxes as a function of energy were computed using Monte Carlo neutron-transport simulations (with MCNP [17]) for the 2015 DEMO baseline [15] design with a helium cooled tritium breeding blanket made from a Pebble-Bed of beryllium and lithium-orthosilicate (abbreviated as HCPB; see [18] for details). Other tritium breeding concepts are also being considered within the EU-DEMO programme, including a water-cooled design with liquid lithium-lead (WCLL), but the neutron-spectra in the reactor-armour locations considered here are not significantly altered by the different blanket materials; WCLL versions of figure 1 are indistinguishable from those shown for HCPB.

Figure 2 shows the neutron flux spectra obtained from those calculations for the two reactor locations considered. Note that W was the armour material in these MCNP simulations; the spectra have the deep flux depressions associated with the giant neutron-capture resonances of W in the 1-100 eV energy range—a phenomenon known as self-shielding [19, 20].

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It is always advisable to perform neutron-transport simulations with the correct material compositions in the geometry. However, for the purposes of the present work, where the focus is on a comparison of the radiological response of W and Mo, MCNP simulations have not been repeated with Mo as the armour material. For the thin armour layers where these spectra were recorded (2 and 5 mm thick for the armour of the blanket first wall and divertor, respectively), the main influence on the spectral shape and total flux comes from the bulk materials behind them: structural steels, coolant, and functional materials. Previous work (the activity analysis associated with [20]) demonstrated that, while subtle changes in the neutron spectrum caused by material variation can have significant impact on transmutation (composition change), the effect on activity is less profound and certainly not significant compared to the logarithmic variations shown in figure 1.

The two neutron spectra (one for the blanket and one for the divertor) were used in calculations performed with the FISPACT-II [21] inventory code; an inventory code predicts the time evolution of material compositions (from which the radiological response can be derived) using numerical solutions to the set of differential equations governing the rate-of-change of each nuclide in the system due to neutron irradiation and decay [21]. FISPACT-II was used with TENDL-2019 [22, 23] nuclear data to predict the material response to either ∼5 years (for the divertor outboard target armour) or ∼15 years (outboard equatorial blanket first wall armour) of pulsed operation; these are typical scenarios planned for DEMO, where the divertor is expected to be replaced every 5 years and the second phase of DEMO will use a single blanket for its entire 15-year campaign [11, 24]. Subsequently, FISPACT-II time-evolution was continued to track the post-operational decay activity and γ-dose-rate. Note that corrections for the capture-resonances, via probability tables, were included in the simulations for both Mo and W—see [20, 21] for details.

Figure 1(a) includes equivalent results for natural W in the two reactor regions considered and the difference compared to Mo is dramatic; W comfortably meets the UK β+γ-activity limit for LLW (shown in the plot as a horizontal line) in both the divertor and blanket armour cases on a reasonable 30-100 year timescale, while Mo exceeds it by several orders of magnitude even after 1000 years. Note that UK-LLW also has an α limit, but this is not relevant here as neither Mo or W produce α-emitting radionuclides under neutron irradiation.

Similarly, the γ-dose-rate from Mo is predicted to be many orders of magnitude higher than that from W from 10-years after the operational life of blanket and divertor components in DEMO. Figure 1(b) charts the time-evolution in γ-dose-rate, in units of Sv/h (Sieverts per hour), one metre from an idealised 1 g 'point source' of either Mo or W—this approximation of dose calculated by FISPACT-II is more conservative (lower) than the alternative, default, 'contact' dose approximation and is more relevant for radiation workers working in a nuclear environment and wearing protective clothing (a full γ-transport simulation is required for a more reliable prediction of γ-dose, see for example [26]). The UK's Health and Safety Executive (HSE) recommends, based on the UK's regulations for ionising radiation [27], a limit of 7.5 µSv/h (shown in the plot as a horizontal dashed line) for areas where workers will be exposed to ionising radiation [28]. While W, meets this limit within a year of post-operation cooling, the results show that Mo might pose a problem—the dose-rate predictions for Mo in the divertor falls below the HSE limit within a year but the dose-rate from Mo in the armour of the blanket remains above it for hundreds of years. Even the divertor result remains close to this limit (and thus still potentially presenting a handling and maintenance problem, especially if manufacturing impurities are taken into account [12]), while the dose-rate from W is predicted to fall below 1 nSv/h within 10 years.

Figure 3 illustrates the reasons behind the long-term high activity (and γ-dose) in Mo; it shows the time-evolution after operation in individual activity contributions from the different radionuclides (or radioisotopes) produced in Mo during the FISPACT-II simulation of 5 years in a divertor armour tile. The absolute activities (figure 3(a)) show that five radionuclides are each produced in sufficient quantities for their respective absolute activities to exceed the UK-LLW—four with half-lives of more than 500 years and a fifth, $^{93 \mathrm{m}}$Nb, with a relatively short half-life, but whose concentration is in secular equilibrium with the long-lived ⁹³Mo that decays to it (see table 1), which is why their respective activities are identical. On the other hand, although Mo is much closer to the limit than W (figure 1(b)), it does not exceed the HSE γ-dose-rate limit beyond around 1 year after operation (figure 3(c)) in this simulation, and thus neither do the dose contributions from those individual radionuclides (or any other).

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Table 1. The primary generation pathways for the important radionuclides generated in natural Mo during exposure to the operating conditions expected for the outboard divertor armour of a typical DEMO concept. For each nuclide, the % contribution for each path corresponds to the results computed by FISPACT-II using TENDL-2019 nuclear data. Pathways here and in subsequent tables were identified using the tree-search algorithm employed in FISPACT-II, invoked via the UNCERT and LOOKAHEAD keywords—see [30] for more details.

Product	T$_{\mathbf{1/2}}$	Pathways	Path %
$^{99 \mathrm{m}}$Tc	6.0 hours	98Mo(n,γ)99Mo(β−)$^{99 \mathrm{m}}$Tc	55.4
		100Mo(n,2n)99Mo(β−)$^{99 \mathrm{m}}$Tc	44.5
99Mo	2.7 days	98Mo(n,γ)99Mo	55.4
		100Mo(n,2n)99Mo	44.5
$^{91 \mathrm{m}}$Nb	61 days	92Mo(n,np)$^{91 \mathrm{m}}$Nb	94.5
$^{93 \mathrm{m}}$Nb	16 years	94Mo(n,np)$^{93 \mathrm{m}}$Nb	68.2
		94Mo(n,d)$^{93 \mathrm{m}}$Nb	21.3
		94Mo(n,2n)93Mo(β+)$^{93 \mathrm{m}}$Nb	6.3
91Nb	680 years	92Mo(n,np)91Nb	84.9a
		92Mo(n,2n)91Mo(β+)91Nb	14.2
93Mo	3500 years	92Mo(n,γ)93Mo	22.0
		94Mo(n,2n)93Mo	77.5
94Nb	20 000 years	94Mo(n,p)94Nb	75.3c
		95Mo(n,np)94Nb	24.2c
99Tc	210 000 years	98Mo(n,γ)99Mo(β−)99Tc	55.4b
		100Mo(n,2n)99Mo(β−)99Tc	44.5b

^aIncludes contribution from the production (via the same path as the ground-state) and subsequent decay of $^{91 \mathrm{m}}$Nb. ^bIncludes contribution from the production and decay of $^{99 \mathrm{m}}$Tc. ^cIncludes contribution from the production and decay of $^{94 \mathrm{m}}$Nb, T_1/2 = 6.3 minutes.

The highest activation and dose contributions at these long decay times comes from ⁹¹Nb, which, in this simulation for the divertor armour, contributes between 60 and 80% of the activity at all decay times greater than 2 years and less than 1000 years (the limit of the simulations in this case)—as shown by the % contribution evolution curves [29] of the same simulation in figure 3(b) and 3(d) for activity and dose, respectively.

The reaction pathways to produce these five nuclides from natural Mo and the relative (%) production contribution of those pathways were automatically calculated by FISPACT-II during the irradiation simulation (a unique feature of the code [21]) and these are shown in table 1. Pathways for three shorter-lived nuclides—$^{99 \mathrm{m}}$Tc, ⁹⁹Mo and $^{91 \mathrm{m}}$Nb—that contribute at least 40% to the total activity during decay times of less than 1 year (see figure 3(b)) are also included for reference (and are relevant for the experimental validation discussed later). Comparing these reaction chains to the isotopic abundance distribution of Mo (section 1.1) we can see that not all Mo stable isotopes are involved in the production of these dominant radionuclides. In particular, neither ⁹⁶Mo or ⁹⁷Mo appear in the table at all, and, moreover, the radionuclides with the three highest contributions to long-term activity in figure 3—⁹³Mo, $^{93 \mathrm{m}}$Nb and ⁹¹Nb—are produced almost entirely by reaction pathways from the two lightest stable isotopes of Mo; ⁹²Mo and ⁹⁴Mo.

The observation—that only some of the stable Mo isotopes cause high activation in Mo—is confirmed by the inventory simulation results of decay-activity and γ-dose in figure 4, where each Mo isotope has been separately exposed to the same DEMO divertor scenario as natural Mo (and W). As expected from the pathway analysis (table 1), ⁹²Mo and ⁹⁴Mo generate higher activity levels (figure 4(a)) at decay times greater than ∼1 year than natural Mo because of the relative increase in production of the main problematic radionuclides discussed above. Meanwhile, the activity from mono-isotopic Mo (probably not feasible, see below) composed of either ⁹⁶Mo or ⁹⁷Mo would actually satisfy UK-LLW limits on the desirable sub-100-year timescale in this DEMO scenario. Simulations for the remaining three isotopes (A = 95,98,100) predict activities above the LLW limit beyond 1000 years, but their activities are still 1–2 orders of magnitude below ⁹²Mo, ⁹⁴Mo and hence natural Mo beyond around 10 years of cooling.

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The authors have previously [2] demonstrated a similar favourable result for ⁹⁶Mo or ⁹⁷Mo from the perspective of contact γ-dose-rate, which is confirmed by the present predictions for γ-dose at 1 m shown in figure 4(b) for the individual stable isotopes of Mo. As in [2], also note that ⁹⁸Mo and ¹⁰⁰Mo have relatively low γ-dose-rate beyond 10-years of cooling because the main long-lived radionuclide produced in them, ⁹⁹Tc (see table 1), is a not a γ-emitter.

The results above suggest a solution that could make Mo more viable for fusion applications—instead of natural Mo, use Mo with an artificially adjusted (tailored) distribution of stable isotopes, preferably dominated by ⁹⁶Mo and ⁹⁷Mo (the exact level of enrichment towards these two isotopes would be defined based on a cost-to-benefit ratio) to reduce or prevent ILW. Previous work by Conn and Johnson [31] also identified ⁹⁷Mo as the most favourable isotope and their factor 100 reduction in radioactivity at 50 years for 99% ⁹⁷Mo agrees with the present findings. If Mo could instead be recycled, which is an attractive alternative to disposal [32] that is higher on the preferred waste management hierarchy [33], figure 4 demonstrates that isotopically-adjusted Mo would also have lower activation (and dose) on remote handling timescales ($\lt\,\sim$10 years), potentially reducing reprocessing costs.

In the earlier work [31], it was recognised that the cost of isotopic adjustment must be balanced against the cost of radioactive waste disposal. Exact costs are difficult to quantify but basic storage of ILW is at least 10 times more costly per unit volume than LLW in the UK [34, 35], and this does not include the eventual cost of the final geological disposal facility (GDF) for ILW compared to a near surface LLW repository. The UK-GDF is predicted to cost ∼£14 billion [34] and a fusion reactor would require a significant proportion of such a facility because of its typically larger expected size compared to equivalent fission plants; thus any reduction in ILW mass could be a significant cost saving.

A cost analysis must also consider the relative benefit of using Mo instead of W as an armour material; if a commercial reactor has much higher availability (or is viable at all) due to the choice of Mo, then greater profit margins could accommodate the higher cost of enriched Mo (compared to natural Mo). The amount of material required for the blanket and divertor armour is relatively small compared to the overall fusion power plant; in the DEMO model used in this work approximately 65 tonnes of Mo—replacing 120 tonnes of W—would be required, compared to, for example, ∼ 4500 tonnes of in-vessel EUROFER [36] steel and more than 20 000 tonnes of 316 grade stainless steel in the reactor vacuum vessel. Even smaller amounts would be needed if Mo were only used instead of W for one application; for example, as a plasma-facing material in the divertor where the irradiation conditions, heat loads, and plasma interactions are the most severe (and thus where the benefit from any improved material performance would be greatest). Around 9 tonnes of Mo would be needed for the ∼5 mm [11] thick armour layer of the divertor (compared to ∼ 17 tonnes of W) in the DEMO model. In these contexts, it is not unfeasible to imagine a switch to Mo, even if the form of Mo required (isotopically tailored) is relatively expensive.

It is also worth noting that the political and public perception of nuclear waste has changed dramatically since the early days of fission. The political 'cost' of having Mo that can be disposed of as LLW in a near-surface waste repository instead of requiring deep-geological disposal for ILW (for which there is currently no solution in many countries, including the UK), could be the difference between gaining a nuclear license or not.

The current industrial standard for isotopic enrichment is via cascades in gas centrifuges and this has been explored for Mo [37], but is likely to always be prohibitively expensive (based on the estimates in [37] it could cost several $100 million to produce enough enriched Mo for the armour of a fusion reactor via gas centrifuges). A more detailed cost analysis is beyond the scope of this paper, but it is clear that new (or refined) industrial-scale separation techniques are needed to reduce the costs. A technique based on a free electron laser of CO₂ [38] has been explored for Mo, while electromagnetic separation [39, 40] is potentially a viable approach to achieve high enrichment of the middle mass range of Mo isotopes (i.e. the ones that would produce low activation Mo) and is the only viable method for isotope separation of many elements, including rare-earth metals [39].

Mo with a modified isotope distribution could also be useful to reduce the long-term activation and waste-disposal issues of convention ferritic/martensitic (F/M) steels, which are the fore-runners of the reduced-activation F/M (RAF/M) steels such as EUROFER [36, 41, 42] that is currently the preferred option for in-vessel fusion-reactor components for EU-DEMO [11, 43, 44]. T91 is an example of a F/M steel that is already widely used as a structural material in light-water reactors and in fossil-fuel plants, particularly in steam pressure vessels and boilers [45, 46], and thus is already manufactured at an industrial scale (unlike some RAF/M steels). However, in common with other F/M steels, T91 contains around 1 wt.% Mo. Based on previous work [47], it would cost around £1–2 million to use isotopically-tailored Mo at this concentration per 100 tonnes of steel. Even scaled to the several thousand tonnes of in-vessel steel required for current DEMO designs, such costs are not unfeasible for devices costing many billions of Euros.

Mo also has potential applications as a structural material in fuel elements to improve safety in future generations of fission power plants [37, 48]. In this case, the barrier to realisation is the very high (thermal) capture cross section for neutrons in natural Mo, which is obviously undesirable when trying to create a sustained nuclear reaction. Once again, isotopic tailoring to reduce the problematic isotopes (in this case mainly ⁹⁵Mo, which has a capture cross section of 13.6 barns at a neutron energy of 0.025 eV [48]) offers a possible solution.

High neutron capture cross sections could also be a problem if Mo is used in significant concentrations in the tritium-breeding zone of fusion reactors, where the loss of neutrons in a material with a high absorption cross section could impact on the TBR (tritium breeding ratio) [49]. This might impact more severely breeding blanket concepts involving Li-Pb eutectic where satisfactory tritium breeding rates are reliant on high ⁶Li enrichment (around 90% [11]). The ⁶Li(n,α)³H cross section is particularly high at low neutron energies and competing capture with Mo could therefore be detrimental.

Notice that in the divertor simulations (figure 4(a)) activity levels of pure ⁹⁶Mo or ⁹⁷Mo are relatively (compared to the much higher activity from other pure isotopes) close to the UK-LLW limit. Indeed, in the other case from figure 1(a), for the blanket first wall armour, even for these two isotopes the generated long-term activity (typically from longer reaction chains involving neutron multiplication, (n,2n) and/or neutron capture reactions to the same radionuclides shown in table 1) would exceed the LLW limit. Thus isotopic tailoring is unlikely to be a complete solution for the waste disposal of fusion components containing Mo (unless regulatory limits can be revised/relaxed for fusion waste [12]). However, isotopically adjusted Mo could be used in a 'mixed solution' with W, where W is used primarily in higher-flux first wall regions and therefore replaced more regularly, while Mo could be used as an armour in less exposed regions (e.g. in the divertor or away from the equator regions of the blanket), thus reducing the frequency with which those components need replacement (assuming Mo proved to be more resilient than W) and thereby reducing maintenance cycles and costs, and improving overall fusion plant availability.

Predictions such as those discussed in this simulation study rely on accurate nuclear code simulations. While the numerical techniques employed by inventory codes like FISPACT-II or neutron transport simulators like MCNP are well-established and validated (see e.g. [50, 51]), it is still the case that the quality and completeness of the underlying nuclear data strongly determines the reliability of predictions and the level of uncertainty; the latter could influence the level of conservativeness in engineering limits, which could impact on cost, and so there is a strong incentive to reduce uncertainty. Of particular importance for simulating the radiological response of Mo (or any other material) under fusion conditions is the accuracy of the integrated reaction rates that govern the production of dominant radionuclides. The remainder of this paper describes efforts at UKAEA to test and validate the nuclear reaction data used with FISPACT-II for Mo by benchmarking simulation results against both historical experimental decay-heat measurements and newly acquired γ-spectroscopy data.

Fe and Al foils were included in the experiments to enable accurate measurement of the neutron flux received at the sample location during irradiation [59]. In the present work, the major lines from ²⁷Mg at 844, 1014 and 171 keV, ²⁴Na lines at 1369 and 2754 keV due to Al activation, along with ⁵⁶Mn (produced in the Fe foil) lines at 847, 1811 and 2113 keV, were used to produce an average estimate of the neutron flux for each experiment. Note that for experiment 81, a transfer issue meant that the acquisition data (counts) from the aluminium foil were not properly recorded and so the flux estimate is based solely on the ⁵⁶Mn peaks in this case. Table 3 gives the details of the eight experiments considered here for Mo, including the results of the Fe/Al-foil flux estimates. % error estimates for the flux evaluations are based on the standard error (i.e. the deviation from the mean) of the average flux estimates summed in quadrature with each individual flux estimate multiplied by the fractional Poisson statistical uncertainty in the background-corrected γ-counts for the associated peak:

$$\begin{equation} \epsilon=\sqrt{C_p+C_B}/C^*_p, \end{equation} \tag{ 1 }$$

where C_p is the raw total count in the detector channels containing the peak of interest, C_B is the total background count subtraction for the peak channels (i.e. via figure 7(b)), and $C^*_p$ is the total background-corrected count for the peak ($\equiv C_p-C_B$). For further discussion of the application of Poisson statistics to radioactive decay and γ-spectroscopy, see [67–69].

The flux estimation was done using the Levenberg–Marquardt algorithm (LMA—a damped least-squares method) to fit a decay function to the counts per (real) time (in seconds), and hence to calculate decay-corrected A₀ values for the end of irradiation activity in Bq. Note that in all cases the fitting was only performed out to a maximum of three times the half-life of the nuclide being analysed, thereby avoiding any problems in the fit that could be caused by including very small counts at long decay times (for that particular nuclide). It is also possible for the peaks of two different radionuclides to overlap sufficiently so that their individual counts cannot be separated from one-another. In the present work, this situation only occurred for the 847 and 844 keV peaks of ⁵⁶Mn and ²⁷Mg, respectively, and in this case, as described in [59], a double exponential fit is performed to obtain the two separate A₀ activities.

In calculating the flux using these reference foils, it is assumed that the reaction pathways (see table 4) to the measured nuclides are well-known and that the nuclear cross section data (from TENDL-2019 [23]) is well-validated. The cross section vector for each reaction is 'folded' (vector dot product) with a normalised ASP neutron irradiation spectra (calculated using a Monte Carlo simulation as part of the work described in [25] and shown unnormalised in figure 2) to calculate the average cross section σ in barns for the ASP spectrum. Using the standard decay equations describing the production and decay of radionuclides [70], A₀, σ and the decay constant λ are used to estimate the experimental flux via:

$$\begin{equation} \phi=\frac{A_0}{N\sigma(1-\exp^{-t_{\textrm{irr}}\lambda})}, \end{equation} \tag{ 2 }$$

where $t_{\textrm{irr}}$ is the irradiation time of the experiment (given in table 3) and N is the total number of atoms of the target (stable) nuclide—in this case of ⁵⁶Fe or ²⁷Al. Note that this approach is only valid if the neutron flux is approximately flat (constant) during the irradiation. The flux profile was monitored during each experiment and adjustments to the deuteron beam were made in real-time to maintain a near-constant flux profile; which was confirmed posteriori by the output of a pair of fission counters that monitored the neutron count near to the ASP target (but were not close enough to provide a reliable measurement of the flux on the samples).

Table 4. Information about the radionuclides measured in the ASP experiments. The FISPACT-II-calculated production pathways and their % contributions were obtained from the simulations with the TENDL-2019 library. Only the γ-peak energies observed in the experiments are listed for each nuclide.

Product	T$_{\mathbf{1/2}}$	Pathways	Path %	Experimentally
	experiment		TENDL-2019	identifiable
			(Exp. 82)	γ-peaks (keV)
56Mn	2.58 hours	56Fe(n,p)56Mn	100.0	846.8, 1810.7, 2113.1
27Mg	9.46 min.	27Al(n,p)27Mg	100.0	170.9, 843.7, 1014.4
24Na	14.96 hours	27Al(n,α)24Na	100.0	1368.6, 2754.0
		97Mo(n,p)$^{97 \mathrm{m}}$Nb	83.7
$^{97 \mathrm{m}}$Nb	53.0 s	98Mo(n,np)$^{97 \mathrm{m}}$Nb	2.1	743.4
		98Mo(n,d)$^{97 \mathrm{m}}$Nb	14.1
$^{91 \mathrm{m}}$Mo	1.08 min.	92Mo(n,2n)$^{91 \mathrm{m}}$Mo	100.0		652.9, 1208.1, 1508.0
$^{89 \mathrm{m}}$Zr	4.13 min.	92Mo(n,α)$^{89 \mathrm{m}}$Zr	100.0	587.8
$^{98 \mathrm{m}}$Nb	51.30 min.	98Mo(n,p)$^{98 \mathrm{m}}$Nb	100.0	722.6, 787.4
		97Mo(n,p)97Nb	81.5a
97Nb	1.23 hours	98Mo(n,np)97Nb	12.1a	657.9
		98Mo(n,d)97Nb	6.3a

^aIncludes contribution from the production and isomeric transition (IT) decay of $^{97 \mathrm{m}}$Nb, but note that different reactions have different probability ratios between ground- and meta-state production (i.e. the distribution of production % values for $^{97 \mathrm{m}}$Nb are different to those of ⁹⁷Nb).

The estimated fluxes are used as input to FISPACT-II inventory simulations to obtain a calculated C activity—see section 3.3.

For the experimental value E, the first stage is to extract the detector counts for each detectable γ-peak of the γ-emitting radionuclides produced during the irradiation of Mo at ASP. Peaks associated with five different radionuclides were identified in the present work; these are listed in table 4 (along with flux-estimator nuclides of Fe and Al), together with their half-lives, and main production pathways according to FISPACT-II simulations with TENDL-2019 for the irradiation time and flux-estimate associated with experiment 82 (see table 3). The identifiable peaks for each radionuclide are listed in table 4 and are labelled in the integral spectrum for experiment 82 (figure 7(a)).

Figure 7(b) demonstrates the process by which the background counts (mainly from Compton scattering since the detector was well shielded using lead) are subtracted, using linear interpolation between the average counts recorded in a range of channels on either side of a peak [59], to give the counts associated with the decaying nuclide—in this case for $^{91 \mathrm{m}}$Mo associated with its γ line at 653 keV. Note that the background subtraction exemplified in figure 7(b) only applies to peaks (or peaks in overlap scenarios) that are away from the Compton edge [70], which was true for all peaks considered in the present work. The fit to the resulting evolution in counts-per-live-second as a function of (real) time for a peak (e.g. as in figure 7(c) for the $^{91 \mathrm{m}}$Mo peak) then gives the experimentally predicted count rate at the end of irradiation C₀, which in turn is used to calculate A₀ via

$$\begin{equation} A_0=\frac{C_0}{D^{\textrm{eff}}(E^{\gamma}_p)I_p}, \end{equation} \tag{ 3 }$$

where $D^{\textrm{eff}}(E^{\gamma})$ is the detector efficiency at γ-energy $E^{\gamma}$, which for the HPGe detector used in the present work is described by a function fit to neutron transport simulations performed on a model of the detector (e.g. as described in [25]). $E^{\gamma}_p$ and I_p are the energy and intensity of peak p, respectively, both taken from decay_2012 decay-data files used by FISPACT-II [21] for TENDL-2019.

The calculated (C) estimate of A₀ is taken directly from a FISPACT-II calculation with the TENDL-2019 data library. The appropriate mass of pure Mo was irradiated for the experimental irradiation time at the estimated flux (section 3.1) and using the calculated neutron spectrum for the sample location shown in figure 2 (the mass, flux-estimate, and irradiation times for each experiment are given in table 3). FISPACT-II automatically outputs the individual radionuclide contributions to the total sample activity, and the required end-of-irradiation values can be easily extracted for the specific nuclides.

Figure 8 shows C/E ratios for the calculated (C) and experimental (E) A₀ activities for the eight Mo experiments. ⁹⁷Nb and $^{97 \mathrm{m}}$Nb results are plotted in the same panel, while the other three panels in the figure show results for single radionuclides (as labelled). Tables B1 and B2 in the appendix give the numerical C, E, C/E values for each data peak. The error estimates on each value, shown as error bars in the figure (and also provided as percentages in the tables), include, for C values, the error of the flux estimate (see table 3) and the error calculated by FISPACT-II using the uncertainty data in TENDL for the relevant cross sections (e.g. as shown in the grey error bands of the cross section figures in figure A1 of the appendix) summed in quadrature, and for E, the activity error based on the Poisson count uncertainty (equation (1)). These uncertainties should be refined to account for other (potentially systematic) errors and correlations, such as uncertainty in the experimental timing information, but not all of this information is available from the experiments, so the present estimates (potentially pessimistic) are the best available and give and indication of the error magnitudes. The lessons learnt in this work will help to inform better experimental methodology with respect to uncertainty quantification in future campaigns.

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Note in figure 8 that not every experiment has produced a C/E value for every possible peak considered. Peaks with total background-corrected counts of less than 400 during the entire measurement time were deemed to be of low statistical quality and were omitted. Also shown for each panel, as a visual guide to the data trend, is the weighted average C/E value, where the weights correspond to the inverse of the variance (square of the error) for each point. The standard deviation from these weighted averages is shown by the grey band in each plot.

3.4.1.  $^{89 \mathrm{m}}$Zr .

3.4.2.  $^{91 \mathrm{m}}$Mo.

3.4.3.  $^{98 \mathrm{m}}$Nb.

3.4.4.  ⁹⁷Nb and $^{97 \mathrm{m}}$Nb.

Considering all of the experimental uncertainties the fact that many of the C/E values are close to one (and all are less than 2), and that in many cases the uncertainties encompass one, is encouraging and demonstrates that the FISPACT-II calculations with TENDL-2019 produce good predictions for irradiation-induced activity in Mo in these scenarios. However, it is worth observing that, in contrast to the FNS benchmark (section 2), none of the reaction pathways interrogated by these experiments are relevant for the dominant channels to isotopes identified in the earlier fusion power plant scenario (compare table 4 to table 1). Experiments involving measurement of such long-lived reaction products will likely require longer irradiations and post-irradiation measurements.

For long-lived nuclides, including the important ⁹¹Nb, ⁹³Mo, and $^{93 \mathrm{m}}$Nb, the dominant production cross sections can have high uncertainty (e.g. the (n,np) channel responsible for the majority of $^{93 \mathrm{m}}$Nb production has a nuclear data uncertainty greater than 50% in TENDL-2019 [23] under the ASP neutron spectrum). This demonstrates the need for future experiments with careful design; i.e. to ensure that the important reaction pathways are explored and that the resulting benchmark is as relevant as possible for Mo in a fusion power plant.