Improved Plutonium and Americium Photon Branching Ratios from Microcalorimeter Gamma Spectroscopy
Michael D. Yoho, Katrina E. Koehler, Daniel T. Becker, Douglas A. Bennett, Matthew H. Carpenter, Mark P. Croce, Johnathon D. Gard, J. A. Ben Mates, David J. Mercer, Nathan J. Ortiz, Daniel R. Schmidt, Chandler M. Smith, Daniel S. Swetz, Aidan D. Tollefson, Joel N. Ullom, Leila R. Vale, Abigail L. Wessels, Duc T. Vo
IImproved Plutonium and Americium Photon BranchingRatios from Microcalorimeter Gamma Spectroscopy
M. D. Yoho a , K. E. Koehler a, ∗ , D. T. Becker c , D. A. Bennett b , M. H.Carpenter a , M. P. Croce a , J. D. Gard c , J. A. B. Mates c , D. J. Mercer a , N. J.Ortiz b,c , D. R. Schmidt b , C. M. Smith a , D. S. Swetz b , A. D. Tollefson a , J. N.Ullom b,c , L. R. Vale b , A. L. Wessels c , D. T. Vo a a Los Alamos National Laboratory, Los Alamos, NM 87545, USA b NIST Boulder Laboratories, Boulder, CO 80305, USA c University of Colorado, Boulder, CO 80309, USA
Abstract
Photon branching ratios are critical input data for activities such as nuclearmaterials protection and accounting because they allow material compositionsto be extracted from measurements of gamma-ray intensities. Uncertaintiesin these branching ratios are often a limiting source of uncertainty in com-position determination. Here, we use high statistics, high resolution (˜60–70eV full-width-at-half-maximum at 100 keV) gamma-ray spectra acquired usingmicrocalorimeter sensors to substantially reduce the uncertainties for 11 pluto-nium (
Pu,
Pu,
Pu) and
Am branching ratios important for materialcontrol and accountability and nuclear forensics in the energy range of 125 keVto 208 keV. We show a reduction in uncertainty of over a factor of three for onebranching ratio and a factor of 2–3 for four branching ratios.
Keywords:
Microcalorimeter, transition edge sensor, branching ratios,non-destructive assay, plutonium, americium ∗ Corresponding authorTel.: +1 (505) 695 4100Email: [email protected]
Preprint submitted to Nuclear Instruments and Methods in Physics Research Section AJune 24, 2020 a r X i v : . [ nu c l - e x ] J un . Introduction Microcalorimetry.
Recent developments in microwave frequency-division mul-tiplexing [1–3] allow the construction of large superconducting transition-edgesensor (TES) arrays such as the array described in [4, 5]. The newly con-structed SOFIA (Spectrometer Optimized for Facility Integrated Applications)instrument used in this work currently uses up to 256 pixels with an intrinsicdetector efficiency comparable to that of a planar HPGe (high-purity germa-nium) detector at 100 keV with energy resolutions around 65 eV in the 20–208keV range [6, 7].
Prior art.
The majority of studies of plutonium and
Am branching ratiosfrom 125–208 keV use a set of radionuclide standards (e.g.
Eu or
Ho)to determine an absolute efficiency curve of an HPGe or Ge(Li) detector [8–15].With this method, it is necessary to determine the total mass of plutonium,so the masses of purified isotope samples are determined via α -spectrometryor isotope dilution mass spectrometry (IDMS). Purified isotopic samples arenecessary to reduce the amount of interferences from neighboring signatures.The dominant uncertainty source is from the absolute efficiency curve determi-nation. For example, [13] assigns uncertainties due to calibration radionuclidebranching ratios and activity, source absorption, source diameter, and changingdetector efficiency over time to determine Pu branching ratios from 45–160keV.Similar to this work, [16] takes a different approach. Non-isotopically ho-mogenous IRMM (Institute for Reference Materials and Measurements) pluto-nium standards are counted and plutonium signatures from 125–220 keV inher-ent in the sample itself are used to determine the relative efficiency curve. Inthis manner, the branching ratios from 148–161 keV are determined withoutmany of the biases inherent to absolute efficiency determination. This workuses the same approach and fixes five well-known plutonium branching ratioswith relative uncertainties ranging from 0.5% to 1% taken from the NationalNuclear Data Center (NNDC) (see Table 1). The excellent resolving power of2icrocalorimetry, about eight times that of planar HPGe detectors, reduces thesystematic biases due to peak interferences, response function fitting, or peakbackground determination.
Table 1: Fixed branching ratios from NNDC [17, 18]. Uncertainties represent 67% confidenceintervals.
E [keV] Isotope γ /decay x 100 Unc. γ /decay x 100 % Unc.129.30 Pu 6 . × − . × − Pu 1 . × − . × − Pu 4 . × − × − Pu 1 . × − × − Pu 5 . × − × − Relevance.
Hoover, et al. determined that nuclear data uncertainty is the limit-ing factor in plutonium isotopic analysis [19]. For example, the prominent Am γ -ray peaks at 125.3 keV and 146.7 keV have branching ratio uncertainties of2.6% and 2.7%, respectively. These Am signatures allow the coupling of the129.3 keV Pu γ -ray to the 104.3 keV Pu γ -ray via other Am γ -rays be-low the plutonium K-edge using a relative efficiency curve. The relatively largebranching ratio uncertainties on these peaks reduces the accuracy and precisionof plutonium material control and accountability measurements which rely onprecise measurement of Pu content. Similarly, the
Am/
Pu chronometerusing the strong
Am signature at 146.7 keV and the strong
Pu signatureat 148.57 keV is limited by branching ratio uncertainty.
2. Experimental
The experimental procedure for acquiring plutonium spectra is well de-scribed in [6]. Counting conditions and reference materials are described inTable 2 and Table 3. CRM136, CBNM61, PIDIE1, and PIDIE6 were counted3ith the BAYMAX (Bimodal Alternate Yield Microcalorimeter Array for X-rays) cryostat using the SLEDGEHAMMER array (Spectrometer to LeverageExtensive Development of Gamma-ray TESs for Huge Arrays using MicrowaveMultiplexed Enabled Readout) during the period October 2018 to January2019 [5]. All other measurements were made on the SOFIA instrument withthe SLEDGEHAMMER array during the period September 2019 to October2019. One to two mm of Cd filters were used to attenuate the
Am signal at59.6 keV. Single spectra were acquired for each item except for CRM137, whichconsists of three separate spectra. Count rates varied from 2 to 12 counts persecond per pixel. Figure 1 depicts a typical plutonium spectrum from 60 keVto 208 keV. Figure 2 demonstrates the excellent resolution of microcalorimetryin comparison to a planar HPGe detector.
Table 2: Certified and working percent mass fractions with respect to total plutonium. Un-certainties in parentheses represent 67% confidence intervals. Mass fraction dates are given inTable 3.
Item Pu Pu Pu Pu AmCBNM61 1.197(1) 62.53(1) 25.41(1) 6.689(4) 1.445(7)CBNM70 0.8458(9) 73.319(5) 18.295(4) 5.463(2) 1.171(6)CBNM84 0.0703(3) 84.338(4) 14.207(4) 1.0275(9) 0.217(1)CBNM93 0.0117(2) 93.412(2) 6.313(2) 0.2235(2) 0.105(1)CRM136 0.222(4) 84.925(8) 12.366(8) 1.902(3)CRM137 0.267(3) 77.55(1) 18.79(1) 2.168(3)CRM138 0.010(1) 91.772(5) 7.955(5) 0.229(1)STDISO3 0.006(1) 96.302(6) 3.562(4) 0.111(2) 0.0172(4)STDISO9 0.021(2) 92.606(8) 6.888(6) 0.411(5) 0.020(1)STDISO12 0.058(2) 86.97(1) 11.81(1) 0.939(3) 0.139(3)STDISO15 0.169(2) 82.11(1) 15.41(1) 1.604(9) 0.068(4)PIDIE1 0.0111(4) 93.765(8) 5.990(7) 0.199(3) 0.228(7)PIDIE6 0.930(6) 66.34(1) 23.89(1) 5.28(2) 3.8(2)4 able 3: Material size and composition.
Item Mass [g] Counts [ × ] Count time [h] Certificate dateCBNM61 6.6 oxide 83 49 20-06-1986CBNM70 6.6 oxide 19 14 20-06-1986CBNM84 6.6 oxide 12 14 20-06-1986CBNM93 6.6 oxide 10 14 20-06-1986CRM136 0.250 sulfate 15 14 01-10-1987CRM137 0.250 sulfate 95 46 01-10-1987CRM138 0.250 sulfate 11 14 01-10-1987STDISO3 11 oxide 12 14 01-07-1986STDISO9 12 oxide 15 14 01-07-1986STDISO12 20 oxide 14 14 01-07-1986STDISO15 12 oxide 15 20 01-07-1986PIDIE1 0.5 oxide 164 83 01-01-1988PIDIE6 0.5 oxide 100 92 01-01-1988 Energy [keV] C oun t s p e r e V b i n Figure 1: CRM137 20 hour spectrum. nergy [keV] C oun t s p e r e V b i n Figure 2: 150 keV region comparison for 20 hr CRM137 spectrum (bottom) and 1 hr planarHPGe spectrum (top).
3. Efficiency Model Validation
The efficiency model is fit during the optimization routine described in Sec-tion 4, but was verified via Monte Carlo modeling with the Monte Carlo N-Particle (MCNP) code version 6.2 [20] for the 0.5 g PIDIE and 5.5 g CBNMreference materials. Figure 3 shows the modeled geometry which consists of theSn absorbers, PuO with ingrown Am and casings, a Cd attenuator, and thedetector package housing. Efficiency curves were then generated by simulatingmonoenergic photon emissions from 125 keV to 208 keV. The efficiency curveused in this work given in Equation 1 takes into account Sn absorption, Puattenuation, Cd attenuation, and geometric efficiency. The efficiency (cid:15) s ( E ( r ))for spectrum s at energy E associated with region r is described by the physicalmodel (cid:15) s ( E ( r )) = K s g s (1 − e µ Sn( E ( r )) x sSn ) e − µ Cd (( E ( r )) x s Cd (1 − e µ PuO2 ( E ( r )) x s PuO2 ) µ PuO ( E ( r )) x s PuO . (1)Here, K s is a scaling factor set for each spectrum such that the efficiency at129.3 keV is (cid:39)
1. Normalization ensures efficiency values during optimizationstay above the machine numerical precision. The terms µ Sn ( E ( r )), µ Cd (( E ( r )),6nd µ PuO ( E ( r )) represent the Sn photo-electric attenuation coefficients, Cdtotal attenuation coefficients, and PuO total attenuation coefficients at energy E associated with region r , respectively. The optimization parameters for eachspectrum s denoted by the terms g s , x s Sn , x s Cd , and x s PuO represent geomet-ric efficiency and Sn, Cd, and PuO thicknesses, respectively. Photo-atomiccross-sectional data is taken from the Evaluated Nuclear Data Files (ENDF)B-VIII.0 [21] based upon data presented in [22, 23]. Cubic spline interpolationswere used to extrapolate between listed reference energies.A similar physical efficiency model has been used successfully for microcalorime-ter data in [24] and is very similar to other well-established physical Pu efficiencycurves such as in [25] and [26]. Figure 4 demonstrates that the fit physical ef-ficiency curve describes the simulated data very well with less than 0.1% bias.Note that there are no visible error bars in the figure since Monte-Carlo simula-tions were run until there were around 10 full energy deposition events for eachsimulated energy emission, leading to around a 0.03% uncertainty for each pointwhich is smaller than the image resolution. The low bias in the fit is due to thefact that efficiency is very gradually curved for the measurement configurationsused in this study between 125 and 220 keV. The previous plutonium branch-ing ratio study [16] over a subset of this energy range reports less than a 0.1%difference in derived branching ratios using a similar physical efficiency modelto Eq. 1 or when using a simple second degree polynomial. This supports theconclusion that many smooth functions will be adequate in this energy rangefor these measurement configurations. Consequently, [16] does not assign ana priori uncertainty to their chosen second degree polynomial efficiency modelbetween 125 and 220 keV.In contrast to this approach, the effect of the choice of efficiency function wasexplored by repeating the entire analysis described in Sections 4 and 5 utilizing athird order polynomial efficiency curve. The derived branching ratios absolutelydiffered on average by 0 . σ from those derived using a physical efficiency curve.For this reason, as well as the aforementioned 0.1% bias on the efficiency curveshown in Figure 4, a 0.2% uncertainty component was added in quadrature to7he final reported branching ratio uncertainties reported in Section 6.There are four free parameters in the physical efficiency model, yet the modelis fit to five branching ratios (see Table 1). The additional branching ratio canbe used as a check on the efficiency model fit. In all cases, the fit efficiencycurve has a low chi-square. (detector housing) (for low energy attenuation) (steel source enclosure) PuO + Am (source) (for energy calibration) (part of detector package) (detector) . c m . c m c m Figure 3: MCNP model for CBNM61.
4. Algorithm
Decay correction.
Activity ratios, α is , with respect to Pu for each isotope i for each spectrum s , are determined by decay-correcting the mass fractions fromTable 2 to the spectrum measurement dates. For CRMs 136-138, the amount8 igure 4: Physical efficiency model for CBNM61. The dots are MCNP simulated efficienciesand the line is the fitted physical model. Efficiency units are arbitrary. of Am was taken from the recently published forensics intercomparison exer-cise analysis of certified reference materials [27]. Decay-corrected activity ratiouncertainties include half-life, mass fraction, and molar mass uncertainties fromTable 4. The uncertainty for the STDISO series mass fractions was determinedby applying the Type B On Bias (BOB) method [28] to the original mass spec-trometry reports.
Areas.
Net region areas, A sr , for each region r associated with each spectrum s ,are determined via the simple peak integration method described in section 5.4of [29] and American National Standards Institute (ANSI) N42.14-1999 sectionC.1 [30]. This work does not utilize response function fitting, since ANSI stan-dard N42.14-1999 section 6.2 [30] recommends utilizing the simpler method forisolated singlet peaks. Using this method and assuming a linear background, A sr = G main − ( G L + G R ) C main /C L + R . (2)In Equation 2, G main , G L , G R , C main , and C L + R denote the gross counts in acentral region, gross counts in left background region, gross counts in the right9 able 4: Isotopic data. All uncertainties are 67% confidence intervals. Half-lives taken from[17]. Isotope Half-life [y] Molar mass [g/mol]
Pu 87.7(1) 238.0495601(19)
Pu 24110(30) 239.0521636(19)
Pu 6561(7) 240.0538138(19)
Pu 14.329(29) 241.0568517(19)
Pu 3.73(3) × Am 432.6(6) 241.0568293(19)background region, the number of bins used to calculate G main , and the numberof bins used in calculated G L and G R , respectively. Figure 5 shows ROIs for twosample peaks. Left and right background regions generally span five histogrambins. In the case that there is a peak interference on either the left or the rightside of the region, that side is assumed to have zero bins and zero counts (e.g. G R = 0 and C L + R = C L as shown in the left panel of Figure 5). Note thatin several instances a region spans multiple photon signatures. Central regionwidths are chosen to encompass > in C oun t s / B i n Bin C oun t s / B i n L RMain L Main
Figure 5: Two ROIs delineated for the 148.57 keV peak and 146.07 keV peak. The left andright background regions are demarcated with red lines. The central region labeled “main”encompasses at least 99.95% of the peak area. The 146.07 keV peak has interference on theright side, so the background is calculated using only the left side. (color figure online) on both sides of the peak, so the background level is determined by examininga single side of a peak.To estimate the largest possible bias, several large, clean peaks in the largest10-g CBNM spectra are considered. To estimate the bias in the spectra of lowburn-up materials, the net peak area for the
Pu 203 keV peak from theCBNM-93 spectrum is measured utilizing background regions on the left andright and also measured utilizing only a single background region on the left.This peak is larger in area, higher in energy, and sitting on a smaller Comptonbackground than any peak in the spectrum analyzed with only a single back-ground region. The difference in measured net peak areas is 0.15%. To estimatethe bias in the spectra of high burn-up materials, a similar analysis was con-ducted on the prominent
Pu 152 keV peak from CBNM-61 spectrum. Forthis peak, the difference in measured net peak areas is 0.13%. This estimatedupper bound of a 0.15% bias is significantly lower than other systematic biasestaken into account in this work and is therefore neglected. If the spectra camefrom larger items that are likely to have high small-angle scattering contribu-tions, such as a kilogram of uranium oxide, then this bias would have to beaddressed. 11 scape Peaks.
Excited Sn K x-rays have a non-negligible probability of escapingthe 0.0380 cm thick absorbers generated by the photo-electric absorption of γ -rays. These escape peaks interfere with some photon signatures at energiesbelow the primary photo-electric absorption energy. The peaks affected by thiseffect relevant to this work are given in Table 5. Other escapes interfering in aregion are dealt with by changing the ROI and background bounds.Interference-free Sn escapes in multiple high-intensity spectra, such as fromthe 208 keV Pu/
Am photo-electric peak, were used to determine the prob-ability of escape (yield) for each x-ray type. Yields for a given Sn escape x-ray(e.g. K α ) were not observed to vary with energy from 125 keV to 208 keV withstatistical significance, as verified with Monte Carlo modeling. These yields anduncertainties are given in Table 5. Table 5: Sn escape x-rays interfere with relevant peaks for branching ratio determination.These interferences are given below with the primary peak, relevant escape x-ray, and peakbeing interfered with. The Sn escape x-ray yields are determined from interference-free peaks.Uncertainties in parentheses represent 67% confidence intervals. The yield is a fraction of thephoto-electric peak.Primary Photo-Peak Sn Escape X-ray Escape Interference PeakE [keV] Isotope Type E [keV] Yield E [keV] E [keV] Isotope169.6
Am K α Pu171.4
Pu K α Pu175.1
Am K β +K β Am175.1
Am K α Am188.2
Pu K β +K β Pu189.4
Pu K β Pu203.6
Pu K β +K β Am From the highest energy region areas to the lowest, corrections are made toeach A sr with yield y v associated with escape emanating from region v using A sr := A sr − y v A sv . (3)12 ptimization. The branching ratio optimization in this work assumes uncor-related, normally distributed region areas. Therefore, this work uses a χ maximum-likelihood estimator given by χ = N s (cid:88) s =1 N r (cid:88) r =1 w sr ( A sr − N i r (cid:88) i =1 α is β ir (cid:15) s ( E ( r ))) . (4)The weighted differences between the measured net region areas A sr andmodeled peak responses are summed for all spectra s and all regions r . N s , N r , and N ir represent the total number of spectra, total number of regions, andtotal number of isotopes with responses in each region r , respectively. β ir is thebranching ratio of isotope i in region r . Note that each isotope has at most oneresponse in any given region. The efficiency curve used in the optimization isdescribed in Equation 1. For each of the 15 spectra, four efficiency parameters( g s , x s Sn , x s Cd and x s PuO ) are optimized, resulting in 60 optimization param-eters. Additionally, 20 branching ratios are optimized. Therefore, there are 80optimization parameters total. Each spectrum has 21 measured regions result-ing in 235 net degrees of freedom. The bounded, limited-memory approximationof the Broyden-Fletcher-Goldfarb-Shanno (L-BFGS-B) optimization algorithmis used for the non-linear χ minimization [31] All optimization parameters areunbounded. Initial conditions for efficiency parameters are set to be g s = 1, x s Sn = 0 . , x s Cd = 0 .
15 cm given adensity of 8.7 g/cm , and x s PuO = 0 . . Initialconditions for the branching ratios β ir are randomly selected from a normaldistribution with a mean equal to the current ENSDF values and a relativestandard deviation of 5%.Randomization of β ir eliminates any potential bias from choosing a set ofinitial conditions in the neighborhood of a local minimum spanning ENSDFvalues. As a quality assurance check, the algorithm was run 200 times, and inall cases the algorithm converged to the same minimum. This demonstrates thealgorithm solution is independent of β ir within the specified ranges.The weights w sr in Equation 4 take into account the net area uncertainty13 A sr and isotopic ratio uncertainty σ i sr using the effective variance method [32].The propagation of uncertainty due to the statistical fluctuation in the Comptonbackground and photo-electric peak for the area calculations is described inANSI standard N42.14-1999 section C.11 [30] which is based upon a discussionin Section 5.4.1 of [29]. The present work utilizes this method to calculatethe net area uncertainties used in the calculation of w sr . In this method, theweight term δ j associated with χ minimization for function f and dependentmeasurement point y j with uncertainty δ y j and independent measurement point x j with an additional uncertainty δ x j is given by δ j = (cid:18) δfδx (cid:19) j ( δx j ) + ( δy j ) . (5)Applying Equation 5 to Equation 4 for both non-zero area and activity ratiouncertainties gives 1 w sr = σ A sr + N ir (cid:88) i =1 ( σ α is (cid:15) s ( E ( r )) β ir ) . (6)Note that Equation 6 requires knowledge of the efficiency and branchingratios. This work sets β ir = β ir . To reduce computational complexity, ef-ficiency (cid:15) s ( E ( r )) for the weights is estimated for each spectrum by fitting a2nd order polynomial efficiency curve in exponential space (see Equation 6 in[33]) to the five fixed branching ratios without using weights. All other uses ofthe detector efficiency in the optimization algorithm use the physical efficiencymodel (Equation 1). The algorithm converges in approximately two minutes fora single thread using ˜16% of total processing power for an i7-7700 3.60 GHzquad-core processor.
5. Uncertainty Analysis
This work applies the GUM (Guide to the Expression of Uncertainty inMeasurement) Supplement 1 Monte Carlo method [34] to determine branchingratio uncertainty. See also [35] for the application of Supplement 101 to γ -ray14pectrometry efficiency determination. Uncertainty is propagated from Pois-son counting statistics, half-lives, molar masses, escape yields, fixed branchingratios, photon energies, and CRM mass fractions. Counts in each spectrumhistogrammed channel are randomly selected from the Poisson distribution. Allother parameters are randomly sampled from the normal distribution with amean equal to the tabulated data or CRM value and standard deviation equalto the tabulated uncertainty. Each Monte Carlo simulation begins prior to CRMmass fraction decay. This captures the correlation between the derived activityratios for all of the spectra due to the use of the same half-lives. The stan-dard deviations of the optimized branching ratio results for 2000 iterations aretaken as the uncertainties. The qualitative uncertainty budget (see Annex B ofSupplement 101 [34]) is determined by taking the standard deviation of resultsfrom only randomly modulating a single uncertainty component. Due to thisqualitative nature, only 200 simulations are run for each uncertainty budgetcomponent. The uncertainty budget depicted in Figure 6 demonstrates thatPoisson statistics uncertainty tends to dominate at higher energies. This is dueto the fact that the intrinsic efficiency of the very thin (0.0380 cm thick) Snabsorbers rapidly deteriorates at higher energies. Some branching ratio uncer-tainties of important signatures for chronometry, such as those of Am γ -raysat 125.3 keV and 146.6 keV are dominated by the uncertainties of the five fixedbranching ratios. This uncertainty of around 0.5% represents an upper-boundthat cannot be imporved upon even if higher statistics spectra are acquired.
6. Results
Branching ratios.
Table 6 gives the branching ratios and uncertainties deter-mined from this work. All branching ratios agree well within 3 σ of ENSDFvalues[17, 18]. Many branching ratio uncertainties, especially below 160 keV,have been reduced substantially, especially those of Am. The high branchingratio uncertainties coming from this work (i.e. 125.21 keV, 160.19 keV, and161.54 keV) are due to insufficient counting statistics and interferences with15 P u . A m . P u . P u . A m . A m . P u . P u . P u . P u . A m . P u . A m . A m . P u . A m . P u . P u . A m . P u . A m . % U n c e r t a i n t y c o n t r i bu t i o n Energy [keV]
Fixed branching ratios Escape peak yields Isotopics Half livesPoisson statistics Molar masses Energies Efficiency model
Figure 6: Posterior uncertainty budget. σ primarilycome from branching ratios that have high uncertainties. Where uncertaintyis substantially improved from ENDSF results (i.e. more than a factor of 1.2),the agreement is in general within 1 σ with the exception of two Am peaksat 146.55 keV and 150.04 keV. These new values for these peaks with substan-tially reduced uncertainties are expected to be better than prior values due tousing the results of the recently published intercomparison of certified referencematerials [27]. The well-measured
Pu branching ratio (9 . × − γ /decay × σ from [17, 18]. However, there is excellent agreement withGunnink [36] (9 . × − γ /decay × . × − γ /decay × Chronometry.
As a quality assurance check, the new measured branching ra-tios and uncertainties from 125–208 keV were input into a NIST independentlydeveloped plutonium isotopic analysis code SAPPY, which is a continuation ofwork reported in [19] and [4]. SAPPY uses γ -ray signatures from 95 keV to208 keV. The reported Am/
Pu activity ratios were then used to deter-mine model separation dates [37] for CRMs 136, 137, and 138. Table 7 showsimprovement in accuracy and precision using the branching ratios derived inthis work. Note that CRM documented model ages depicted in Table 7 aretaken from [38]. CRM136 and CRM137 were well separated via anion-exchangeand recrystallization and had no measurable residual
Am. CRM138 was sep-arated via recrystallization and had measurable residual
Am. Therefore, thedocumented CRM138 separation date in Table 7 is taken to be the impliedpurification date on page 4 of [38].Improvements in accuracy are not significant because the CRM materialswere used in the optimization, although the branching ratio optimization uses17 able 6: Comparison of NNDC [17] branching ratios (BRs) to those of this work.
Pu BRsat 164 keV and 208 keV assume secular equilibrium with
U. Relative % uncertainties ( µ )represent 67% confidence intervals. BR units are in γ /decay x 100.Energy [keV] Isotope NNDC BR µ BR [%] This work BR µ BR [%] µ BR Agreement125.21
Pu 5.63 × − × −
13 -0.2125.3
Am 4.08 × − × − Pu 2.83 × − × − Pu 1.19 × − × − Am 4.61 × − × − Am 7.40 × − × − Pu 9.29 × − × − Pu 6.68 × − × − Pu 6.20 × −
19 5.82 × −
331 -2.5161.45
Pu 1.23 × − × − Am 1.50 × − × − Pu 4.56 × − × − Am 6.67 × − × − Am 1.73 × − × − Pu 1.10 × − × − Am 1.82 × − × − Pu 1.09 × −
10 8.63 × − Pu 8.30 × − × − Am 2.16 × − × − Pu 5.19 × − × − Am 7.91 × − × − Table 7: Model age results. Uncertainties represent 67% confidence intervals. Old denotesthe use of NNDC branching ratios. New denotes the use of the branching ratios of this work.
Item Documentedseparationdate [38] Model sepa-ration date Uncertainty[days] Difference[days]CRM136 (old) 15-Mar-70 13-Mar-69 183 -367CRM136 (new) 15-Mar-70 11-Sep-69 146 -184CRM137 (old) 30-Sep-70 22-Apr-70 146 -157CRM137 (new) 30-Sep-70 22-Oct-70 99 22CRM138 (old) 12-Jul-62 06-Aug-62 407 25CRM 138 (new) 12-Jul-62 25-Jan-63 369 197
7. Conclusions
This work has used multiple certified and working reference materials to mea-sure Pu and Am γ -ray branching ratios from 125–208 keV with microcalorime-try. Many branching ratio uncertainties of decays important for non-destructiveplutonium isotopic analysis and nuclear chronometry have been significantly im-proved. For example, this work reports relative Am branching ratio uncer-19ainties for γ -rays at 125.3 keV and 146.65 keV of 1% and 0.8% as opposed tothe currently listed uncertainties of 2.7% and 2.6%, respectively. In an applica-tion to the Am/
Pu parent-daughter ratio for CRMs 136-138 relevant fornondestructive nuclear forensics chronometry, the new branching ratios resultedin improved uncertainty on separation dates. These results support the methodof using microcalorimetry for measuring gamma branching ratios.The uncertainty budget (see Figure 6) demonstrates that although uncer-tainty is currently limited by poisson statistics, the ultimate limiting uncertaintycomes from the fixed branching ratios which have uncertainties around 0.5% to1.0%. Future work will entail using improved pixel arrays to get more countingstatistics on the well-characterized CBNM and CRM 136–138 reference materi-als.
8. Acknowledgements
This work was supported by the G. T. Seaborg Institute, the US Depart-ment of Energy (DOE) Nuclear Energy’s Fuel Cycle Research and Develop-ment (FCR&D), Materials Protection, Accounting and Control Technologies(MPACT) Campaign and Nuclear Energy University Program (NEUP), andthe NIST Innovations in Measurement Science program.
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