ASTM E261-16(2021)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E261 − 16 (Reapproved 2021)
Standard Practice for
Determining Neutron Fluence, Fluence Rate, and Spectra by
Radioactivation Techniques
This standard is issued under the fixed designation E261; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope tion Rates and Thermal Neutron Fluence Rates by Radio-
activation Techniques
1.1 Thispracticedescribesproceduresforthedetermination
E263Test Method for Measuring Fast-Neutron Reaction
of neutron fluence rate, fluence, and energy spectra from the
Rates by Radioactivation of Iron
radioactivity that is induced in a detector specimen.
E264Test Method for Measuring Fast-Neutron Reaction
1.2 The practice is directed toward the determination of
Rates by Radioactivation of Nickel
these quantities in connection with radiation effects on mate-
E265Test Method for Measuring Reaction Rates and Fast-
rials.
Neutron Fluences by Radioactivation of Sulfur-32
1.3 For application of these techniques to reactor vessel E266Test Method for Measuring Fast-Neutron Reaction
Rates by Radioactivation of Aluminum
surveillance, see also Test Methods E1005.
E343Test Method for Measuring Reaction Rates by Analy-
1.4 This standard does not purport to address all of the
sis of Molybdenum-99 Radioactivity From Fission Do-
safety concerns, if any, associated with its use. It is the
simeters (Withdrawn 2002)
responsibility of the user of this standard to establish appro-
E393Test Method for Measuring Reaction Rates by Analy-
priate safety, health, and environmental practices and deter-
sis of Barium-140 From Fission Dosimeters
mine the applicability of regulatory limitations prior to use.
E481Test Method for Measuring Neutron Fluence Rates by
NOTE 1—Detailed methods for individual detectors are given in the
Radioactivation of Cobalt and Silver
following ASTM test methods: E262, E263, E264, E265, E266, E343,
E523Test Method for Measuring Fast-Neutron Reaction
E393, E481, E523, E526, E704, E705, and E854.
Rates by Radioactivation of Copper
1.5 This international standard was developed in accor-
E526Test Method for Measuring Fast-Neutron Reaction
dance with internationally recognized principles on standard-
Rates by Radioactivation of Titanium
ization established in the Decision on Principles for the
E693Practice for Characterizing Neutron Exposures in Iron
Development of International Standards, Guides and Recom-
and Low Alloy Steels in Terms of Displacements Per
mendations issued by the World Trade Organization Technical
Atom (DPA)
Barriers to Trade (TBT) Committee.
E704Test Method for Measuring Reaction Rates by Radio-
activation of Uranium-238
2. Referenced Documents
E705Test Method for Measuring Reaction Rates by Radio-
2.1 ASTM Standards:
activation of Neptunium-237
E170Terminology Relating to Radiation Measurements and
E722PracticeforCharacterizingNeutronFluenceSpectrain
Dosimetry
Terms of an Equivalent Monoenergetic Neutron Fluence
E181Test Methods for Detector Calibration andAnalysis of
for Radiation-Hardness Testing of Electronics
Radionuclides
E844Guide for Sensor Set Design and Irradiation for
E262Test Method for Determining Thermal Neutron Reac-
Reactor Surveillance
E854Test Method for Application and Analysis of Solid
State Track Recorder (SSTR) Monitors for Reactor Sur-
This practice is under the jurisdiction of ASTM Committee E10 on Nuclear
veillance
Technology and Applications and is the direct responsibility of Subcommittee
E944Guide for Application of Neutron Spectrum Adjust-
E10.05 on Nuclear Radiation Metrology.
ment Methods in Reactor Surveillance
Current edition approved Sept. 1, 2021. Published October 2021. Originally
approved in 1965 as E261–65T. Last previous edition approved in 2016 as E1005Test Method for Application and Analysis of Radio-
E261–16. DOI: 10.1520/E0261-16R21.
metric Monitors for Reactor Vessel Surveillance
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on The last approved version of this historical standard is referenced on
the ASTM website. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E261 − 16 (2021)
E1018Guide for Application of ASTM Evaluated Cross 8. Irradiation Procedures
Section Data File
8.1 The irradiations are carried out in two ways depending
E2005Guide for Benchmark Testing of Reactor Dosimetry
upon whether the instantaneous fluence rate or the fluence is
in Standard and Reference Neutron Fields
being determined. For fluence rate, irradiate the detector for a
2.2 ISO Standard: short period at sufficiently low power that handling difficulties
JCGM100:2008Evaluationofmeasurementdata—Guideto
and shielding requirements are minimized. Then extrapolate
the expression of uncertainty in measurement the resulting fluence rate value to the value anticipated for full
JCGM 104:2009Evaluation of measurement data—An in-
reactorpower.Thistechniqueissometimesusedforthefluence
troduction to the “Guide to the expression of uncertainty mapping of reactors (1, 2).
in measurement” and related documents
8.2 The determination of fluence is most often required in
JCGM 101:2008 Evaluation of measurement data—
experiments on radiation effects on materials. Irradiate the
Supplement 1 to the “Guide to the expression of uncer-
detectors for the same duration as the experiment at a position
tainty in measurement” – Propogation of distributions
in the reactor where, as closely as possible, they will experi-
using a Monte Carlo method
ence the same fluence, or will bracket the fluence of the
JCGM 102:2011 Evaluation of measurement data—
position of interest. When feasible, place the detectors in the
Supplement 2 to the “Guide to the expression of uncer-
experiment capsule. In this case, long-term irradiations are
tainty in measurement” – Extension to any number of
often required.
output quantities
8.3 Itisdesirable,butnotrequired,thattheneutrondetector
JCGM 106:2012Evaluation of measurement data—The role
be irradiated during the entire time period considered and that
of measurement uncertainty in conformity assessment
a measurable part of the activity generated during the initial
period of irradiation be present in the detector at the end of the
3. Terminology
irradiation. Therefore, the effective half-life, t' = 0.693/λ'
1/2
3.1 Descriptions of terms relating to dosimetry are found in
(seeEq6),ofthereactionproductshouldnotbemuchlessthan
Terminology E170.
the total elapsed time from the initial exposure to the final
shutdown.
4. Summary of Practice
8.4 Asmentionedin9.10through9.11,theuseofcadmium-
4.1 A sample containing a known amount of the nuclide to
shielded detectors is convenient in separating contributions to
be activated is placed in the neutron field. The sample is
the measured activity from thermal (E170) and epithermal
removed after a measured period of time and the induced
(E170) neutrons.Also, cadmium shielding is helpful in reduc-
activity is determined.
ing activities due to impurities and the loss of the activated
nuclide by thermal-neutron absorption. The recommended
5. Significance and Use
thicknesses of cadmium is 1 mm. When bare and cadmium-
shielded samples are placed in the same vicinity, take care to
5.1 Transmutation Processes—The effect on materials of
bombardment by neutrons depends on the energy of the avoid partial shielding of the bare detectors by the cadmium-
shielded ones.
neutrons; therefore, it is important that the energy distribution
of the neutron fluence, as well as the total fluence, be
9. Calculation
determined.
9.1 Fluence:
6. Counting Apparatus 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 with
6.1 A number of instruments are used to determine the
energies between E and E + dE.When focusing on the neutron
disintegration rate of the radioactive product of the neutron-
spectrum, the notation φ(E) is sometimes used. φ(E) has an
induced reaction. These include the scintillation counters,
implicit dependence on time. In many cases, the neutron
ionization chambers, proportional counters, Geiger tubes, and
spectrum does not vary with time.
solidstatedetectors.Recommendationsofcountersforparticu-
9.1.2 The neutron fluence rate φ is the integral over energy
lar applications are given in Test Methods E181.
of the differential neutron fluence rate.
7. Requirements for Activation-Detector Materials
φ 5 φ E dE (1)
* ~ !
7.1 Considerations concerning the suitability of a material φ has an implicit dependence on time.
for use as an activation detector are found in Guide E844.
9.1.3 φ(E) may be determined by computer calculations
7.2 The amounts of fissionable material needed for fission
using neutron transport codes or by adjustment techniques
threshold detectors are rather small and the availability of the
using radioactivation data from multiple-foil irradiations.
material is limited. Licenses from the U.S. Nuclear Regulatory
9.1.4 The neutron fluence, Φ, is related to the time varying
Commission are required for possession.
differential neutron fluence rate by the following expression:
7.3 A detailed description of procedures for the use of
fission threshold detectors is given in Test Methods E343,
The boldface numbers in parentheses refer to a list of references at the end of
E393, and E854, and Guide E844. this standard.
E261 − 16 (2021)
` t
A 5λD/ 1 2 exp 2λ t exp 2λ t (8)
@~ ~ !! ~ !#
c w
Φ 5 * * φ~E,t!dt dE (2)
0 t
where:
where:
λ = decay constant for the radioactive nuclide,
t –t = duration of the irradiation period
2 1
t = time interval for counting,
c
t = time elapsed between the end of the irradiation period
9.2 Spectrum-Averaged Cross Sections:
w
9.2.1 Spectrum-averaged cross sections (E170) are used in and the start of the counting period, and
D = number of disintegrations (net number of counts cor-
reactionratecalculations.Aspectrum-averagedcrosssectionis
rected for background, random and true coincidence
defined as follows:
losses, efficiency of the counting system, and fraction
`
σ E φ E dE
* ~ ! ~ !
of the sample counted) in the interval t .
c
σ¯ 5 (3)
`
φ E dE
* ~ !
9.5.2 If, as is often the case, the counting period is short
compared to the half-life (=0.693⁄λ) of the radioactive
where:
nuclide, the activity is well approximated as follows:
σ(E) = microscopiccrosssectionfortheisotopeandreaction
A 5 D/@t exp 2λ t # (9)
~ !
c w
of interest.σ¯ has an implicit dependence on time and
may change if the neutron spectrum changes.
9.5.3 The number of radioactive product nuclei, N,is
p
9.2.2 In order to calculate the spectrum-averaged cross
related to the reaction rate by the following equation:
section, the differential cross section of the nuclide and the
dN ⁄dt 5 NR 2 N λ' (10)
p R p
neutron spectrum over the neutron energy range for which the
nuclide has a non-negligible cross section must be known.
9.5.4 Solution of Eq 10, for the case where the neutron
When cross-section and spectrum information are not
spectrum and N are constant and N =0 at t=0, yields the
p
available, alternative procedures may be used; suggested alter-
following expression for the activity of a foil:
natives are discussed in 9.10 – 9.12, and in the methods for
' '
A 5 N λ 5 ~λ ⁄ λ !NR ~1 2 exp~2λ t !! (11)
p R i
individual detectors.
9.5.5 For irradiations at constant fluence rate, the saturation
9.3 Reaction Rate:
activity (E170), A , is calculated as follows:
9.3.1 The reaction rate per nucleus, R , for a given reaction
s
R
'
is related to the fluence rate by:
A 5 A/ 1 2 exp 2λ t (12)
~ ~ !!
s i
`
R 5 σ E φ E dE (4)
* ~ ! ~ !
where:
R R
t = exposure duration.
i
where:
It follows from Eq 11 and Eq 12 that:
σ (E) = microscopic cross section for the isotope and reac-
R
'
tion of interest.
A 5 ~λ ⁄ λ ! NR (13)
S R
9.3.2 It follows that:
The saturation activity corresponds to the number of disin-
R
R
tegrationsperfoilperunittimeforthesteady-stateconditionin
R 5σ¯ φ or φ 5 (5)
R R
σ¯
R
which the rate of production of the radioactive nuclide is equal
9.4 Effective Decay Constant: to the rate of loss by radioactive decay and transmutation. The
9.4.1 The effective decay constant, λ', which may be a activity A approaches the saturation activity, A , but does not
s
function of time, is related to the decay constant λ as follows:
surpass it, as the exposure duration increases (exp(-λ't)→0).
`
9.5.6 The isotopic content of the target nuclide may be
λ' 5λ1 σ E φ E dE (6)
* ~ ! ~ !
a
reduced during the irradiation by more than one transmutation
process and it may be increased by transmutation of other
where:
nuclides so that the rate of change of the number of target
σ (E) = theneutronabsorptioncrosssectionfortheproduct
a
nuclei with time is described by a number of terms:
nuclide.
n m
9.4.2 The effective decay constant accounts for burnup of a
dN/dt52N R 1 R 1 N R (14)
S D
R ( i ( j j
t51 j51
product nuclide during irradiation.Application of the effective
decay constant for irradiation under varying fluence rates is
where:
discussed in this section and in the detailed methods for
i = discrete transmutation path for removal of the target
individual detectors.
isotope, and
9.5 Activity:
j = discrete transmutation reaction whereby the target iso-
9.5.1 The activity of the sample, A, is the decay rate of the
topeisproducedfromisotope N andeachofthe R and
j i
product nuclei of interest, N .
R terms could be calculated from equations similar to
p
j
Eq 4, using the appropriate cross sections.
A 5 N λ (7)
p
9.5.6.1 The R termmaypredominateand,if R isconstant,
The activity at the end of the exposure period is calculated
R R
from an activation foil count rate as follows: Eq 14 can be solved as
E261 − 16 (2021)
N 5 N exp 2 R t (15) 9.6.4.4 Iftheproductof(λ' t)isverysmallforallirradiation
~ !
0 R
i i
using the approximation that the change in target composi-
periods,thevaluesof A calculatedfromEq17areproportional
i
tion is negligible and replacing N by N .
to (R ) and t.
s i i
9.6.4.5 If the spectrum averaged cross section is also con-
9.5.6.2 During irradiation, the effective decay rate may be
stant over all irradiation periods, (R ) is proportional to the
increased by transmutations of the product isotope (see Eq 6).
R i
magnitude of the neutron fluence rate.
9.6 Long Term Irradiations:
9.6.4.6 It is normally assumed that the fluence rate is
9.6.1 Long irradiations for materials testing programs and
directly proportional to the power generation rate in the
reactor pressure vessel surveillance are common. Long irradia-
adjacent fuel.
tionsusuallyinvolveoperationatvariouspowerlevels,includ-
9.6.5 Undertheconditionsassumedin9.6.4.4,Eq17canbe
ing extended zero-power periods; thus, appropriate corrections
written as:
must be made for depletion of the target nuclide, decay and
burnout of the radioactive nuclide, and variations in neutron
A 5 A ~P /P!~1 2 exp~2λ't !! (19)
i S i i
fluencerate.Multipleirradiationsandnuclideburnupmustalso
and Eq 18 can be written as:
be considered in short-irradiation calculations where reaction-
product half-lives are relatively short and nuclide cross sec-
N
i
~A ! 5 A K ~1 2 exp~2λ 't !! (20)
S D
tions are high. n i s i i
N
o
9.6.2 Long irradiations usually involve operation at various
where:
power levels, and changes in isotopic content of the system;
A = the saturation activity corresponding to a reference
under such conditions φ(E, t) can show large variations with s
power level, P,
time.
P = actual power generation rate during the irradiation
i
9.6.3 Itisusualtoassume,however,thattheneutronfluence
period,
rate is directly proportional to reactor power; under these
K =
n
i
P λ'
conditions, the fluence can be well approximated by: j
~P /P!exp 2λ' 11 2 1 t , and
S F S DG D
i ( j
P λ
j5i11
n
φ
Φ 5 P t (16)
S D
( i i
P
i51
N = i21
i
P
j
N exp 2R t .
S D
o R ( j
where:
P
j51
φ/P = average value of the neutron fluence rate, φ,ata
NOTE 2—For a single irradiation period at reference power, K =1.000
i
reference power level, P,
and Eq 20 reduces to Eq 12.
th
t = duration of the i operating period during which the
i
9.6.6 In some cases radioactive products are also produced
reactor operated at approximately constant power,
from radioactive nuclei that built in (for example, fission
and
products produced from Pu that arises from neutron capture
P = reactor power level during that operating period.
i
in U). In these cases the number of atoms of the new target
9.6.3.1 Alternate methods include measuring the power
isotope(s) must be calculated for each time interval and Eq 17
generation rate in a fraction of the reactor volume adjacent to
used to determine the additional activity to be added to that
the volume of interest.
from the original target nuclide.
9.6.4 In a manner similar to power, the activity may be
9.7 The number of target nuclei can often be assumed to be
summed over the reactor operating periods. The activity for
equal to N , the number prior to irradiation.
each operating period decays in subsequent periods, however,
making the summation more complex.
N 5 N Fm/M (21)
0 A
9.6.4.1 The total irradiation period can be divided into a
where:
continuous series of periods during each of which φ(E)is
th
N = Avogadro’s number
essentially constant. Then the activity generated during the i A
23 −1
= 6.022 × 10 mole ,
irradiation period is:
F = atom fraction of the target nuclide in the target
A 5 @λN ~R /λ'! #~1 2 exp~2λ' t !! (17)
i i R i i i
element,
m = mass of target element, g, and
where:
M = atomic mass of the target element.
th
N = number of target atoms during the i period, and
i
th
t = duration of the i period.
i 9.7.1 Calculations of the isotopic concentration after irra-
th
diation is discussed in 9.5 and in the detailed methods for
9.6.4.2 The activity remaining from the i period at the end
th
individual detectors.
of the n period can be calculated as the following equation:
9.7.2 Cross sections should be processed from an appropri-
n
A 5 A exp 2 λ' t (18) ate cross-section library that includes covariance data. Guide
~ ! S D
n i i ( j j
j5i11
E1018 provides information and recommendations on how to
select the cross section library. The International Reactor
9.6.4.3 The total activity of the foil at the end of the
irradiation duration is thus the sum of all the (A ) terms. Dosimetry File (IRDF-2002) (3) is one good source for cross
n i
E261 − 16 (2021)
sections, as is its successor, the International Reactor Dosim- ized by a neutron temperature, T. The reference neutron
etry and Fusion File (4). The SNLRMLcross section compen- temperature, T , is defined as 293.6 K. The neutron tempera-
dium (5) provides a processed fine-group representation of ture T is the value which provides the best fit of the neutron
recommended dosimetry cross sections and covariance matri- spectrumtoaMaxwellianform.Seedefinitioninparagraph3.6
ces. of Test Method E262. When the absorption is not strong the
9.7.3 If spectrum-averaged cross-section or spectrum data neutron temperature should approximate the physical tempera-
ture of the scattering medium, though it commonly exceeds it
arenotavailable,oneofthealternativeproceduresdiscussedin
9.10 to 9.12 may be used to calculate an approximate neutron up to 10 %.
fluence rate from the saturation activity.
9.9.2 The thermal-neutron component overlaps the
epithermal-neutron component somewhat while the
9.8 Lethargy:
epithermal-neutroncomponentandthefast-neutroncomponent
9.8.1 For certain purposes it is more convenient to describe
alsooverlaps.Theexactenergylimitsbetweenthecomponents
a neutron fluence spectrum in terms of fluence per unit
are somewhat arbitrary but the choice is influenced by the
lethargy,Φ(U), rather than in terms of fluence per unit energy,
cross-section characteristics of the isotopes used to detect the
Φ(E). Lethargy, U, is defined as follows:
neutrons in each energy range. The energy limits adopted for
U 5 1n E /E (22)
~ !
this practice are 0 to 0.55 eV for thermal neutrons,
5=T⁄T 0.0253 eV to 0.10 MeV for epithermal neutrons, and
where E =anarbitrarilychosenupperenergylimit;10MeV ~ !
0.10 MeV to ∞ for fast neutrons.
and 14.918 MeV (0.4 lethargy units above 10 MeV) are
energies often chosen for E . The relationship between Φ(U)
9.10 Thermal-Neutron Fluence Rate:
and Φ(E) is:
9.10.1 The thermal-neutron fluence rate is designated as
Φ~U!dU 5 E·Φ~E!dE (23)
(nv) . This represents an integral:
th
`
Neutron spectra are sometimes plotted as E·Φ(E) versus
nv 5 n v vdv (24)
~ ! * ~ !
th
energy. This allows the plotting of a wide range of fluence on
where n(v) is the thermal neutron density as a function of
a linear plot and shows 1/E portions of the spectrum as
velocity, and v is the velocity.
horizontal lines. If plotted with a linear lethargy axis and a
logarithmic energy axis, equal areas have equal fluence. For a Maxwell-Boltzmann thermal neutron distribution of
neutron temperature T:
9.9 Neutron Spectra:
9.9.1 Areactorneutronspectrumcanbeconsideredasbeing
nv 5 n v (25)
~ !
th th T
divided into three idealized energy ranges describing the
=π
neutrons as thermal, epithermal (or resonance), and fast. Since
T
these ranges have distinctive distributions, they are a natural
S v 5 v 5 2200m/s at T 5 T 5 293.6KD (26)
Œ
T 0 0
T
division of neutrons by energy for thermal reactor spectra. 0
9.9.1.1 The neutrons emitted by fission of U have an
9.10.2 Many of the reaction cross sections for thermal
average energy of approximately 2 MeV and the number of
neutrons have a 1/v dependence. For those cases, the reaction
neutrons per unit lethargy interval decreases rapidly on either
rate is independent of the neutron temperature.This is because
side of this average energy. The major portion of the neutrons
the reaction rate is proportional to the neutron velocity times
withenergiesabove1or2MeVare“first-flight”neutrons;that
the neutron cross section. For 1/v cross sections, these terms
is, fission neutrons that have not lost any of their original
cancel.Thisallowstheuseoftheconventionalthermalneutron
energy through interaction with atoms. Thus, the fast-neutron
fluence rate φ :
fluence spectra have the shape of the U fission spectrum,
φ 5 n v (27)
0 th 0
modified by the non-uniform removal of neutrons from some
energy regions by interactions with atoms in the reactor
Here, n isthethermalneutrondensity,and v isanarbitrary
th 0
materials.
neutron velocity, usually taken to be 2200 m/s, the most
9.9.1.2 Neutrons are slowed (lose energy) primarily by
probable speed of the Maxwellian distribution for a standard
elastic interactions with atoms; the average energy lost per
temperatureof20.44°C(293.6K).Inthiscase,thereactionrate
collision is proportional to the neutron energy before the
R for thermal neutrons is:
R,th
interaction. Thus, at lower energies where the “slowing-down
σ v
o o
fluence” becomes much larger than the fluence due to first-
R 5 *σ~E!n ~E! vdE 5 * n ~E!vdE 5 σ v n 5σ φ
R,th th th 0 0 th 0 0
v
flightfissionneutrons,Φ(U)isapproximatelyaconstantovera
(28)
large range of energies and Φ(E) is approximately inversely
σ is the neutron cross section corresponding to v , and is
0 0
proportionaltotheenergy.Thisistheepithermalor1/Eportion
usually called the 2200 m/s cross section.
of the spectrum.
9.9.1.3 At still lower energies, the energy transfer between 9.10.2.1 Thermal neutron cross sections are usually tabu-
the neutrons and atoms is influenced by the thermal vibrations lated as the value for a neutron speed of v = 2200-m/s (See
of the atoms.The thermalized neutrons have a distribution that Table 1). Conventions for thermal neutron fluence rate (see
is approximately Maxwellian (except when a strong neutron Annex A1) use the neutron density multiplied by the standard
absorber is present). The Maxwellian distribution is character- speed of 2200 m/s. The conventional thermal neutron fluence
E261 − 16 (2021)
TABLE 1 Thermal-Neutron Detectors
B
Product Nucleus
Thermal Cross
End Point
Element Reaction D D D Comments
A
C E Yield (%) Yield (%)
γ D
Section (b)
Half-Life
E
β
(keV) γ per Reaction β per Reaction
(keV)
164 165 E
Dysprosium Dy(n,γ) Dy 2650. ± 3.8 % 2.334(1) h 94.700(3) 3.80(5) 1286.6(10) 83.(2)
715.328(20) 0.578(9) 1191.9(9) 15.(2)
1079.63(3) 0.0999(17) 291.5(9) 1.7(2)
115 116m F
Indium In(n,γ) In 166.413 ± 0.6 % 54.29(17) min 1293.56(2) 84.8(12) 1014(4) 54.2(6)
1097.28(2) 58.5(8) 876.(4) 32.5(3)
818.68(2) 12.13(14) 604.(4) 10.3(14)
2112.29(2) 15.09(22)
197 198 G,H
Gold Au(n,γ) Au 98.69 ± 0.14 % 2.6948(12) d 1087.6842(7) 0.1589(18) 960.5(5) 98.990(9)
675.8836(7) 0.805(5)
411.80205(17) 95.62(47)
59 60 G
Cobalt Co(n,γ) Co 37.233 ± 0.16 % 1925.28(14) d 1173.228(3) 99.85(3) 317.05(20) 99.88(3)
1332.492(4) 99.9826(6) 1490.29(20) 0.12(3)
55 56 G
Manganese Mn(n,γ) Mn 13.413 ± 1.5 % 2.5789(1) h 846.7638(19) 98.85(3) 2848.86(21) 56.6(7)
1810.726(4) 26.9(4) 1038.09(21) 27.5(4)
2113.092(6) 14.2(3) 735.70(21) 14.5(3)
23 24 G
Sodium Na(n,γ) Na 0.528 ± 0.95 % 14.997 (12) h 1368.626(5) 99.9935(5) 1392.56(8) 99.855(5)
2754.007(11) 99.872(8)
A
2200 ms cross section (E = 0.0253 eV, T = 20°C), taken from the cross section files recommended in Ref (5). Uncertainty data is taken from Ref (6) for all thermal cross
sections unless otherwise noted.
B
Sources for half life and gamma radiation data in this table are consistent with that from Ref (5).
C
Original source is Ref (7).
D
Original source is Ref (6).
E
Source for cross section is Ref (6). This dosimetry reaction is not in Ref (5).
F
This number represents an update of information in Ref (5) and represents an update in the original source data.
G
Original source for decay radiations is Ref (8). This reference is a standard for detector calibration and takes precedence for isotopes used as calibration standards.
H
Cross sections and uncertainty come from Ref (9).
rate,φ , is the same as that used in the Stoughton and Halperin nor is that necessary for the calculation of other reaction rates
convention, see Eq A1.4. whose cross sections are approximately proportional to 1/v.
9.10.4 It is strongly recommended that Ref (10) be studied,
NOTE3—Usingtheneutrondensitytimes v isnotthesameasusingthe
particularly with regard to the issue of corrections required for
thermal neutron density times v .
theMaxwelliantemperatureofthethermalneutronsandforthe
9.10.3 A detailed procedure for the measurement of
departure of activation detector cross section from a 1/v
thermal-neutronfluencerateisgiveninTestMethodE262.See
behavior. Westcott (11) and others subsequently (12) have
also Test Method E481.
tabulated correction factors, known as Westcott-g-factors,
9.10.3.1 There have been many misunderstandings among
whichcorrecttheresponseoftabulatedreactionsfordepartures
experimenters because various conventions for expressing
of their cross section from the ideal 1/v response in a
thermal fluence are in use. See Annex A1. For example, the
Maxwellianthermalspectrum,atvariousneutrontemperatures,
conventional 2200 m/s thermal-neutron fluence rate, φ,isnot
T. The Wescott g-factor is used in all the thermal neutron
the thermal-neutron fluence rate (nv) from Eq 25
th
fluence conventions discussed in Annex A1, not just the
Westcott convention.
2 T
buta factor smaller:
Œ
9.10.5 When the Westcott g-factor is used, Eq 28 becomes:
T
= 0
π
φ 5 n v 5 R /gσ (30)
0 th 0 R,th 0
T
nv 5 1.128 φ (29)
~ ! Œ
th 0
9.10.6 In order to separate the activities due to thermal and
T
where, in Eq 26 and Eq 29:
epithermal neutrons, bare and cadmium-covered foils are
exposedunderidenticalconditionsandtheactivitiesmeasured.
T = the thermal neutron temperature, a parameter of the
The method, called the cadmium-difference method, is based
Maxwellian distribution chosen to best fit the actual
on the fact that cadmium is an effective absorber of neutrons
thermal neutron spectrum.
below some energy, E , but it passes neutrons of energies
Cd
9.10.3.2 The thermal neutron temperature is typically larger above E . E is known as the “effective cadmium cut-off
Cd Cd
than the physical temperature of the moderator because of the energy” (see Terminology E170). Its value depends upon the
spectrum-hardeningcausedbyabsorption.Becausetheneutron cadmium thickness and other factors (13, 14). For a 1-mm
temperature is often unknown, the conversion from the con- thick cadmium shield in an isotropic neutron field, E may be
Cd
ventional 2200 m/s thermal-neutron fluence-rate to the true taken to be about 0.55 eV. The cadmium ratio (E170), CR, for
thermal-neutron fluence rate using Eq 29, is not usually done, a given neutron flux is:
E261 − 16 (2021)
R Also let the resonance absorption cross section beσ .Then
B
res
CR 5 (31)
R the reaction rate for the cadmium-covered detector is given as
Cd
follows:
where R and R = the reaction rates for the bare and
B Cd
` `
cadmium-covered configurations, respectively.When both epi-
R 5 σ E φ E dE1 σ E φ E dE (35)
* ~ ! ~ ! * ~ ! ~ !
Cd 1/v res
E E
Cd Cd
thermal and thermal neutrons are present in the radiation field,
The analysis of Dancoff (15, 16) makes use of the above
an expression relating the subcadmium fluence rate due to
expressionsandshowsthat,ifthefluencehasa1/Edependence
neutron of energies below E to the reaction rate, R, observed
Cd
for a bare detector, is as follows:
φ E
th Cd
φ 5 Œ (36)
e
R CR 2 1
2 11α CR 2 1 E
~ !~ !
th
φ 5 (32)
sc
gσ CR
o
where E = kT is the energy of neutrons in thermal
th
whereφ istheconventional2200m/ssubcadmium-neutron equilibriumwiththeenvironment(theenergycorrespondingto
sc
fluence rate, which is approximately equal to the 2200 m/s the most probable velocity in the Maxwellian distribution) and
thermal-neutron fluence rate, φ , with small correction factors α is given as follows:
that are defined in A1.2.3 and A1.3.4.
`
σ E φ E dE
* ~ ! ~ !
res
9.10.7 A knowledge of the thermal-neutron fluence rate is E
Cd
α 5 (37)
`
often important in making fast-neutron fluence rate measure-
σ ~E!φ ~E! dE
*
1/v
E
Cd
ments because of interfering activities produced as a result of
thermal-neutron absorption by the nuclide being activated, by or from Eq 33 and Eq 34
its activation products, or by impurities in the test specimen.
=
E ` σ ~E!
Cd res
Alsotheremaybeareductioninthemeasuredactivitybecause
α 5S D dE (38)
*
2k E E
Cd
ofthetransmutationlossor“burn-up”oftheactivationproduct
of the fast-neutron reaction due to thermal-neutron absorption.
The validity of Eq 33 may be tested by determiningφ with
e
Furthermore, thermal-neutron measurements are necessary in
several detectors. If the values of φ are not equal, this is an
e
connectionwithreactorphysicsanalysisandinordertopredict
indication that Eq 33 is not an appropriate assumption. The
the radioactivity in reactor components. Finally, although
integral:
thermal neutrons are not generally capable of producing
` σ ~E!
res
radiation damage in materials by direct neutron collision, * dE (39)
E
E
Cd
indirect mechanisms exist for thermal-neutron damage. One
in Eq 38 is known as the reduced resonance integral.
such mechanism is associated with the atomic displacements
Tabulations of the resonance integral are available (12, 17, 18,
produced upon atomic recoil following thermal-neutron ab-
19, 20), for most resonance detectors. These are usually
sorption and the emission of a capture gamma ray.
tabulated for either E = 0.5 eV or E = 0.55 eV. The
Cd Cd
9.11 Epithermal-Neutron Fluence Rate:
difference is small unless there is a resonance in the neighbor-
9.11.1 In this section, we consider the detection of neutrons
hood of the cadmium cut-off energy. For a l/v-detector, the
with energies extending from those of thermal neutrons to
resonance integral is reduced by 0.0225σ if E is increased
0 Cd
about 0.1 MeV. These neutrons are called epithermal neutrons
from 0.5 eV to 0.55 eV. For thick detector foils, the “effective
or resonance neutrons. In this range of energies, the neutron
resonanceintegral” (18)mustbeused,thatincludescorrections
absorption may be divided into two parts. For the first, the
for self-shielding, Doppler broadening of the resonances, and
cross section varies as the reciprocal of the neutron velocity.
resonance fluence depression. In some tabulations, the term
The second is “resonance absorption,” that is characterized by
“resonance integral” is taken to include the 1/v-absorption
a large increase in cross section over a narrow energy range.
contribution. In Table 2, values of the resonance integral are
For the slowing-down spectrum of certain types of nuclear
given that include the 1/v-absorption contribution. Also, the
reactors, the neutron fluence spectrum in the epithermal range
values refer to infinitely thin foils.
of energies may be considered to be inversely proportional to
9.12 Fast-Neutron Fluence Rate:
the energy. In these cases, we may write the following:
9.12.1 The energy at which to separate “fast neutrons” from
φ
e
“resonanceenergyneutrons”isarbitrarilychosenheretobe0.1
φ~E! 5 (33)
E
MeV. The spectral shape as given by the differential fluence
rate, φ(E), can in principle be determined from the measured
from which it can be shown that the epithermal fluence rate
reactionratesofseveraldetectorsthatareactivatedbydifferent
parameter, φ , is the fluence rate per unit interval in ln(E).
e
parts of the neutron energy spectrum. The effective cross
9.11.2 The cross section for 1/v-absorption is inversely
sectionσ¯ iscalculatedfromEq3foraknownspectrumsimilar
j
proportionaltothespeedoftheneutronortothesquare-rootof
to the spectrum for the unknown field being measured; the
the neutron energy, so that we may write the following:
integral fluence rate is then calculated from the measured
= =
σ 5 k / E 5σ E /E (34)
reaction rate for the detector according to Eq 5. A number of
1/v 0 0 0
detectors are exposed for which trial values of σ¯ have been
j
where:
calculated. The resulting reaction rates can be analyzed,
E = kT = 0.0253 eV
0 0
yieldingacurveforφ(E)versus E.Themethodofobtainingthe
E261 − 16 (2021)
TABLE 2 Resonance Integrals for Various Detector Materials
Such a calibration is useful for reducing experimental and
A,B
Cross Section interpretationalerrorsquiteapartfromthemethodemployedto
Reaction
(barn) % Uncertainty
reduce counting data to a neutron fluence.
U(n,f)FP 269.27 0.27 %
238 −3
9.12.3.1 The fission spectrum is the most widely and con-
U(n,f)FP 2.162 x 10 9.2 %
Pu(n,f)FP 286.96 0.26 %
sistently studied fast-neutron energy distribution. A host of
Am(n,f)FP 8.2550 2.1 %
documented differential measurements define the Cf and
Np(n,f)FP 0.21446 27.2 %
23 24
U fission neutron spectra to better than 62.5% and 65%
Na(n,γ) Na 0.311 3.2 %
45 46
Sc(n,γ) Sc 12.0 4.2 %
respectively, over the primary energy range of 0.25 to 8 MeV
58 59
Fe(n,γ) Fe 1.7 5.9 %
(24, 25, 26). The use of standard fission fields is described in
59 60
Co(n,γ) Co 75.9 2.6 %
63 64
Guide E2005.
Cu(n,γ) Cu 4.97 1.6 %
115 116m
In(n,γ) In 3300 3.0 %
9.12.3.2 TheformofEq5forestablishinganeutronfluence
197 198
Au(n,γ) Au 1550 1.8 %
from individual threshold detector responses based on fission
232 233
Th(n,γ) Th 85 3.5 %
238 239
U(n,γ) U 277 1.1 % spectrum calibration is as follows:
6 4
Li(n,X) He 422.45 0.14 %
10 4 R σ¯
B(n,X) He 1721.06 0.16 % R χ
Φ 5 3 3Φ (42)
s χ
A R σ¯
χ s
Resonance integral uses a 1/E function for the source term and uses integration
limits of 0.5 eV and 100 keV. The fission and (n, α) integrals were computed with
where:
the NJOY94 code using a resonance reconstruction temperature of 300°C and a
reconstruction accuracy of 0.1 %. The (n,γ) capture integrals were taken from Ref
Φ = calibrated neutron fluence for the neutron field under
s
(12).
study,
B
Source for cross sections and covariance matrices is consistent with the
R = measured detector response in the study spectrum (a
recommendations in Ref (5).
R
reaction probability, disintegration rate, or any repro-
ducible activation detector response quantity, for
adjusted neutron energy spectrum, fluence rate, and fluence is example, the gamma counting rate at a fixed time,
corrected for irradiation time history),
discussed in Practice E944, in which the applicable computer
R = measured detector response (equivalent to R ) for the
codes are reviewed. Note that proper application of the
χ R
fission spectrum calibration,
procedure requires prior information on the spectrum shape
σ¯ = spectrum-averaged cross section for the study spec-
which should be obtained by means of neutron transport s
trum (obtained with a spectrum from neutron transport
calculations. The measured reaction rate data result in im-
calculation or from spectrum adjustment schemes
proved precision in the adjusted neutron spectrum.
based on the distinctive threshold responses of a set of
9.12.2 An alternate procedure is to consider the detectors as
integral detectors as described in 9.12.1, 9.12.2, and
havingthresholdproperties.Foranidealthresholddetector,the
elsewhere),
cross section for activation is a step-function; that is, it is zero
σ¯ = spectrum-averaged cross section for the fission spec-
χ
for neutrons with energies below a certain energy E (the
i
trum (calculated with the same detector cross sections
“thresholdenergy”)andconstantforneutronenergiesabove E.
i
used for σ¯ , and with the fission spectrum shape
s
The constant value at energies above E is the “threshold cross
i
associated with the spectrum assumed for the neutron
section,”σ¯ (E>E). Then the effective threshold cross section
j i
field under study, for example, the fission source
for the assumed spectrum, obtained where possible from a
spectrum in a neutron transport calculation), and
transport calculation, is given as follows:
Φ = fission neutron fluence for the detector calibration
χ
` `
σ¯ E.E 5 σ E φ E dE / φ E dE (40)
~ ! * ~ ! ~ ! * ~ ! exposure.
j i @ # @ #
0 E
i
9.12.3.3 Spectrum-averaged cross sections calculated for
The integral in the denominator of this equation is the
235 252
the U and Cf benchmark fission standard fields using the
integral neutron fluence rate with energies above E,φ(E>E).
i i
SNLRML recommended cross sections (5) are given in Table
Hence,theintegralfluencerateaboveenergy E isgiven,inthis
i
3.The 5%, 50%, and 95% response ranges are also indicated
ideal case, as follows:
in the table.
R
R
9.12.3.4 Neutron fluence measurements with activation de-
φ~E.E ! 5 (41)
i
σ¯ ~E.E !
i
tectors depend upon gamma detection efficiencies, number of
where, as before, R , the reaction rate, is determined detector atoms and isotopic abundance, decay constants,
R
experimentally from Eq 13.If φ(E>E) is determined for a branching ratios, fission yields, and competing activities.
i
number of detectors, that is, for a number of values of E, the Calibration in a benchmark neutron field can eliminate most of
i
differentialfluencerate,φ(E),canbededucedbydifferentiating these detector response factors or reduce their error contribu-
the curve of φ(E>E) versus E. tion. In addition, the uncertainty in absolute cross section
i i
9.12.3 Another procedure for obtaining a neutron fluence scales, which is generally difficult to assess, is not involved in
fromasetofthresholddetectorsusingEq5istocalibrateeach the cross section ratio and hence in the fluence determination.
detector in a benchmark neutron field. Fission spectrum neu- Furthermore, the effects of cross section shape errors are
trons are available for this purpose, and for many applications, reduced to the extent that the benchmark and study spectra are
to provide an appropriate energy spectrum (21, 22, 23, 24). similar.
E261 − 16 (2021)
TABLE 3 Fission-Spectrum-Averaged Cross Sections and Related Parameters for Threshold Activation Detectors
252 B 235 C 252 D
Cf Spontaneous Fission Field U Thermal Fission Field Cf Response Range (MeV)
A
E F E F
Reaction
Low Median High
Calculation Observation Calculation Observation
G G
C/E C/E
(mb) (mb) (mb) (mb)
E E E
05 50 95
Np(n,f)FP 1335.046 1361.0 0.981 1330.114 1344.0 0.9897 0.69 2.03 6.06
(9.2 %, 0.23 %) (1.58 %) (9.43 %) (9.33 %, 4.31 %) (4.0 %) (11.0 %)
U(n,f)FP 315.39 325.0 0.970 306.23 309.0 0.991 1.45 2.73 7.12
(0.53 %, 0.4 %) (1.63 %) (1.76 %) (0.53 %, 4.21 %) (2.6 %) (4.98 %)
103 103m
Rh(n,n’) Rh 714.45 757.0 0.944 706.02 733.0 0.963 0.74 2.34 6.05
(3.08 %, 0.27 %) (4.0 %) (5.06 %) (3.1 %, 4.14 %) (5.2 %) (7.33 %)
93 93m
Nb(n,n’) Nb 142.65 149.0 0.957 139.97 146.2 0.957 0.97 2.67 6.08
(3.04 %, 0.36 %) (7.0 %) (7.64 %) (3.06 %, 4.14 %) (8.6 %) (10.02 %)
115 115m
In(n,n’) In 189.8 197.6 0.961 186.35 190.3 0.979 1.13 2.63 6.15
(2.16 %, 0.38 %) (1.3 %) (2.55 %) (2.17 %, 4.17 %) (3.84 %) (6.07 %)
47 47
Ti(n,p) Sc 19.38 19.29 1.005 17.95 19.0 0.946 1.75 3.80 8.17
(3.76%, 0.63%) (1.66 %) (4.16%) (3.7%, 4.26%) (7.4%) (9.3%)
32 32
S(n,p) P 70.44 72.62 0.970 64.69 66.8 0.968 2.31 4.03 7.74
(4.01 %, 0.75 %) (3.5 %) (5.38 %) (4.0 %, 4.86 %) (5.54 %) (8.39 %)
58 58
Ni(n,p) Co 115.31 117.6 0.981 105.69 108.5 0.974 2.05 4.08 7.90
(2.40 %, 0.73 %) (1.3 %) (2.83 %) (2.43 %, 4.52 %) (5.0 %) (7.16 %)
54 54
Fe(n,p) Mn 88.12 86.92 1.014 80.18 80.5 0.996 2.32 4.23 7.93
(2.14 %, 0.79 %) (1.34 %) (2.65 %) (2.17 %, 4.69 %) (2.86 %) (5.91 %)
46 46
Ti(n,p) Sc 12.56 14.09 0.891 10.43 11.6 0.899 3.76 5.90 9.92
(2.45 %, 1.18 %) (1.76 %) (3.24 %) (2.46 %, 5.4 %) (3.45 %) (6.86 %)
56 56
Fe(n,p) Mn 1.370 1.466 0.934 1.029 1.09 0.944 5.51 7.49 11.91
(2.23 %, 1.45 %) (1.77 %) (3.20 %) (2.33 %, 6.58 %) (3.67 %) (7.89 %)
63 60
Cu(n,α) Co 0.678 0.689 0.984 0.521 0.50 1.042 4.65 7.24 11.52
(2.83 %, 1.38 %) (1.98 %) (3.72 %) (2.85 %, 6.05 %) (11.0 %) (12.87 %)
27 23
Al(n,α) Na 1.04 1.017 1.019 0.727 0.706 1.030 6.53 8.61 12.44
(1.36 %, 1.61 %) (1.47 %) (2.57 %) (1.40 %, 6.95 %) (3.97 %) (8.13 %)
A
Cross section and covariance matrices are consistent with the sources detailed in Ref (5).
B
Spectrum taken from Ref (27), MT = 9861, MF = 5, MT = 8. Uncertainty in the spectrum is taken from Ref (27), MT = 9861, MF = 35, MT = 18.
C
Spectrum taken from Ref (27), MT = 9228, MF = 5, MT = 18. Uncertainty in the spectrum is taken from Ref (28).
D
One half of the detector response occurs below an energy given by E ; 95 % of the detector response occurs below E and 5 % below E .
50 95 05
E
The cross section and spectrum components of uncertainty, respectively, appear in parentheses.
F
Observed cross sections are taken from Refs (29), (30), (31), and (32). The measurement uncertainty appears in parentheses.
G
The uncertainty in the ratio represents a sum in quadrature of the experimental uncertainty and the calculated uncertainty.
9.12.3.5 Themagnitudeofcrosssectionerrorsforactivation Tabulationsareavailable(seeTestMethodsE704andE705)
detectors used in dosimetry may be judged from the disagree- for the fission yields of various fission products for several
ment between measurement and prediction for fission neutron fissionable nuclides and for thermal and fast neutrons.
252 235
spectra. An extensive data base for Cf and U fission 9.13.3 Several methods have been used for the collection
sources exists and has been evaluated.The resulting C/E ratios and counting of the fission products; these include (1) direct
are presented in Table 3. countingofthefissionfoil,(seeTestMethodsE704andE705),
(2) an aluminum catcher technique in which Np fission
9.13 Fission Threshold Detectors:
recoils are deposited on a thin aluminum catcher foil and then
9.13.1 The fission threshold detectors are particularly im-
140 137
counted (35, 36, 37), and (3) the counting of Ba, Cs or
portant as fast-neutron detectors because their effective thresh-
other fission products, following chemical separation from the
old energies lie in the low MeV range (see Table 3). The
fission foils (refer to Test Methods E343 and E393), and (4)
detection of neutrons in this range of energies is of special
radiation damage techniques such as Test Method E854.
interest because the peak in the fission spectrum occurs at
239 235
9.13.4 The
...