At the WSU TRIGA reactor, a 2.2 mg piece of 93.15% enriched uranium foil was irradiated for 2 h at 500 kW to produce 5.37 × 10¹³ fissions as determined through gamma analysis of peak fission products. Following irradiation, the sample was transported to PNNL for dissolution with 10 mL of 3M HNO₃ and subsequently screened to determine the total sample activity. From this stock solution, an aliquot equivalent to 1 × 10¹² fissions was prepared and dried down by evaporation onto a 2.2225 cm diameter filter paper and laminated in Kapton tape. The filter paper was shipped to LANL and measured by SOFIA and HPGe detectors beginning 4 days after the irradiation. Figure 5 presents the measured spectrum derived from microcalorimetry (black) and a low-energy germanium detector (brown).

Key interferences of short-lived isotopes were resolved using the microcalorimeter that would otherwise be infeasible using germanium. Figure 6 illustrates the peak separation of Ba-140 and Ce-144, which have half-lives of 12.751(4) days and 284.91(5) days, and gamma rays at 132.687(1) keV and 133.515(2) keV, respectively. Figure 7 illustrates clear separation of the Sm-153 gamma-line, a crucial, refractory wing fission product with elevated sensitivity to the energy of the incident, fission inducing neutron. Figures 6, 7 are expanded views of the spectrum in Figure 5. Quantification of fission product activity by gamma-ray microcal was not calculated from this measurement. Measurement of the sample alongside a well-characterized isotopic standard, or measurement in an efficiency calibrated geometry, would be necessary to extract these values. Efficiency calculations for quantification are an ongoing research focus for our collaboration, and further discussion is provided in Section 3.4.

At HFIR, SOFIA was placed in the Neutron Activation Analysis laboratory adjacent to the reactor, and samples were immediately measured after irradiation via transport by pneumatic tube. The spectra obtained represent the microcalorimeter measurements taken with the shortest amount of time after irradiation to date. Targets of natural uranium (NU), plutonium standards, and mixtures of the two were irradiated during the 511 cycle (February 2025) and immediately measured with the SOFIA microcalorimeter. The NU and Pu targets were irradiated for 90 s when the reactor flux was approximately 4.3 × 10¹³ n/cm²·s in the pneumatic transfer tube that passes just outside of the permanent beryllium reflector. Irradiation times for the uranium and plutonium mixtures were reduced to 60 s to compensate for a 22% increase in the neutron flux that routinely occurs later in HFIR cycles. All samples were measured starting approximately 30–45 s post-irradiation. SOFIA observed between 4,000 and 8,000 counts per second on the full TES array at the beginning of the measurement, with the counts dying to less than 100 counts per second after about 45 min.

The irradiations at HFIR enabled observation of temporally dynamic low energy gamma signatures from short-lived fission products. Figure 8 shows the half-life estimates for each energy bin between 0 and 100 keV using an NU target. Each bin was evaluated, rather than each peak, because it is difficult to define regions of interest (ROIs) for individual unresolved peaks with short half-lives. The spectrum shown vertically in Figure 8 was created from the first 5 minutes of the measurement. Dark, opaque dots represent high-confidence half-life estimates, ranging from 275 s to 26 min. Further analysis is underway for radionuclide identification, nuclear data studies, and U/Pu quantification.

Another interesting application for short-lived isotope characterization is within the field of medical isotopes. In particular, Ac-225, with half-life of 9.92 days, has become a promising targeted-alpha therapy treatment for cancer (Thiele and Wilson, 2018). Ac-225 is scarce, historically produced through extraction from a Th-229 “cow” in only a handful of laboratories. The Th-229 alpha decays to Ra-225 with a 7340-year half life, which then beta decays to Ac-225 (14.9-day half life). Accelerator-based methods are in use to vastly increase production (John, 2019). However, Ac-227 is an impurity which inevitably arises in accelerator production, with a half-life of 21.8 years. The presence of Ac-227 is problematic because it can accumulate in the liver, causing long-term damage to healthy cells. Characterizing the Ac-227 in Ac-225 for targeted alpha therapy is therefore important. An opportunity for gamma-ray microcal is to discern the extremely weak Ac-227 signatures. Figure 9 compares microcal gamma-ray spectra from an actinium sample obtained through accelerator-based methods and an actinium sample separated from a Th-229 cow. A gamma-ray peak from Th-227, a daughter of Ac-227, is highlighted in a spectrum from a sample obtained through accelerator production of actinium for targeted alpha therapy, which is distinctly not seen in the traditional Th-229 cow technique. None of these features are discernible in the HPGe spectrum. Using microcalorimeter decay energy spectroscopy, the signatures of Ac-227 were quantified (Tollefson et al., 2021), and the current results suggest gamma-ray microcal measurements are likewise a useful technique for medical actinium characterization.

One of the main advantages of having such high energy resolution with microcal measurements is that small peaks can be seen due to the high signal to noise ratio. We can approximate the relative statistical uncertainty of the peak as follows:

σ / S = σ B   2 + σ S   2 S , where the uncertainties in the background ( σ B ) and signal ( σ S ) are added in quadrature and the signal, S, is the counts above background. With reasonably high backgrounds, we can approximate σ B = N b i n s · μ B , where the number of bins ( N b i n s ) is the number of spectral bins required to span 5 FWHM centered around the peak and μ B is the average number of counts in a background bin. The uncertainty in the signal (counts above background) is approximated as S . The principal advantage for quantifying weak peaks here is that microcal improves signal to noise by reducing the background uncertainty since the peak is more localized in energy (i.e., N b i n s is lower). To achieve 1% statistical uncertainty on the Th-227 50.13 keV peak area, this would require 12,000 counts above background (in this case, determined from the microcal spectrum of the Th-229 cow between 49.9 keV and 50.4 keV, ∼3.8 FWHM). To achieve 10% statistical uncertainty, this would require 600 counts in this peak. Background levels change as a function of total source activity, so these and all following calculations are only approximations. The microcal spectra shown in Figure 9 were taken for 4,000 s and represents a measurement with approximately 10% statistical precision. The HPGe spectrum is of the accelerator product, and was obtained beginning at the same time as the microcal spectrum of the accelerator product, running for a live time of 665 s. The HPGe spectrum shown was obtained by a coaxial HPGe detector, unlike most of the other HPGe spectra shown in this paper. After the actinium samples were synthesized, there was only a short window of time to obtain spectra, and a higher energy resolution HPGe detector was not available. Future measurements involving a detailed comparison between HPGe and microcal would necessitate a planar HPGe detector. Due to the narrow FWHM of the Th-227 peak (131 eV), however, it is not expected that even a planar detector would resolve this peak. Reproducing this measurement, using well-characterized isotopic standards along with the actinium samples for efficiency calibration, will be necessary for using these peak results for quantifying the amount of Ac-227 present.

Yet another application of gamma-ray microcal is for highly precise enrichment measurements. As high-assay low-enriched uranium (HALEU) fuel becomes more central in the development of advanced nuclear reactors, precision in enrichment measurements becomes more crucial (IAEA, 2020). HALEU may have enrichments up to 20%, while 20% enrichment and above is considered highly enriched uranium (HEU). For HALEU enriched over 19%, therefore, uncertainty must be low enough to determine with confidence that the material does not in fact fall into the highly enriched category. Gamma-ray techniques are frequently used already for nondestructive enrichment calculations. Precision may be enhanced by gamma-ray microcal, because it resolves more peaks which can be used in the enrichment calculation. The region from 89 keV to 94 keV is particularly rich with closely spaced peaks (Figure 10), which are well-resolved by microcal. These spectra are from uranium standards NBS031 (0.31% U-235) and NBL0005-20 (20% U-235). For NBS031, the microcal measurement was 130,000 s, and the HPGe measurement 3,265 s live time. For NBL0005-20, the microcal measurement was 120,000 s and the HPGe was 1,075 s live time. The high energy resolution also distinguishes the shape of x-ray peaks from that of gamma-ray peaks: x-rays have a Lorentzian line shape, while gamma-rays have a Gaussian profile. For gamma-ray microcal enrichment calculations, a fixed-response analysis method (Sampson et al., 1989; Vo, 2021) is under development (Becker et al., 2023). The technique computes the relative efficiency curve to extract a calculation of enrichment. For this, multiple peaks are needed for fitting across an extended energy range. The greater number of well-resolved uranium and thorium peaks will provide more points for the relative efficiency curve calculation. Further, reduced statistical uncertainty in the narrower peak areas of microcal spectra compared to HPGe are expected to contribute to reduced uncertainty in the isotopic percentage calculation. This is discussed in greater detail below for the case of Pu isotopics.

The HPGe spectra shown here and throughout the paper are, in general, not necessarily taken at the same time or with the same measurement geometry as the microcal spectra, unless otherwise specified. All spectra are only intended to illustrate examples in which a microcal spectrum may prove particularly useful over an HPGe spectrum due to the higher number of peaks resolved.

For samples older than about 6 months old, uranium isotopic composition calculation by gamma-ray spectrometry relies on daughter products of U-238, particularly Pa-234 m. For samples where the uranium is freshly separated from daughter products, the sample is not yet in secular equilibrium, and gamma rays emitted directly by U-238 are needed. There are only two direct gamma rays from U-238 at 49.55 keV and 113.5 keV. These peaks are difficult to resolve with lower-resolution detectors due to their low branching fractions (0.064 photons per 100 decays and 0.0102 decays per 100 decays, respectively) and interference from nearby peaks. However, they are visible using gamma-ray microcal, as seen in Figure 11, which shows the 113-keV region of the same microcal and HPGe spectra of NBS031 as in Figure 10. Microcal is expected to enable more precise enrichment measurements for freshly separated uranium. In this spectrum, the number of gamma-rays in the 113.5 keV peak at the 1% and 10% level with approximately 20,000 and 1,400 counts, respectively, over the light blue region in Figure 11. In this 130,000-s spectrum measuring depleted uranium, this peak area was quantified with approximately 7% statistical uncertainty.

The high resolution of gamma-ray microcal enables highly resolved plutonium spectra. This is valuable to calculations of plutonium isotopic ratios with increased precision. Figure 12 displays highly resolved plutonium peaks for several different burnups in the plutonium standard CBNM series compared to a HPGe spectrum. These peaks are used in the fixed response analysis method calculations for calculation of the percentage of each Pu isotope within the sample (Sampson et al., 1989; Vo 2021; Becker et al., 2023). High resolution of peaks enables lower statistical uncertainty in peak area calculations. Peaks may be well separated enough to allow a region of interest (ROI) calculation to count the number of photons measured within a peak, which results in a lower uncertainty than peak fitting. For peaks which still require fitting to a Gaussian or Lorentzian profile due to neighboring peak interferences, statistical uncertainty still tends to be reduced due to the narrower peak shape of a microcal peak compared to HPGe.

Improvement in statistical uncertainty in calculation of the peak area ratios for isotopes of Pu showed as much as a factor of 5.3 improvement over the statistical uncertainty obtained from peak areas in HPGe (Hoover et al., 2014). The lower statistical uncertainty was most notable for closely spaced peaks such as those from Pu-238 and Pu-239, and less notable for peaks which are already prominent and well-isolated in HPGe spectra such as Pu-241 and Pu-239.

Again, like the HPGe spectra throughout this paper, the HPGe spectrum in Figure 12 is meant to be a representative example to demonstrate the greater richness of peaks observed in a microcal spectrum. Quantitative analysis of HPGe peak areas is not performed in this paper. The quantitative comparisons between HPGe and microcal discussed here are derived from the cited works (Hoover et al., 2014; Yoho et al., 2020a) and not the spectra shown.

Calculation of the isotopic percentages requires not only the peak areas, but also nuclear data, namely, half-lives and gamma-ray emission probabilities. For many gamma-ray peaks in U and Pu, it has been found that the limiting factor in uncertainty is the gamma-ray emission probability (Yoho et al., 2020a). There are therefore opportunities for gamma-ray microcal to improve the uncertainty nuclear data by measuring well-characterized isotopic standards and using the microcal peaks to calculate more precise values for the gamma-ray emission probabilities. Initial implementations of this analysis for Pu isotopic standards improved uncertainties for several gamma-ray emission probabilities by up to a factor of 3.5 times lower than the National Nuclear Data Center (NNDC) uncertainty values (Yoho et al., 2020a). The uncertainty budgets for the top seven most improved branching ratios from (Yoho et al., 2020a) are given in Figure 13. This figure shows the areas of uncertainty with most room for improvement in microcal measurements. For each of the gamma rays investigated, the largest contributions to uncertainty were the fixed branching ratios of other gamma rays used in the calculation and Poisson statistics. This highlights that even these seven branching ratios can be measured more precisely with longer measurements and higher count rates, which should become more feasible as work progresses to make transition edge sensors faster and arrays of pixels larger. There is also ongoing work to improve atomic data, notably x-ray lineshapes and energies (Wessels et al., 2023). The field of neutron activation analysis is also identified as an area from which reduced uncertainty in gamma-ray energies would be highly beneficial. Microcal offers significant potential for improving nuclear and atomic data for other applications.

Another signature well-suited for microcalorimeter gamma-ray measurements is that of Np-237 (Croce et al., 2021). The Np-237 peak has the energy of 86.48 keV and can be well-resolved from the neighboring peak originating from Pa-233, its daughter. This, along with the ability to observe well-resolved U-238 peaks, presents a potential for gamma-ray radiochronometry. The parent-to-daughter ratios of U-238/Pa-234 m and Np-237/Pa-233 are useful radiochronometry ratios (Mayer et al., 2013). This avenue has not yet been explored with gamma-ray microcal, but future work exploring the precision and uncertainty limits of the technique is anticipated.

Finally, opportunities for observing other rarely-observed peaks abound in gamma-ray microcal spectra of Pu. These include observations of weak Pu-242 gamma-ray peaks (Teti et al., 2023; Mercer et al., 2022) and a previously unseen peak triplet in Am-241 (Koehler et al., 2021).

A significant signature enabled by microcal is the ability to estimate the uranium to plutonium ratio in spent fuel from x-ray signatures. Uranium and plutonium fluorescence x-ray peak areas are correlated to the amount of uranium and plutonium in the sample. Taking the ratio of the areas of the x-ray peaks is a way to extract the U/Pu ratio within the sample (Rasmussen and Cohan., 1962; Rudy et al., 2006). The U/Pu ratio is an important indicator for burnup of the fuel (Mayer et al., 2013). The longer the fuel has been irradiated, the higher the burnup, and the higher the ratio of plutonium to uranium will be, as the uranium captures more and more neutrons and transmutes to plutonium.

In the Advanced Gas Reactor (AGR) experiments (Pham et al., 2021), tristructural isotropic (TRISO) fuel, a type of advanced reactor fuel (Demkowicz et al., 2019), was irradiated at the INL Advanced Test Reactor. Gamma-ray microcal spectra were obtained for dissolved TRISO and for solid TRISO fuel compacts. Figure 14a shows a 60,000-s spectrum obtained by SOFIA of the U Kα₁ (K-L₃), Pu Kα₁, and Pu Kα₂ (K-L₂) x-rays in irradiated TRISO compact 2–633. The item has a burnup of 7.46% fissions per initial metal atom (FIMA) and was measured after a cooling time of 134 months. Both Pu x-rays in particular are observable in the microcal spectrum due to the lower signal to noise ratio enabled by microcal. For comparison, a 3387-s live time HPGe spectrum of TRISO compact 5–223 is shown. This item has even higher burnup (14.33% FIMA), and therefore a higher percentage of plutonium than the 2–633 item, and was measured after a cooling time of 38 months. However, the HPGe Pu Kα₂ peak in particular is obscured by the neighboring U Kα₁. In this microcal spectrum, the X-rays could be quantified at the 1% and 10% level with approximately 40,000 counts and 3,400 counts, respectively. In this spectrum, for example, we are able to quantify the Pu Kα₁ peak with approximately 2% statistical uncertainty. The calculation of the x-ray peak ratios is therefore enabled.

The Pu Kα₂/U Kα₁ is a particularly useful ratio, as the peaks are close in energy, and there is negligible variation in the efficiency curve between measurements, so the peaks may be meaningfully compared. A plot of the Pu Kα₂/U Kα₁ peak ratios as a function of burnup in fissions per initial metal atom (FIMA) is provided in Figure 14b. Because the intensity of the x-ray is related to the amount of material present, the peak area ratio of Pu Kα₂/U Kα₁ should be related to the ratio of Pu/U in the fuel. There is an increasing trend, as may be expected, due to the increasing formation of Pu with increased burnup. More work will be needed, however, to explain the exact shape of the curve. Further studies on more materials across a greater range of reactor conditions will help to fill in points on the curve and extract a functional form. From a complete set of data across many burnups, it may be possible to predict burnup from the ratio of the x-ray peak areas, previously only feasible with destructive techniques. We do not find a trend for the Pu Kα₁/U Kα₁ values. We believe that across the wider energy range, there is more variation in the efficiency, and therefore a simple Pu Kα₁/U Kα₁ ratio is less meaningful without accounting for the efficiency.

The intensity of U and Pu x-rays can also be an indicator for the concentration of U and Pu in a source. U and Pu x-rays are prominent in microcal spectra of irradiated AGR compacts, for example, but are not seen in dilute solutions. In dilute solution, the U, Pu, and beta-emitting fission products are much less concentrated. Therefore, self-fluorescence of the U and Pu x-rays and x-ray fluorescence induced by the beta emissions are both much less probable. Such an x-ray signature obtained from a sample of unknown origin provides evidence as to the density and U/Pu concentration within the sample, helping to quickly discern the sample form.

Highly resolved gamma-ray peaks from fission products also have great potential for indicators about the fuel origin. Eu-154 and Eu-155 are strong candidate isotopes for use in calculation of cooling time, or time since irradiation (Croce et al., 2023). Eu-154 has already been used in ratios with other isotopes to estimate cooling time and burnup (Favalli et al., 2016). Gamma-ray microcal enables potentially more accurate measures of cooling time through comparison of Eu-154 with Eu-155, because a nearby Eu-155 peak is also resolvable (Schreiber et al., 2023). For example, HERMES-400 obtained a 600,000-s spectrum from electrorefiner salt solution (Frederickson and Yoo., 2023), a solution containing fission products from spent fuel separated from uranium and transuranic products. Notable interferences of Eu-155 from Np-239 near 106 keV were resolved, which may allow for a better estimate of the Eu-155 concentration in the sample (Figure 15). The Eu-155 peak at 105.3 keV could be quantified at the 1% and 10% level with approximately 18,000 counts and 1,200 counts, respectively. In this spectrum, we are able to quantify this peak with approximately 3.5% statistical uncertainty. This peak area may be compared to the peak area of Eu-154 at 123.07 keV for cooling time estimates. For comparison of visible peaks, a 14,400-s live time HPGe spectrum of the same item, measured 70 days earlier, is shown. In general, gamma-ray microcal could become a tool to monitor material through all steps of nuclear fuel cycle operations, including potential reprocessing operations such as electrorefinery. The rich quantity of gamma rays in spent fuel materials provides a variety of signatures that could be useful in material tracking.