# ASTM E261-16

Designation: E261 − 16Standard Practice forDetermining Neutron Fluence, Fluence Rate, and Spectra byRadioactivation Techniques1This standard is issued under the fixed designation E261; 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 practice describes procedures for the determinationof neutron fluence rate, fluence, and energy spectra from theradioactivity that is induced in a detector specimen.1.2 The practice is directed toward the determination ofthese quantities in connection with radiation effects on mate-rials.1.3 For application of these techniques to reactor vesselsurveillance, see also Test Methods E1005.1.4 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.NOTE 1—Detailed methods for individual detectors are given in thefollowing ASTM test methods: E262, E263, E264, E265, E266, E343,E393, E481, E523, E526, E704, E705, and E854.2. Referenced Documents2.1 ASTM Standards:2E170 Terminology Relating to Radiation Measurements andDosimetryE181 Test Methods for Detector Calibration and Analysis ofRadionuclidesE262 Test Method for Determining Thermal Neutron Reac-tion Rates and Thermal Neutron Fluence Rates by Radio-activation TechniquesE263 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of IronE264 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of NickelE265 Test Method for Measuring Reaction Rates and Fast-Neutron Fluences by Radioactivation of Sulfur-32E266 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of AluminumE343 Test Method for Measuring Reaction Rates by Analy-sis of Molybdenum-99 Radioactivity From Fission Do-simeters (Withdrawn 2002)3E393 Test Method for Measuring Reaction Rates by Analy-sis of Barium-140 From Fission DosimetersE481 Test Method for Measuring Neutron Fluence Rates byRadioactivation of Cobalt and SilverE523 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of CopperE526 Test Method for Measuring Fast-Neutron ReactionRates by Radioactivation of TitaniumE693 Practice for Characterizing Neutron Exposures in Ironand Low Alloy Steels in Terms of Displacements PerAtom (DPA), E 706(ID)E704 Test Method for Measuring Reaction Rates by Radio-activation of Uranium-238E705 Test Method for Measuring Reaction Rates by Radio-activation of Neptunium-237E722 Practice for Characterizing Neutron Fluence Spectra inTerms of an Equivalent Monoenergetic Neutron Fluencefor Radiation-Hardness Testing of ElectronicsE844 Guide for Sensor Set Design and Irradiation forReactor Surveillance, E 706 (IIC)E854 Test Method for Application and Analysis of SolidState Track Recorder (SSTR) Monitors for ReactorSurveillance, E706(IIIB)E944 Guide for Application of Neutron Spectrum Adjust-ment Methods in Reactor Surveillance, E 706 (IIA)E1005 Test Method for Application and Analysis of Radio-metric Monitors for Reactor Vessel SurveillanceE1018 Guide for Application of ASTM Evaluated CrossSection Data File, Matrix E706 (IIB)E2005 Guide for Benchmark Testing of Reactor Dosimetryin Standard and Reference Neutron Fields1This practice is under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applications and is the direct responsibility of SubcommitteeE10.05 on Nuclear Radiation Metrology.Current edition approved Oct. 1, 2016. Published November 2016. Originallyapproved in 1965 as E261 – 65 T. Last previous edition approved in 2015 asE261 – 15. DOI: 10.1520/E0261-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States12.2 ISO Standard:JCGM 100:2008 Evaluation of measurement data—Guide tothe expression of uncertainty in measurementJCGM 104:2009 Evaluation of measurement data—An in-troduction to the “Guide to the expression of uncertaintyin measurement” and related documentsJCGM 101:2008 Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncer-tainty in measurement” – Propogation of distributionsusing a Monte Carlo methodJCGM 102:2011 Evaluation of measurement data—Supplement 2 to the “Guide to the expression of uncer-tainty in measurement” – Extension to any number ofoutput quantitiesJCGM 106:2012 Evaluation of measurement data—The roleof measurement uncertainty in conformity assessment3. Terminology3.1 Descriptions of terms relating to dosimetry are found inTerminology E170.4. Summary of Practice4.1 A sample containing a known amount of the nuclide tobe activated is placed in the neutron field. The sample isremoved after a measured period of time and the inducedactivity is determined.5. Significance and Use5.1 Transmutation Processes—The effect on materials ofbombardment by neutrons depends on the energy of theneutrons; therefore, it is important that the energy distributionof the neutron fluence, as well as the total fluence, bedetermined.6. Counting Apparatus6.1 A number of instruments are used to determine thedisintegration rate of the radioactive product of the neutron-induced reaction. These include the scintillation counters,ionization chambers, proportional counters, Geiger tubes, andsolid state detectors. Recommendations of counters for particu-lar applications are given in Test Methods E181.7. Requirements for Activation-Detector Materials7.1 Considerations concerning the suitability of a materialfor use as an activation detector are found in Guide E844.7.2 The amounts of fissionable material needed for fissionthreshold detectors are rather small and the availability of thematerial is limited. Licenses from the U.S. Nuclear RegulatoryCommission are required for possession.7.3 A detailed description of procedures for the use offission threshold detectors is given in Test Methods E343,E393, and E854, and Guide E844.8. Irradiation Procedures8.1 The irradiations are carried out in two ways dependingupon whether the instantaneous fluence rate or the fluence isbeing determined. For fluence rate, irradiate the detector for ashort period at sufficiently low power that handling difficultiesand shielding requirements are minimized. Then extrapolatethe resulting fluence rate value to the value anticipated for fullreactor power. This technique is sometimes used for the fluencemapping of reactors (1, 2).48.2 The determination of fluence is most often required inexperiments on radiation effects on materials. Irradiate thedetectors for the same duration as the experiment at a positionin the reactor where, as closely as possible, they will experi-ence the same fluence, or will bracket the fluence of theposition of interest. When feasible, place the detectors in theexperiment capsule. In this case, long-term irradiations areoften required.8.3 It is desirable, but not required, that the neutron detectorbe irradiated during the entire time period considered and thata measurable part of the activity generated during the initialperiod of irradiation be present in the detector at the end of theirradiation. Therefore, the effective half-life, t 1/2= 0.693/λ (see Eq 6), of the reaction product should not be much less thanthe total elapsed time from the initial exposure to the finalshutdown.8.4 As mentioned in 9.10 through 9.11, the use of cadmium-shielded detectors is convenient in separating contributions tothe measured activity from thermal (E170) and epithermal(E170) neutrons. Also, cadmium shielding is helpful in reduc-ing activities due to impurities and the loss of the activatednuclide by thermal-neutron absorption. The recommendedthicknesses of cadmium is 1 mm. When bare and cadmium-shielded samples are placed in the same vicinity, take care toavoid partial shielding of the bare detectors by the cadmium-shielded ones.9. Calculation9.1 Fluence:9.1.1 φ(E, t) is the differential neutron fluence rate; that is,the fluence rate per unit energy per unit time for neutrons withenergies between E and E + dE. When focusing on the neutronspectrum, the notation φ(E) is sometimes used. φ(E) has animplicit dependence on time. In many cases, the neutronspectrum does not vary with time.9.1.2 The neutron fluence rate φ is the integral over energyof the differential neutron fluence rate.φ 5 * φ~E!dE (1)φ has an implicit dependence on time.9.1.3 φ(E) may be determined by computer calculationsusing neutron transport codes or by adjustment techniquesusing radioactivation data from multiple-foil irradiations.9.1.4 The neutron fluence, Φ, is related to the time varyingdifferential neutron fluence rate by the following expression:Φ 5 *0`*t1t2φ~E,t!dt dE (2)where:t2–t1= duration of the irradiation period4The boldface numbers in parentheses refer to a list of references at the end ofthis standard.E261 − 1629.2 Spectrum-Averaged Cross Sections:9.2.1 Spectrum-averaged cross sections (E170) are used inreaction rate calculations.Aspectrum-averaged cross section isdefined as follows:σ¯ 5*0`σ ~E! φ~E! dE*0`φ ~E! dE(3)where:σ(E) = microscopic cross section for the isotope and reactionof interest. σ¯ has an implicit dependence on time andmay change if the neutron spectrum changes.9.2.2 In order to calculate the spectrum-averaged crosssection, the differential cross section of the nuclide and theneutron spectrum over the neutron energy range for which thenuclide has a non-negligible cross section must be known.When cross-section and spectrum information are notavailable, alternative procedures may be used; suggested alter-natives are discussed in 9.10 – 9.12, and in the methods forindividual detectors.9.3 Reaction Rate:9.3.1 The reaction rate per nucleus, RR, for a given reactionis related to the fluence rate by:RR5 *0`σR~E!φ~E!dE (4)where:σR(E) = microscopic cross section for the isotope and reac-tion of interest.9.3.2 It follows that:RR5 σ¯Rφ or φ 5RRσ¯R(5)9.4 Effective Decay Constant:9.4.1 The effective decay constant, λ , which may be afunction of time, is related to the decay constant λ as follows:λ 5 λ1*0`σa~E!φ~E! dE (6)where:σa(E) = the neutron absorption cross section for the productnuclide.9.4.2 The effective decay constant accounts for burnup of aproduct nuclide during irradiation. Application of the effectivedecay constant for irradiation under varying fluence rates isdiscussed in this section and in the detailed methods forindividual detectors.9.5 Activity:9.5.1 The activity of the sample, A, is the decay rate of theproduct nuclei of interest, Np.A 5 Npλ (7)The activity at the end of the exposure period is calculatedfrom an activation foil count rate as follows:A 5 λD/@~1 2 exp~2λ tc!!exp~2λ tw!# (8)where:λ = decay constant for the radioactive nuclide,tc= time interval for counting,tw= time elapsed between the end of the irradiation periodand the start of the counting period, andD = number of disintegrations (net number of counts cor-rected for background, random and true coincidencelosses, efficiency of the counting system, and fractionof the sample counted) in the interval tc.9.5.2 If, as is often the case, the counting period is shortcompared to the half-life ( = 0.693⁄λ) of the radioactivenuclide, the activity is well approximated as follows:A 5 D/@tcexp~2λ tw!# (9)9.5.3 The number of radioactive product nuclei, Np,isrelated to the reaction rate by the following equation:dNp⁄dt 5 NRR2 Npλ (10)9.5.4 Solution of Eq 10, for the case where the neutronspectrum and N are constant and Np=0 at t=0, yields thefollowing expression for the activity of a foil:A 5 Npλ 5 ~λ ⁄ λ !NRR~1 2 exp~2λ ti!! (11)9.5.5 For irradiations at constant fluence rate, the saturationactivity (E170), As, is calculated as follows:As5 A/~1 2 exp~2λ ti!! (12)where:ti= exposure duration.It follows from Eq 11 and Eq 12 that:AS5 ~λ ⁄ λ ! NRR(13)The saturation activity corresponds to the number of disin-tegrations per foil per unit time for the steady-state condition inwhich the rate of production of the radioactive nuclide is equalto the rate of loss by radioactive decay and transmutation. Theactivity A approaches the saturation activity, As, but does notsurpass it, as the exposure duration increases (exp(-λ t)→0).9.5.6 The isotopic content of the target nuclide may bereduced during the irradiation by more than one transmutationprocess and it may be increased by transmutation of othernuclides so that the rate of change of the number of targetnuclei with time is described by a number of terms:dN/dt 52NSRR1(t51nRiD1(j51mNjRj(14)where:i = discrete transmutation path for removal of the targetisotope, andj = discrete transmutation reaction whereby the target iso-tope is produced from isotope Njand each of the RiandRjterms could be calculated from equations similar toEq 4, using the appropriate cross sections.9.5.6.1 The RRterm may predominate and, if RRis constant,Eq 14 can be solved asN 5 N0exp ~2 RRt! (15)using the approximation that the change in target composi-tion is negligible and replacing N by N0.9.5.6.2 During irradiation, the effective decay rate may beincreased by transmutations of the product isotope (see Eq 6).E261 − 1639.6 Long Term Irradiations:9.6.1 Long irradiations for materials testing programs andreactor pressure vessel surveillance are common. Long irradia-tions usually involve operation at various power levels, includ-ing extended zero-power periods; thus, appropriate correctionsmust be made for depletion of the target nuclide, decay andburnout of the radioactive nuclide, and variations in neutronfluence rate. Multiple irradiations and nuclide burnup must alsobe considered in short-irradiation calculations where reaction-product half-lives are relatively short and nuclide cross sec-tions are high.9.6.2 Long irradiations usually involve operation at variouspower levels, and changes in isotopic content of the system;under such conditions φ(E, t) can show large variations withtime.9.6.3 It is usual to assume, however, that the neutron fluencerate is directly proportional to reactor power; under theseconditions, the fluence can be well approximated by:Φ 5SφPD(i51nPiti(16)where:φ/P = average value of the neutron fluence rate, φ,atareference power level, P,ti= duration of the ithoperating period during which thereactor operated at approximately constant power,andPi= reactor power level during that operating period.9.6.3.1 Alternate methods include measuring the powergener