Introduction

Beta–gamma systems used for the detection of radioxenon isotopes are one of two technologies deployed by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) to detect underground nuclear explosions. Because of the inert nature of xenon, the radioactive isotopes of xenon are the most likely fission produced isotopes to vent during or after a subsurface nuclear test. Several radioxenon system have been developed in support of the collection, purifying and counting of the four CTBT relevant of xenon (131mXe, 133Xe, 133mXe, and 135Xe), that are produced in the greatest abundance with the longest half-lives from a nuclear explosion [1–3]. As part of the development of the radioxenon analysis capability at the International Data Center (IDC) a set of test spectra was needed for validation and verification of the analysis code. Standard high-purity-germanium (HPGe) spectra code can be used for gamma-ray analysis; however, a set of test beta–gamma coincidence data was only available from experimentally derived spectra using poorly understood radioxenon spikes [4–6]. What was needed for rigorous algorithm testing was a full range of beta–gamma spectra that included pure radioxenon signatures for each of the four relevant isotopes and admixtures of these isotopes that covered a broad range of isotopic concentrations. An additional need beyond validation and verification of the radioxenon concentrations is beta–gamma training spectra for the radioxenon data analysts at the IDC and NDC’s and during on-site inspection field exercises.

To address these issues, the Nuclear Explosion Monitoring and Policy program at Pacific Northwest National Laboratory (PNNL) developed the beta–gamma simulator (BGSim). The program can generate IDC formated beta–gamma spectra with variable radioxenon concentrations for each of the four radioxenon isotopes, 131mXe, 133Xe, 133mXe, and 135Xe. It also can include user selected amounts of background counts and 222Rn and its daughters 214Pb, and 214Bi, which can occasional contaminate the radioxenon gas samples measured in the nuclear detector. To maximize the flexibility of the program, a number of additional parameters can be varied.

The total number of decays that populate the gamma single, beta–single and beta–gamma two-dimensional histograms are generated from these parameters. The parameters dealing with time are used with isotopic half-lives to account for the decay the atoms. Figure 1 shows the Sample webpage layout page with input for the number of atoms, the time elements, the number of background counts per minute, the detector live time, and the number of cubic centimeters of stable xenon (used to convert the radioxenon activities into activity concentration).

Fig. 1
figure 1

A screen capture of the main web-based page of BGSim showing the various parameter input tables and the resultant one and two-dimensional histograms. The graphs show the radiometric response from a mixed 131mXe, 133mXe, 133Xe, and 135Xe sample

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As the user changes the input parameters, the program automatically recalcuates and displays the gamma and beta singles spectra (red), the beta–gated gamma and gamma-gated beta projections (blue), and the associated two-dimensional histograms, which are displayed on the far right panel. The program provides the radioxenon concentrations on this page as well, but due to calibration and data analysis techniques, these are considered estimates only.

Experimental

The detector used in BGSim is a beta–gamma coincidence detector, composed of a NaI(Tl)-and-scintillating plastic beta cell housed inside the well detector [7]. The NaI detector is 8.9 cm in outer diameter, 11.1 cm long, has a well with a diameter of 3.2 cm, and is 5.1 cm deep. The gas scintillation cell is 1.4 cm diameter and 2.5 cm long, is surrounded by 0.2 cm thick polyvinyl toluene (PVT) beta detector and 0.2 cm thick PVT end caps. The gas was dry air at one atmosphere of pressure. The beta counter was surrounded by an absorber made of acrylonitrile butadiene styrene with wall thickness of 0.25 cm and end cap thickness of 0.5 cm. GEANT-4 was used to model the radiation transport characteristics of the beta–gamma detector [8, 9]. The data sets, one for each isotope, are a listing of ~1,000,000 beta and gamma energies; BGSim picks the required number of events at random from this listing. This process has the benefit of maintaining the statistical distribution for the number of atoms used and creating a unique file each time a file is generated.

The ingrowth of 133Xe from 133mXe was not included. This allowed the effects of 133mXe to be easily differentiated from 133Xe without the need to account for the production, collection, processing and counting times. Should the user wish to include the 133Xe ingrowth, the calculation will have to be done outside the existing program. Future updates will include a switch to remove or account for the ingrowth as the user desires. In addition no effects are included due to detector optics or electronics signal processing so that different scintillation detectors could be investigated. The threshold and energy resolution parameters are specific to the nuclear detectors used and can be modified within BGSim to better account for variations between detector types [7, 10–13]. These parameters are listed in Table 1.

Table 1 A list of parameters the user can input to vary the calculations performed by BGSim
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The Radioactive Decay Module of GEANT-4 was used to generate the radiometric signatures of the decaying isotopes, including all possible products (e.g. Auger electrons, conversion electrons (CE), X-rays, gamma rays, and beta particles). The energy deposited in each of the detectors was recorded, accounting for the detector efficiency in both the NaI(Tl) and the plastic scintillation cell, but assumes a 0 keV lower level discriminator with no energy smearing.

The simulated data was binned in 256-channel energy spectra for the beta and gamma detectors, with a two-dimensional (256 × 256 channel) spectrum (2-D) for the coincidence data as seen in Fig. 2. The 2-D histogram is broken up into 10 regions (ROI’s) of interest that correspond to the four radioxenon isotopes and a region for the daughter products of 222Rn (green box) [14–16].

Fig. 2
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An example of the 2-D histogram with a pure 133mXe sample

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Figure 2 shows a physically impossible spectrum for a pure 133mXe sample because it does not contain the ingrowth of 133Xe from the 133mXe decays. The main distribution is from a 30 keV X-ray in coincidence with a 199 keV CE. The Compton scatter line is generated by a 229 keV gamma scattering off the plastic scintillator producing a Compton scatter electron. The Compton response intersects with several of the ROI’s and is an interference of 133mXe in the 133Xe 80 keV ROI (red box) and the 135Xe 250 keV ROI (purple box). The bleed over of the CE distribution also causes interferences in the 131mXe ROI and the 30 keV 133Xe ROI. This is significant because these interferences would be difficult to determine with a real detector as the 133mXe decays to 133Xe and samples will always have both isotopes [17, 18].

Comparison of the output of BGSim has been done to identify differences between the model and an actual beta–gamma detector response. Figure 3 shows the results for the beta distribution for 133Xe and the gamma spectra for 135Xe. The number of counts used in BGSim was adjusted to account for the total number of counts in the dominate decay for each isotope; 133Xe the 30 keV X-ray gated on the CE plus beta distribution was used and for 135Xe the 250 keV gamma gated on the beta distribution was used. The beta distribution for 133Xe had the greatest difference between the detector and the simulation and indicates that the stable Xe gas needs to be included in the simulation to better account for energy loss of the beta particles. This loss of energy in the real detector tends to bunch the beta energies towards the low beta energies and increases the peak height of the 45 keV CE. The 135Xe response was very closely matched for the gamma spectra; however, there is a difference of 5 % between the detector and BGSim for the 250 keV gamma and the 30 keV X-ray. This suggests that an additional layer of material is needed in the simulation to account for low energy attenuation in the real gamma detector.

Fig. 3
figure 3

Left hand figure shows the differences in the beta distributions for a real detector and that generated by BGSim for 133Xe. The right-hand figure shows the differences in the gamma response for a real detector and BGSim for 135Xe

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Both of these differences shown in Fig. 3 need to be addressed if simulations are to be used to determine difficult-to-determine physical parameters for more refined concentration calculations. Some of these parameters are discussed in the results sections and they highlight the need to both understand the detector response and where possible, account for the differences between the simulations and real detectors [19].

Results and discussion

The methods used to convert the raw 2-D histogram counts into atmospheric concentrations have been developed over a number of years [16, 20]. Several isotopic interferences that are difficult and in some cases impossible to measure have been investigated using BGSim. Until recently, the interference of 135Xe with 133Xe and 133mXe was not possible to study, due to the short half-life of 135Xe as well as a lack of a pure sample of 135Xe with no 133Xe and 133mXe [21, 22]. Figure 6 shows the BGSim-generated histograms for 135Xe. The beta-only graph shows that the additional counts from 135Xe (green) interfere across the entire 133Xe beta spectral range. The determination of the 135Xe concentration is made using the 250 keV gamma in coincidence with a 910 keV beta distribution [23]. As seen in the 2-D histogram of Fig. 6, this decay has a 90 % branching ratio [24]. An additional set of interferences between all four of the radioxenon isotopes exists in the 30 keV X-ray region. The 131mXe, 133Xe and now the 135Xe isotopes can be determined using experimentally determined spectra.

Study of the metastable MDCs with respect to varying 133Xe concentrations

Because the 133Xe interferes with the two metastable isotopes in the X-ray region, it is important to understand the limitations of the detectability of these isotopes across the full range of concentrations that might be measured. Using BGSim to explore this dependence for 133mXe yielded the data shown in Fig. 4 [25]. The graph on the left shows the depedence of the minimum-detectable-concentration (MDC) for 133mXe with respect to high concentrations of 133Xe (>2 mBq/SCM). The fitting curve shows that the functional dependence has a scaling factor that accounts for the detection efficiency, the half-lives, branching ratios, and an approximate square-root function of the 133Xe concentration. This functional dependence is expected for high statistical counts. The graph on the right shows the dependence of the MDC for 133mXe with respect to low concentrations of 133Xe (<1 mBq/SCM). In this graph the MDC values fluctuate due to the increased statistical uncertainty of the 133Xe concentrations and the functional dependence goes as the fifth-root of the 133Xe concentration.

Fig. 4
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Two plots of the effect that varying concentrations of 133Xe have on the MDC for 133mXe

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This assessment of the MDC indicates the dynamic range of the ratios of 133mXe/133Xe and 131mXe/133Xe that can be measured by field systems [26]. A measurement of 100 mBq/SCM of 133Xe gives an MDC for 133mXe of 1.7 mBq/SCM or a ratio of 1.7 %. Figure 5 shows the 133mXe versus the 133Xe concentrations measured for a number of post-nuclear explosion data taken from underground tests at the Neveda Test Site [27]. The line shows the power function for the 133mXe MDC derived from the high concentration plot in Fig. 3; 133mXe values above the line would be detectable, while values below the line would not be detectable using current field systems’ parameters. The ratio data itself follows a 3.0 % line and indicates that the measurements were taken 24 h after the underground test.

Fig. 5
figure 5

A log–log plot showing the 133mXe versus 133Xe activity measurements for a number of underground nuclear tests conducted at the Nevada Test site. The red line indicates the 133mXe activity concentrations that would not be detectable because the 133Xe level was too high for current detectors. (Color figure online)

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Physics processes: 135Xe

An additional interference that is difficult to measure across a range of isotopic concentrations is the interference of the 30 keV X-ray/CE/beta radiometric signature by 135Xe [28]. This difficulty arose from the lack of pure 135Xe spikes which has since been addressed by a number of research teams [21, 22].

The 135Xe 30 keV X-ray/CE/beta interference can lead to mis-identification of 133mXe, 133Xe, and 131mXe Fig. 6. This interference, if not accounted for, can lead to an assessment of three relevant radioxenon isotopes, whereas only 133Xe and 135Xe were in the sample. Such samples can arise from nuclear reactor operations or medical isotope production and should not be classified as originating in a nuclear explosion. Figure 7 shows the relative contribution that the 135Xe isotopes causes in the interference regions for 133Xe (green squares), 133mXe (red diamonds), and 131mXe isotope (blue triangles).

Fig. 6
figure 6

The contribution of 135Xe to other ROIs shows up clearly using only 135Xe as seen in the left panel. The spectra on right show the 135Xe interference in the 30 keV beta/CE region with both the 133Xe and 133mXe affected

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Fig. 7
figure 7

Graph showing the contribution from 135Xe for each of the other three isotopes that emit a beta/CE/X-ray or CE/X-ray in the 30 keV region

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Use of BGSim as part of training exercises

To date, two exercises have made use of the output from BGSim; the first a recent Japanese NDC exerciseFootnote 1 to test their radionuclide analysts and the second was the 2014 Integrated Field Exercise (IFE2014) in Jordan. During the Japanese NDC exercise five sample files with associated background files were generated as part of a mock exercise. The IFE14 exercise used BGSim to produce several sample files during the exercise to simulate data from the Transportable Xenon Laboratory. These data sets were part of the scenario development team data injections to advance or retard the progress of the OSI inspectors during the exercise [29].

Conclusions

The development of BGSim has allowed a number of necessary data analysis methods and outcomes to be investigated. Using the program, the effects of the interferences that arise from all of the radioxenon isotopes have been investigated and have shown the importance that such interferences play in the overall sensitivity and detectability of the isotopes. Further work will improve upon both the physics simulations component of BGSim, as well as automation to provide a full range of beta–gamma spectra with respect to varying input parameters. The use of BGSim to provide realistic radioxenon beta–gamma spectra has been demonstrated and additional data set are likely to be generated from BGSim in the future.