Designation: C1500 − 08 (Reapproved 2017)Standard Test Method forNondestructive Assay of Plutonium by Passive NeutronMultiplicity Counting1This standard is issued under the fixed designation C1500; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method describes the nondestructive assay ofplutonium in forms such as metal, oxide, scrap, residue, orwaste using passive neutron multiplicity counting. This testmethod provides results that are usually more accurate thanconventional neutron coincidence counting. The method can beapplied to a large variety of plutonium items in variouscontainers including cans, 208-L drums, or 1900-L StandardWaste Boxes. It has been used to assay items whose plutoniumcontent ranges from1gto1000s of g.1.2 There are several electronics or mathematical ap-proaches available for multiplicity analysis, including themultiplicity shift register, the Euratom Time CorrelationAnalyzer, and the List Mode Module, as described briefly inRef. (1).21.3 This test method is primarily intended to address theassay of240Pu-effective by moments-based multiplicity analy-sis using shift register electronics (1, 2, 3) and high efficiencyneutron counters specifically designed for multiplicity analysis.1.4 This test method requires knowledge of the relativeabundances of the plutonium isotopes to determine the totalplutonium mass (See Test Method C1030).1.5 This test method may also be applied to modifiedneutron coincidence counters (4) which were not specificallydesigned as multiplicity counters (that is, HLNCC, AWCC,etc), with a corresponding degradation of results.1.6 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.7 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3C1030 Test Method for Determination of Plutonium IsotopicComposition by Gamma-Ray SpectrometryC1207 Test Method for Nondestructive Assay of Plutoniumin Scrap and Waste by Passive Neutron CoincidenceCountingC1458 Test Method for Nondestructive Assay of Plutonium,Tritium and241Am by Calorimetric AssayC1490 Guide for the Selection, Training and Qualification ofNondestructive Assay (NDA) PersonnelC1592 Guide for Nondestructive Assay MeasurementsC1673 Terminology of C26.10 Nondestructive Assay Meth-ods3. Terminology3.1 Definitions:3.1.1 Terms shall be defined in accordance with Terminol-ogy C1673 except for the following:3.1.2 gate fractions, n—the fraction of the total coincidenceevents that occur within the coincidence gate.3.1.2.1 doubles gate fraction (fd),n—the fraction of thetheoretical double coincidences that can be detected within thecoincidence gate (see Eq 1).3.1.2.2 triples gate fraction (ft),n—the fraction of thetheoretical triple coincidences that can be detected within thecoincidence gate (see Eq 2).3.1.3 factorial moment of order, n—this is a derived quantitycalculated by summing the neutron multiplicity distributionweighted by ν!/(ν – n)! where n is the order of the moment.3.1.4 induced fission neutron multiplicities (νi1, νi2, νi3),n—the factorial moments of the induced fission neutron mul-tiplicity distribution. Typically multiplicity analysis will utilize1This test method is under the jurisdiction of ASTM Committee C26 on NuclearFuel Cycle and is the direct responsibility of Subcommittee C26.10 on NonDestructive Assay.Current edition approved Jan. 1, 2017. Published January 2017. Originallyapproved in 2002. Last previous edition approved in 2008 as C1500 – 08. DOI:10.1520/C1500-08R17.2The boldface numbers in parentheses refer to the list of references at the end ofthis standard.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1the data from fast neutron-induced fission of239Pu to calculatethese moments (5, 6).4. Summary of Test Method4.1 The item is placed in the sample chamber or “well” ofthe multiplicity counter, and the emitted neutrons are detectedby the3He tubes that surround the well.4.2 The detected neutron multiplicity distribution is pro-cessed by the multiplicity shift register electronics package toobtain the number of neutrons of each multiplicity in the (R +A) and (A) gates. Gates are pictorially depicted in Fig. 1.4.3 The first three moments of the (R + A) and (A)multiplicity distributions are computed to obtain the singles (ortotals), the doubles (or reals), and the triples. Using these threecalculated values, it is possible to solve for 3 unknown itemproperties, the240Pu-effective mass, the self-multiplication,and the α ratio. Details of the calculations may be found inAnnex A1.4.4 The total plutonium mass is then determined from theknown plutonium isotopic ratios and the240Pu-effective mass.4.5 Corrections are routinely made for neutron background,cosmic ray effects, small changes in detector efficiency withtime, and electronic deadtimes.4.6 Optional algorithms are available to correct for thebiases caused by spatial variations in self-multiplication orchanges in the neutron die-away time.4.7 Multiplicity counters should be carefully designed byMonte Carlo techniques to minimize variations in detectionefficiency caused by spatial effects and energy spectrumeffects. Corrections are not routinely made for neutron detec-tion efficiency variations across the item, energy spectrumeffects on detection efficiency, or neutron capture in the item.5. Significance and Use5.1 This test method is useful for determining the plutoniumcontent of items such as impure Pu oxide, mixed Pu/U oxide,oxidized Pu metal, Pu scrap and waste, Pu process residues,and weapons components.5.2 Measurements made with this test method may besuitable for safeguards or waste characterization requirementssuch as:5.2.1 Nuclear materials accountability,5.2.2 Inventory verification (7),5.2.3 Confirmation of nuclear materials content (8),5.2.4 Resolution of shipper/receiver differences (9),5.2.5 Excess weapons materials inspections (10, 11),5.2.6 Safeguards termination on waste (12, 13),5.2.7 Determination of fissile equivalent content (14).5.3 A significant feature of neutron multiplicity counting isits ability to capture more information than neutron coinci-dence counting because of the availability of a third measuredparameter, leading to reduced measurement bias for mostmaterial categories for which suitable precision can be at-tained. This feature also makes it possible to assay somein-plant materials that are not amenable to conventionalcoincidence counting, including moist or impure plutoniumoxide, oxidized metal, and some categories of scrap, waste, andresidues (10).5.4 Calibration for many material types does not requirerepresentative standards. Thus, the technique can be used forinventory verification without calibration standards (7), al-though measurement bias may be lower if representativestandards were available.5.4.1 The repeatability of the measurement results due tocounting statistics is related to the quantity of nuclear material,interfering neutrons, and the count time of the measurement(15).5.4.2 For certain materials such as small Pu, items of lessthan 1 g, some Pu-bearing waste, or very impure Pu processresidues where the (α,n) reaction rate overwhelms the triplessignal, multiplicity information may not be useful because ofthe poor counting statistics of the triple coincidences withinpractical counting times (12).5.5 For pure Pu metal, pure oxide, or other well-characterized materials, the additional multiplicity informationis not needed, and conventional coincidence counting willprovide better repeatability because the low counting statisticsFIG. 1 (a) Simplified probability distribution showing the approximately exponential decay, as a function of time, for detecting a secondneutron from a single fission event. The probability of detecting a random neutron is constant with time. (b) Typical coincidence timingparameters.C1500 − 08 (2017)2of the triple coincidences are not used. Conventional coinci-dence information can be obtained either by changing tocoincidence analyzer mode, or analyzing the multiplicity datain coincidence mode.5.6 The mathematical analysis of neutron multiplicity datais based on several assumptions that are detailed in Annex A1.The mathematical model considered is a point in space, withassumptions that neutron detection efficiency, die-away time,and multiplication are constant across the entire item (16, 17).As the measurement deviates from these assumptions, thebiases will increase.5.6.1 Bias in passive neutron multiplicity measurements isrelated to deviations from the “point model” such as variationsin detection efficiency, matrix composition, or distribution ofnuclear material in the item’s interior.5.6.2 Heterogeneity in the distribution of nuclear material,neutron moderators, and neutron absorbers may introducebiases that affect the accuracy of the results. Measurementsmade on items with homogeneous contents will be moreaccurate than those made on items with inhomogeneouscontents.6. Interferences6.1 For measurements of items containing one or morelumps that are each several hundred grams or more ofplutonium metal, multiplication effects are not adequatelycorrected by the point model analysis (18). Variable-multiplication bias corrections must be applied.6.2 For items with high (α,n) reaction rates, the additionaluncorrelated neutrons will significantly increase the accidentalcoincidence rate. The practical application of multiplicitycounting is usually limited to items where the ratio of (α,n) tospontaneous fission neutrons (α) is low, that is, less than 10 (7).6.3 For measurement of large items with high (α,n) reactionrates, the neutrons from (α,n) reactions can introduce biases iftheir energy spectra are different from the spontaneous fissionenergy spectrum. The ratio of the singles in the inner and outerrings can provide a warning flag for this effect (19).6.3.1 High mass, high α items will produce large count rateswith large accidental coincidence rates. Sometimes this pre-vents obtaining a meaningful result.6.4 Neutron moderation by low atomic mass materials in theitem affects neutron detection efficiency, neutron multiplicationin the item, and neutron absorption by poisons. For nominallevels of neutron moderation, the multiplicity analysis willautomatically correct the assay for changes in multiplication.The presence of neutron poisons or other absorbers in themeasurement item will introduce bias. Determination of thecorrection factors required for these items will have to beindividually determined.6.5 It is important to keep neutron background levels fromexternal sources as low and constant as practical for measure-ment of low Pu mass items. High backgrounds may produce abias during measurement. This becomes important as pluto-nium mass decreases.6.6 Cosmic rays can produce single, double, and tripleneutrons from spallation events within the detector or nearbyhardware. The relative effect is greatest on the triples, and nextgreatest on the doubles. Cosmic ray effects increase in signifi-cance for assay items containing large quantities of high atomicnumber matrix constituents and small gram quantities ofplutonium. Multiplicity data analysis software packages shouldinclude correction algorithms for count bursts caused bycosmic rays.6.7 Other spontaneous fission nuclides (for example, curiumor californium) will increase the coincident neutron countrates, causing a positive bias in the plutonium assay thatmultiplicity counting does not correct for. The triples/doublesratio can sometimes be used as a warning flag.6.8 Total counting rates should be limited to about 900 kHzto limit the triples deadtime correction to about 50 % and toensure that less than 25 % of the shift register steps areoccupied. Otherwise incorrect assay results may be obtaineddue to inadequate electronic deadtime corrections.6.9 Unless instrument design takes high gamma-ray fieldinto account, high gamma-ray exposure levels from the itemmay interfere with the neutron measurement through pile-upeffects if the dose is higher than about 1 R/h at the3He tubes.7. Apparatus7.1 Multiplicity Counters:7.1.1 Neutron multiplicity counters are similar in design andconstruction to conventional neutron coincidence counters, asdescribed in Test Method C1207. Both are thermal neutrondetector systems that utilize polyethylene-moderated3He pro-portional counters. However, multiplicity counters are de-signed to maximize neutron counting efficiency and minimizeneutron die-away time, with detection efficiencies that aremuch less dependent on neutron energy. Cylindrical multiplic-ity well counters typically have 3 to 5 rings of3He tubes andabsolute neutron detection efficiencies of 40 to 60 %, whereasconventional coincidence counters typically have 1 or 2 ringsof3He tubes and efficiencies of 15 to 25 %. A multiplicitycounter for the assay of cans of plutonium is illustrated in Fig.2 (20).7.1.2 Multiplicity counters are designed to keep the radialand axial efficiency profile of the sample cavity as flat aspossible (within several percent) to minimize the effects ofitem placement or item size in the cavity. Provision forreproducible item positioning in the cavity is still recom-mended for best results.7.1.3 Multiplicity counters are designed with a nearly flatneutron detection efficiency as a function of the neutron energyspectrum, largely through the use of multiple rings of3Hetubes placed at different depths in the polyethylene moderatormaterial.7.1.4 Multiplicity counters usually have a thick externallayer of polyethylene shielding to reduce the contribution ofbackground neutrons from external sources.7.1.5 Existing conventional neutron coincidence countersare sometimes used for multiplicity analysis. The quality of themultiplicity results will depend on the extent to which theconverted counters meet the multiplicity design criteria giv