Introduction

Protactinium-233 (233Pa) is an important tracer for radiochemical analysis of 231Pa [1,2,3]. Whereas 231Pa undergoes alpha decay without significant \(\gamma\)-ray emission, 233Pa decays by \(\beta\)-particle emission accompanied by numerous \(\gamma\)-rays (Fig. 1); as such the 231Pa \(\gamma\)-ray signal can be used for monitoring Pa separations.

Fig. 1
figure 1

Adapted from DDEP [6, 7]

Simplified 233Pa decay scheme.

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In the field of nuclear forensics, there is an outstanding challenge for producing well-characterized 233Pa solutions for use as a spike in Isotope Dilution Mass Spectrometry (IDMS) analysis of 231Pa for 231Pa/235U dating [4, 5]. The present work is motivated by a project led by Lawrence Livermore National Laboratory (LLNL) to produce a reference material characterized for amount of 231Pa. This reference material will allow for traceable calibrations of the necessary short-lived 233Pa spikes (half-life: 26.98  ± 0.02 days [6, 7]). That project requires a 233Pa spike with well characterized concentration (mol/g) for reverse-IDMS measurements. One method for obtaining that concentration is to measure the 233Pa massic activity (Bq/g) of the spike solution and then use the half-life to convert to concentration. To that end, LLNL sent aliquots of their spike solution to multiple radionuclide metrology laboratories for assay. Here, we report the results from the National Institute of Standards and Technology (NIST).

This project presented an opportunity to measure the massic activity by live-timed 4πβ-γ anticoincidence counting (LTAC) of a very pure 233Pa solution. Previous standardizations have relied on the equilibrium conditions of 233Pa with its parent 237Np, taking advantage of the relative ease of measuring absolute alpha decay of 237Np rather than beta decay of 233Pa [8,9,10,11,12,13,14,15,16,17]. In some of those works, both nuclides were measured in equilibrium using 4πβ-γ coincidence [15, 16]. The \(\gamma\)-ray emission probabilities (\(P_{\gamma }\)) for 233Pa decay have been evaluated [7, 14, 18]. The \(P_{\gamma }\) for the 312 keV transition as measured by [17] differs significantly from the evaluated value. A subsequent study [10] agrees with the evaluated value. The \(P_{\gamma }\) in question has implications for the 237Np and 232Th neutron capture cross sections. The present work provides an independent measurement of the 312-keV \(P_{\gamma }\).

Experimental

Source preparation

The final purification of the 233Pa solution occurred at LLNL on 27 June 2017 at 15:50 PDT, which serves as the reference time for the activity measurements reported here. The solution consisted of 2 mol L−1 HNO3 + 0.1 mol L−1 HF. The activity ratio of 237Np to 233Pa at separation was \(< 1 \cdot 10^{ - 8}\) [Williams, R.W.; personal communication 2017]. Approximately 5.3 g of the 233Pa solution was shipped to NIST in a Teflon vial.

In July 2017, the LLNL vial was opened at NIST. Approximately 0.04 g to 0.16 g was transferred gravimetrically into each of 8 liquid scintillation (LS) vials containing 4 mL of either “Ultima Gold”Footnote 1 (2 vials) or “Ultima Gold AB” scintillants (Perkin Elmer, Waltham, MA, USA). Additional 2 mol L−1 HNO3 carrier was added to bring the aqueous content of the LS sources up to 2% for Ultima Gold and 6% for Ultima Gold AB. The 233Pa solution was diluted with carrier by a factor of 1.2960 ± 0.0006 for gravimetrically filling a standard 5 mL NIST ampoule [19] for which our high purity germanium (HPGe) detectors are calibrated. All of the gravimetric transfers were done by measuring by difference the masses of solution dispensed from an aspirating polyethylene pipette (“pycnometer”) using a 6-digit microbalance.

4πβ-γ anticoincidence measurements

The 4πβ-γ anticoincidence (LTAC) method was used to determine the massic activity of the 233Pa solution. The NIST LTAC system and Monte Carlo analysis method have been described previously [20, 21]. In brief, the 4πβ detector consists of a liquid scintillation (LS) source coupled to a single photomultiplier tube. The \(\gamma\)-ray (and X-ray) detector is a NaI(Tl) well detector. A digital data acquisition system is used to record the pulse heights and time stamps from both detectors. The data are processed offline by the multiple channel anticoincidence method with shared, controllable extending dead time [22]. The LS efficiency is varied by changing the lower-level discriminator for the LS amplitude in the software.

Up to 3 NaI(Tl) gates were used in anti-coincidence mode to monitor the LS inefficiency for three different subsets of decays. The output of the data processing was the LS rate (\(N_{LS} )\), and the NaI(Tl) anticoincident-to-total ratios (\(Y_{i}\)) for each of the 3 gates. A linear combination of the \(Y_{i}\) is adopted as the effective LS inefficiency,

$$Y_{\text{eff}} = \sum a_{i} Y_{\text{i}} ,$$
(1)

where the \(a_{i}\) are weighting factors. Either a linear or quadratic least-squares fit of the LS rate (\(N_{\text{LS}}\)) vs. \(Y_{\text{eff}}\) is carried out and extrapolated to \(Y_{\text{eff}} = 0\), to obtain the nominal source decay rate (\(N_{0}\)). The linear fit equation with free parameters \(N_{0}\), \(k\), and the \(a_{i}\) is,

$$N_{LS} = N_{0} \left( {1 - k Y_{\text{eff}} } \right)$$
(2)

Due to the complex decay scheme, \(N_{0}\) from the fit can differ from the true activity. To correct for this, a Monte Carlo simulation, using Geant4 library [23], of the entire experiment was performed with identical extrapolations as for the data. A correction factor, \(F\), was derived by the ratio of \(N_{0}\) to the “true” activity input to the Monte Carlo.

The final massic activity (\(A\)) was determined for each source from \(N_{0}\), \(F\), and mass, m of the 233Pa solution in the source.

$$A_{m} = \frac{{F N_{0} }}{m}$$
(3)

The free parameter in the Monte Carlo simulation is the scintillation efficiency, which was set to 4500 UV photons per MeV of electron energy, which matched the experimental LS spectrum (Fig. 2). The three NaI(Tl) gates were set to be sensitive to various decay pathways (Table 1), such that the LS efficiency for each path could be extrapolated to 100% (\(Y_{i} = 0\)). Since 233Pa does have a significant \(\beta\) branch to the 233U ground state (\(\beta_{0}\)), without emission of a photon, the LS efficiency of that branch is not monitored by any of the gates. However, since all the \(\beta\) spectra are of similar shape (same nucleus, all first-forbidden), one can use a linear combination of \(Y_{i}^{'} {\text{s}}\) from other transitions to represent the inefficiency for detecting \(\beta_{0}\) [22]. However, given the complicated decay scheme, including numerous conversion electrons, achieving a linear extrapolation using the three \(Y_{i}\) values is not necessarily possible. Therefore, the Monte Carlo correction, F, was employed throughout.

Fig. 2
figure 2

Measured (solid black lines) and simulated (dashed red lines) spectra from LS (left) and NaI(Tl) (right) detectors, where C is counts with arbitrary scaling and E is approximate energy, proportional to pulse height. In the LS spectrum, the three peaks correspond to conversion electrons. In the NaI(Tl) spectrum, the three gates used for LTAC are shown

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Table 1 Energy gates in the LTAC NaI(Tl) detector
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HPGe detector measurements

Gamma-ray spectrometry measurements were carried out to determine the \(\gamma\)-ray emitting impurities in the source and the source activity. Five different HPGe detectors (both n-type and p-type detectors) with well-characterized efficiency curves [24] were used to determine the source activity. A total of ten measurements were performed for the standard 5 mL NIST ampoule using seven different source measurement geometries. For these different measurement geometries, the sources were placed above and on the side of the HPGe detectors at several source-to-detector distances varying between 20 and 50 cm. For each measurement, the live time was 1 day. The activity was calculated based on the 300.129 keV, 311.904 keV, 340.476 keV, 398.492 keV and 415.764 keV \(\gamma\)-ray peaks and the 2010 DDEP (Decay Data Evaluation Project) evaluated emission probabilities (\(P_{\gamma }\)’s) and half-life [6, 7]. The full-energy-peak efficiency values for the HPGe detectors were previously determined using standard 5 mL NIST ampoules containing calibrated solutions of radionuclides that cover an energy range from 35 to 1.8 MeV and which were placed at the same source-to-detector distances as those used in the present measurements. The efficiency curves were fitted using two different methods (sixth degree polynomial and dual polynomial fit (spline function) with a cross-over point at around 200 keV) in order to assess possible variability in the calculated values for the different \(\gamma\)-ray energies for 233Pa.

Results

4πβ-γ anticoincidence measurements

Each of the 8 LS sources was measured either 2 or 3 times between 7 July 2017 and 28 July 2017 (Fig. 3). No systematic difference was seen between the results for the two LS cocktails, and the source-to-source standard deviation was 0.17%. There was no statistically-significant trend in activity measurement versus time for a given source, averaged over all sources. However, for the four sources that were measured over a longer (5 day) period, three of them showed a decreasing trend of intercept value over time. To conservatively account for any LS cocktail instability, the average decrease in intercept value for those 4 sources was included as an uncertainty component in the massic activity determination.

To check for long-lived impurities, one source was measured again on 4 December 2017, after the 233Pa had decayed by 6 half-lives. The measured activity differed from the mean of the earlier measurements by (− 0.5 ± 1.4)%.Footnote 2 This uncertainty would correspond to a limit on long-lived \(\alpha\)- or \(\beta\)-emitting impurities of about 0.04% at the midpoint of the July measurements (2017-07-20 07:00 EST).

Fig. 3
figure 3

Decay-corrected LTAC measurement results for 8 LS sources (named in caption). Top: massic activity, \(A_{m}\). Bottom: decay-corrected \(A_{m}\) plotted as a percent difference (\(\Delta\)) from the average (excluding the final measurement, used only as an impurity check). Results from linear efficiency extrapolations (Function 1 in Table 2) are shown

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Various efficiency extrapolation functions were used to test the sensitivity of the extrapolation intercept to the functional form (linear or quadratic) and number of \(\gamma\)-ray gates (up to 3) included. Example efficiency extrapolations and fit residuals are shown in Fig. 4. The various fits are summarized in Table 2 and the relative results are shown in Fig. 5.

Fig. 4
figure 4

Example efficiency extrapolation from source UGAB1. Linear (solid black line) and quadratic (dashed red line) are indistinguishable by eye. Residuals for linear (black circles) and quadratic (red diamonds) are shown

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Table 2 Summary of extrapolation functions used to analyze the LTAC data
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Fig. 5
figure 5

Percent difference (triangle) from the average result for 6 different extrapolation functions, without (filled cicle) and with (rectangle) Monte Carlo correction factor (F). The corrected values show less model-dependence

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The final value for the LTAC 233Pa massic activity determination was taken as the mean of methods 1, 2, and 3 in Table 2. Those three values were chosen since they included the highest-efficiency LS data, therefore had the shortest extrapolation in \(Y_{\text{eff}}\). However, the standard deviation of all 6 values were used in the uncertainty analysis. The final LTAC 233Pa massic activity at the reference time of 27 June 2017 15:50 PDT was \(2.361 \cdot 10^{4}\) Bq g−1 with a combined standard uncertainty of 0.33%. The uncertainty analysis is summarized in Table 3.

Table 3 Uncertainty evaluation [25, 26] for the LTAC determination of the 233Pa massic activity
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HPGe detector impurity measurements

No \(\gamma\)-ray emitting impurities were observed in the source. The estimated limits of detection for the photon-emitting impurities as of August 1, 2017 were: 90 \(\gamma\) s−1 for energies between 15 and 35 keV, 20 \(\gamma\) s−1 for energies between 40 and 55 keV, 30 \(\gamma\) s−1 for energies between 60 and 180 keV, 18 \(\gamma\) s−1 for energies between 185 and 280 keV, 40 \(\gamma\) s−1 for energies between 258 and 330 keV, 14 \(\gamma\) s−1 for energies between 340 and 430 keV, and 4.8 \(\gamma\) s−1 for energies between 440 and 2000 keV.

HPGe detector activity determination

The peak areas used to determine the 233Pa activity were obtained using Genie 2000 (Canberra Industries, Inc., Meriden, CT, USA) (using interactive peak fit without the fit singlet option). Due to the low counting rates, no pile-up corrections were necessary. Decay corrections during the measurement time and to the reference time were performed for all measurements. The dilution mass of solution in the HPGe ampoule and dilution factor were used to calculate a massic activity of the NIST-1 solution. The measured massic activity of 233Pa at the reference time was \(2.611 \cdot 10^{4}\) Bq g−1 with a combined standard uncertainty of 0.93%. The uncertainty evaluation is summarized in Table 4.

Table 4 Uncertainty analysis for the 233Pa massic activity determined by HPGe \(\gamma\)-ray spectrometry
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HPGe detector \(\varvec{\gamma}\)-ray emission probability (\(\varvec{P}_{\varvec{\gamma}}\)) determination

The HPGe measurements of the 233Pa source and the LTAC massic activity determination were used to determine the emission probability of five of the main \(\gamma\)-ray lines. For the determination of the \(P_{\gamma }\) values, the same corrections as for the HPGe activity determination were applied. The activity of the source used for the HPGe measurements was (59.420 ± 0. 196) kBq at the reference time of 20 July 2017, 7:00 AM EST. The \(P_{\gamma }\) values determined in this work are listed in Table 5 together with the most-recent values from DDEP [6, 7]. The result for the 312 keV \(P_{\gamma }\) is shown in Fig. 6, along with recent experimental and evaluation results. The present work is in good agreement with recent evaluations, though disagrees with the anomalously-high \(P_{\gamma }\) from [17].

Table 5 Measured \(P_{\gamma }\) values for five main \(\gamma\)-ray lines of 233Pa
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Fig. 6
figure 6

Recent \(P_{\gamma }\) results for the 312 keV \(\gamma\)-ray in 233Pa decay. Blue diamonds are evaluations, open squares are previous experimental results and the red open circle is the present work. ENDSF refers to [18] and DDEP to [6, 7]

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Discussion

The LTAC determination of 233Pa massic activity using multiple \(\gamma\)-ray gates proved robust against a variety of extrapolation functions. By implementing Monte Carlo correction factors, the variance in extrapolation intercepts among extrapolation functions and efficiency domains was reduced significantly. Furthermore, the lack of radionuclidic impurities detected by both HPGe \(\gamma\)-ray analysis and the consistent LTAC 233Pa activity results over 6 half-lives, indicate that the 233Pa solution is quite pure, making it an excellent reference material.

By combining the 4πβ-γ anticoincidence result with the evaluated half-life of 233Pa (26.98 ± 0.02) d, and Avogadro’s number, we obtain a concentration of the measured 233Pa atom mole concentration at the reference date of \(1.471 \cdot 10^{ - 10}\) mol/kg with a combined standard uncertainty of 0.34%. This can now be used as a reference for isotope dilution mass spectrometry of 231Pa, which was carried out using the solution shortly after separation.

The HPGe \(\gamma\)-ray measurement result for the massic activity of 231Pa agrees with the LTAC value, differing by (\(- \,0.8 \pm 1.1)\)%, where the uncertainty is the combined standard uncertainty on the difference, ignoring small correlations due to half-life. This excellent agreement confirms the LTAC activity value and is also an indication that the uncertainty on the \(\gamma\)-ray emission probabilities used in the HPGe analysis were reasonable. Conversely, by combining LTAC and HPGe measurements, our derived values for the \(P_{\gamma }\) values are in good agreement with published values. Our value for the strong 312 keV \(\gamma\)-ray agrees with, and has a smaller uncertainty than, the evaluated value. In essence, that result validates our direct measurement of 233Pa by LTAC, compared to earlier indirect values based on 237Np parent measurements and equilibrium assumptions.