ASTM E262-17

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E262 − 13 E262 − 17
Standard Test Method for
Determining Thermal Neutron Reaction Rates and Thermal
Neutron Fluence Rates by Radioactivation Techniques
This standard is issued under the fixed designation E262; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 The purpose of this test method is to define a general procedure for determining an unknown thermal-neutron fluence rate
by neutron activation techniques. It is not practicable to describe completely a technique applicable to the large number of
experimental situations that require the measurement of a thermal-neutron fluence rate. Therefore, this method is presented so that
the user may adapt to histheir particular situation the fundamental procedures of the following techniques.
1.1.1 Radiometric counting technique using pure cobalt, pure gold, pure indium, cobalt-aluminum, alloy, gold-aluminum alloy,
or indium-aluminum alloy.
1.1.2 Standard comparison technique using pure gold, or gold-aluminum alloy, and
1.1.3 Secondary standard comparison techniques using pure indium, indium-aluminum alloy, pure dysprosium, or dysprosium-
aluminum alloy.
1.2 The techniques presented are limited to measurements at room temperatures. However, special problems when making
thermal-neutron fluence rate measurements in high-temperature environments are discussed in 9.2. For those circumstances where
the use of cadmium as a thermal shield is undesirable because of potential spectrum perturbations or of temperatures above the
melting point of cadmium, the method described in Test Method E481 can be used in some cases. Alternatively, gadolinium filters
may be used instead of cadmium. For high temperature applications in which aluminum alloys are unsuitable, other alloys such
as cobalt-nickel or cobalt-vanadium have been used.
1.3 This test method may be used to determine the equivalent 2200 m/s fluence rate. The accurate determination of the actual
thermal neutron fluence rate requires knowledge of the neutron temperature, and determination of the neutron temperature is not
within the scope of the standard.
1.4 The techniques presented are suitable only for neutron fields having a significant thermal neutron component, in which
moderating materials are present, and for which the average scattering cross section is large compared to the average absorption
cross section in the thermal neutron energy range.
1.5 Table 1 indicates the useful neutron-fluence ranges for each detector material.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.7 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.
2. Referenced Documents
2.1 ASTM Standards:
E170 Terminology Relating to Radiation Measurements and Dosimetry
E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
E181 Test Methods for Detector Calibration and Analysis of Radionuclides
This method is under the jurisdiction of ASTM Committee E10 on Nuclear Technology and Applicationsand is the direct responsibility of Subcommittee E10.05 on
Nuclear Radiation Metrology.
Current edition approved Jan. 1, 2013Aug. 1, 2017. Published February 2013September 2017. Originally approved in 1965. Last previous edition approved in 20082013
as E262-08.-13. DOI: 10.1520/E0262-13.10.1520/E0262-17.
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
Standardsvolume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E262 − 17
TABLE 1 Useful Neutron Fluence Ranges of Foil Material
' Useful Range
Foil Material Form
(neutrons/cm )
3 12
Indium pure or alloyed with 10 to 10
aluminum
7 14
Gold pure or alloyed with 10 to 10
aluminum
3 10
Dysprosium pure or alloyed with 10 to 10
aluminum
14 20
Cobalt pure or alloyed with 10 to 10
aluminum
E261 Practice for Determining Neutron Fluence, Fluence Rate, and Spectra by Radioactivation Techniques
E481 Test Method for Measuring Neutron Fluence Rates by Radioactivation of Cobalt and Silver
3. Terminology
3.1 cadmium ratio—see Terminology E170.
3.2 Calibration Techniques:
3.2.1 radiometric—the radiometric technique uses foil properties, decay properties of the activation product, the detector
efficiency, and cross section to derive the neutron fluence rate. When beta counting is used, it becomes problematic to determine
the absolute detector efficiency, and calibration is usually performed by exposing the foil to a Standard or Secondary Standard field.
3.2.2 standard comparison—the standard comparison technique compares activity from a foil irradiated in a standard ofor
reference field to the activity from a foil irradiated in the unknown field to derive the neutron fluence rate.
3.2.3 secondary standard comparison—the secondary standard comparison technique is the same as the standard comparison
technique, except that the reference field is not a well-calibrated national reference, and is usually local to the facility. This is
sometimes done because a foil with a short half-life undergoes too much decay in transit from a Standardstandard source.
3.2.3.1 Discussion—
The standard comparison technique is the most accurate. Among the foils discussed in this standard, only gold has a suitable
half-life for standard counting: long enough to allow transport of the foil from the standards laboratory to the facility for counting,
and short enough to allow reuse of the foil. One might consider moving the radiation detector to the national standard location to
accommodate a short half-life.
3.3 equivalent 2200 m/s fluence—see Terminology E170.
3.4 foil—material whose induced radioactivity is used to help determine the properties of a neutron field. Typical foil shapes
are thin discs or rectangles, but wire segments are another common shape. In this document, all activation materials of every shape
will be called “foils” for the sake of brevity. Foils are also often called “radiometric dosimeters” or “radiometric monitors.”
3.5 Maxwell-Boltzmann distribution—the Maxwell-Boltzman distribution is a probability distribution which describes the
energy or velocity distribution of particles in equilibrium at a given temperature. For neutrons, this is given by:
1/2
2 E
2E/kT
n~E!dE 5 n e dE
th 3/2
~kT!
=π
or
3⁄2
mv
4 m
~ !
2 2 2kT
n v dv 5 n v e dv
~ ! S D
th
2kT
=
π
where:
n = the number of thermal neutrons per volume,
th
m = the neutron mass (931 MeV),
−5 −1
k = Boltzmann’s constant (8.617 × 10 ev K ,
T = the neutron temperature,
v and E = the neutron velocity and energy, respectively.
3.6 thermal neutron fluence rate (Φ )—
th
`
v·n v dv
* ~ !
where:
v = the neutron velocity and n(v) is the thermal neutron density as a function of velocity.
E262 − 17
3.7 Thermal neutron fluence rate conventions:
3.7.1 Stoughton and Halperin convention—the neutron spectrum is separated into a thermal part and a 1/E part. The 2200 m/s
neutron fluence rate, Φ , is the hypothetical neutron fluence rate in which all the thermal neutrons have a velocity of 2200 m/s.
The 1/E part of the spectrum is not included. The Stoughton and Halperin convention is followed in this standard.
3.7.2 Westcott convention—Φ is the hypothetical neutron fluence rate in which all the neutrons have a velocity of 2200 m/s,
which gives the same activation as the total neutron fluence incident on a 1/v detector.
3.7.2.1 Discussion—
See Theory section and Precision and Bias section for further discussion.
3.7 Thermal neutron fluence rate conventions:
3.7.1 Stoughton and Halperin convention—the neutron spectrum is separated into a thermal part and a 1/E part. The 2200 m/s
neutron fluence rate, Φ , is the hypothetical neutron fluence rate in which all the thermal neutrons have a velocity of 2200 m/s.
The 1/E part of the spectrum is not included. The Stoughton and Halperin convention is followed in this standard.
3.7.2 Westcott convention—Φ is the hypothetical neutron fluence rate in which all the neutrons have a velocity of 2200 m/s,
which gives the same activation as the total neutron fluence incident on a 1/v detector.
3.7.2.1 Discussion—
See Theory section and Precision and Bias section for further discussion.
3.7.3 Hogdahl convention—the Hogdahl convention is similar to the Stoughton and Halperin convention, but separates out the
subcadmium fluence as a separate entitity, φ . See Practice E261 for further discussion.
sc
3.8 thermal neutrons—See Terminology E170.
3.9 neutron temperature, T—an adjustable parameter used to give the best fit of a calculated or measured thermal neutron speed
distribution to the Maxwell-Boltzmann distribution. Because of increasing absorption for lower energy neutrons, the neutron
temperature is usually higher than the temperature of the moderating materials in the system of interest.
3.10 2200 m/s cross section—see Terminology E170.
4. Significance and Use
4.1 This test method can be extended to use any material that has the necessary nuclear and activation properties that suit the
experimenter’s particular situation. No attempt has been made to fully describe the myriad problems of counting techniques,
neutron-fluence depression, and thick-foil self-shielding. It is assumed that the experimenter will refer to existing literature on these
subjects. This test method does offer a referee technique (the standard gold foil irradiation at National Institute of Standards and
Technology (NIST)) foil) to aid the experimenter when he isthey are in doubt of histheir ability to perform the radiometric
technique with sufficient accuracy.
4.2 The standard comparison technique uses a set of foils that are as nearly identical as possible in shape and mass. The foils
are fabricated from any material that activates by an (n, γ) reaction, preferably having a cross section approximately inversely
proportional to neutron speed in the thermal energy range. Some of the foils are irradiated in a known neutron field (at NIST) or
other standards laboratory). The foils are counted in a fixed geometry on a stable radiation-detecting instrument. The neutron
induced neutron-induced reaction rate of the foils is computed from the counting data, and the ratio of the known neutron fluence
rate to the computed reaction rate is determined. For any given foil, neutron energy spectrum, and counting set-up, this ratio is a
constant. Other foils from the identical set can now be exposed to an unknown neutron field. The magnitude of the fluence rate
in the unknown field can be obtained by comparing the reaction rates as determined from the counting data from the unknown and
reference field, with proper corrections to account for spectral differences between the two fields (see Section 5). One important
feature of this technique is that it eliminates the need for knowing the detector efficiency.
4.3 This test method follows the Stoughton and Halperin convention for reporting thermal neutron fluence. Other conventions
are the Wescott convention (followed in Test Method E481) and the Hogdahl convention. Practice E261 explains the three
conventions and gives conversion formulae relating values determined by the different conventions. Reference (1) discusses the
three thermal-neutron conventions in detail.
5. Theory
5.1 1/v Cross Sections—It is not possible using radioactivation techniques to determine the true thermal neutron fluence rate
without making some assumptions about the spectral shapes of both the thermal and epithermal components of the neutron density.
The boldface numbers in parentheses refer to the list of references appended to this method.
E262 − 17
For most purposes, however, the information required is only that needed to make calculations of activation and other reaction rates
for various materials exposed to the neutron field. For reactions in which the cross section varies inversely as the neutron speed
(1/v cross sections) the reaction rates are proportional to the total neutron density and do not depend on the spectrum shape. Many
radioactivation detectors have reaction cross sections in the thermal energy range which approximate to 1/v cross sections (1/v
detectors). Departures from the 1/v shape can be accounted for by means of correction factors.
5.2 Fluence Rate Conventions:
5.2.1 The purpose of a fluence rate convention (formerly called “flux convention”) is to describe a neutron field in terms of a
few parameters that can be conveniently used to calculate reaction rates. The best known fluence rate conventions relating to
thermal neutron fields are the Westcott convention (2) and the Stoughton and Halperin convention (3). Both make use of the
concept of an equivalent 2200 m/s fluence rate, that is equal to the product of the neutron density and the standard speed, v , equal
to 2200 m/s which is the most probable speed of Maxwellian thermal neutrons when the characteristic temperature is 293.59°K.
In the Westcott convention, it is the total neutron density (thermal plus epithermal) which is multiplied by v to form the “Westcott
flux”, but in the Stoughton and Halperin convention, the conventional fluence rate is the product of the Maxwellian thermal neutron
density and v . The latter convention is the one followed in this method:
φ 5 n v (1)
0 th 0
where φ is the equivalent (or conventional) 2200 m/s thermal fluence rate and n represents the thermal neutron density, which
0 th
is proportional to the reaction rate per atom in a 1/v detector exposed to thermal neutrons:
R 5 n σ v 5 σ φ (2)
~ !
s th 0 0 0 0
R 5 n σ v 5 σ φ (2)
0 th 0 0 0 0
5.2.2 (R ) represents only that part of the reaction rate that is induced by thermal neutrons, which have the Maxwellian
s 0
spectrum shape. σ is the 2200 m/s cross section. For a non-1/v detector Eq 2 needs to be replaced by:
~R ! 5 n gσ v 5 gσ φ (3)
s th 0 0 0 0
R 5 n gσ v 5 gσ φ (3)
0 th 0 0 0 0
where g is a correction factor that accounts for the departures from the ideal 1/v detector cross section in the thermal energy
range. The same factor appears in the Westcott convention Ref (2), and is usually referred to as the Westcott g factor. g depends
on the neutron temperature, T, , and is defined as follows:
n
3 3⁄2 2
1 ` 4 v T v T
0 0
g 5 ·exp 2 σ v dv (4)
* S DS D F S DS DG ~ !
1/2
v σ π v T v T
0 0 0 0
5.2.3 If the thermal neutron spectrum truly follows the Maxwellian distribution and if the neutron temperature is known, it is
possible to calculate the true thermal neutron fluence rate by multiplying the conventional (equivalent 2200 m/s) thermal fluence
rate by the factor:
1⁄2
v 4T
n
5 (5)
S D
v πT
0 0
1⁄2
v 4T
5 (5)
S D
v πT
0 0
where v is the Maxwellian mean speed for neutron temperature T, and T is the standard temperature of 293.4°K. This conversion
is most often unnecessary and is usually not made because the temperature T may be unknown. Naturally, it is essential when
reporting results to be absolutely clear whether the true thermal fluence rate or the equivalent 2200 m/s thermal fluence rate or the
equivalent 2200 m/s total (Westcott) fluence rate is used. If the true thermal fluence rate is used, then its value must be accompanied
by the associated temperature value.
5.3 Epithermal Neutrons—In order to determine the effects of epithermal neutrons, that are invariably present together with
thermal neutrons, cadmium covered foil irradiations are made. It is important to realize that some epithermal neutrons can have
energies below the effective cadmium cut-off energy, E . The lowest energy of epithermal neutrons is usually taken to be equal
cd
to 5kT (where k is Boltzmann’s constant) that is equal to 0.13 eV for room temperature (293°K) neutrons (2), though 4 kT has been
recommended for some reactors (4). In order to correct for these, it is necessary to make some assumption about the epithermal
neutron spectrum shape, and the assumption made in Refs 2 and 3 is that the epithermal neutron fluence rate per unit energy is
proportional to 1/E:
φ E 5 φ /E E$ 5kT (6)
~ !
e e
where φ is an epithermal fluence parameter equal to the fluence rate per unit energy, φ (E), at 1 eV. This assumption is usually
e e
adequate for the purpose of correcting thermal neutron fluence rate measurements for epithermal neutrons at energies below the
(1+α)
cadmium cut-off. To represent the epithermal fluence more correctly, however, many authors have shown that the use of a 1/E
spectrum shape is preferable, where α is an empirical parameter. Refs (5-11).
E262 − 17
5.4 Resonance Integral:
5.4.1 The resonance integral for an ideal dilute detector is defined as follows:
` dE
I 5 σ~E! (7)
*
E
E
cd
5.4.2 The cadmium cut-off energy is taken to be 0.55 eV for a cylindrical cadmium box of wall thickness 1 mm. (12). The data
needed to correct for epithermal neutron reactions in the methods described are the values of I /gσ for each reaction (see Table
0 0
2). These values, taken from Refs (13-15), are based on integral measurements.
5.5 Reaction Rate:
5.5.1 The reaction rate per atom, for an isotope exposed to a mixed thermal and epithermal neutron field is given by:
R 5 φ gσ 1φ gσ @f 1w'/g1I /gσ # (8)
s 0 0 e 0 1 0 0
R 5 φ gσ 1φ gσ @f 1w'/g1I /gσ # (8)
0 0 e 0 1 0 0
f is a function that describes the epithermal activation of a 1/v detector in the energy range 5kT to E :
1 cd
1⁄2
E kT dE
cd
f 5 (9)
*
S D
5kT E E
5.5.2 For E equal to 0.55eV and T equal to 293.4°K, f = 0.468. w' in Eq 8 is a function which accounts for departure of the
cd 0 1
cross section from the 1/v law in the energy range 5kT to E :
cd
1⁄2
1 E kT dE
cd
w'5 σ~E! 2 gσ (10)
* F S D G
5kT
σ E E
Some values of w' for T equal 293.4°K are given in Table 2.
5.5.3 For a cadmium covered foil, the reaction rate is given as:
R 5 φ I (11)
s,Cd e 0
R 5 φ I (11)
Cd e 0
5.5.4 This can be used to eliminate the unknown epithermal fluence rate parameter, φ , from Eq 8. After rearrangement, one
e
obtains an expression for the saturation activity due to thermal neutrons only:
gσ σ w'
0 0
φ gσ 5 R 5 R 2 R 11 f 1 (12)
~ !
S D
0 0 s 0 s s,Cd 1
I I
0 0
gσ σ w'
0 0
φ gσ 5 R 5 R 2 R 11 f 1 (12)
S D
0 0 0 Cd 1
I I
0 0
5.6 Neutron Self-Shielding:
5.6.1 Unless extremely thin or dilute alloy materials are used, all of the measurement methods are subject to the effects of
neutron self-shielding. The modified version of Eq 12 which takes into account both a thermal self-shielding factor G , and an
th
epithermal self shielding factor G is:
res
TABLE 2 Nuclear Data from References (16, 13, 15, 17)
I
g (T =
Reaction σ barns w'
gσ
293 K) 0
59 60
Co(n,γ) Co 37.233 ± 0.16 % 1.0 1.98 ± .034 0
197 198
Au(n,γ) Au 98.69 ± 0.09 % 1.005 15.7 ± 0.3 .0500
115 116
ln(n,γ) ln 166.413 ± 0.6 % 1.0194 15.8 ± 0.5 .2953
164 165
Dy(n,γ) Dy 2650 ± 2.6 % 0.987 0.13 ± 0.01 0
TABLE 2 Nuclear Data from References
I
g (T =
A
Reaction σ barns w'
0 A
gσ
300 K) 0
59 60 B C
Co(n,γ) Co 37.18 ± 0.16 % 1.000 1.98 ± .034 0
197 198 B C
Au(n,γ) Au 98.65 ± 0.09 % 1.005 15.7 ± 0.3 .0500
115 116 A C
ln(n,γ) ln 159 ± 1 % 1.020 16.01 ± 0.51 .2953
164 165 A D
Dy(n,γ) Dy 2650 ± 2.6 % 0.987 0.13 ± 0.01 0
A 116m
Ref 16. σ adjusted from ln by 0.79.
B
Ref 15.
C
Ref 17.
D
Ref 13.
E262 − 17
R
φ gσ 5
0 0
G
th
~R !
s 0
φ gσ 5 (13)
0 0
G
th
1 gσ σ w'
0 0
5 R 2 R 11 f 1 (13)
F S DG
s s,Cd 1
G G I G I
th res 0 res 0
1 gσ σ w'
0 0
5 R 2 R 11 f 1 (13)
F S DG
Cd 1
G G I G I
th res 0 res 0
5.6.2 Values of the self-shielding factors G and G for several foils and wires are given in Tables 3-7. In the literature, values
th res
for the resonance self-shielding factor are given in two ways, and those must not be confused. G , as used here, is a factor by
res
which multiplies the resonance integral as defined in Eq 7. G' is a self-shielding factor that multiplies the reduced resonance
res
integral from which the 1/v part of the cross section has been subtracted. The necessary conversion factor that has been applied
where needed in Tables 3-7 is:
gσ
G 5 G' 1~12 G' ! 0.429 (14)
res res res
I
5.7 The tables in this test method may be used to provide self-shielding factors. For materials and dimensions not in the tables,
neutron transport codes may be used. Reference (1) provides formulae for determining self-shielding for foils and wires.
5.8 Fluence Depression Factors—Thermal fluence depression is an additional perturbation that occurs when an absorber is
surrounded by a moderator. Because the effects are sensitive to the details of individual situations, it is not possible to provide
correction factors here. References (24-32) describe these effects. The problem is avoided when foils are exposed in cavities of
very large volume compared to the detector volume. In other cases, a rough guide is that the external perturbation effect is usually
less than the thermal self-shielding effect, and much less when the hydrogenous moderator is absent.
6. Apparatus
6.1 Radiation-Detection Instruments:
6.1.1 The radiation detectors that may be used in neutron activation techniques are described in the Standard Methods, E181.
In addition, or as an alternative, a calibration high-pressure ionization chamber may be used. Details for its construction and
calibration may be found in Ref (33).
6.2 Precision Punch:
6.2.1 A precision punch is required to fabricate a set of identical foils for the standard foil technique. The punch must cut foils
that have smooth edges. Since finding such a punch commercially available is difficult, it is recommended that the punch be custom
made. It is possible to have several dies made to fit one punch so that a variety of foil sizes can be obtained. Normally, foil
diameters are 12.7 mm (0.500 in.) or less. The precision punch is one of the most important items in the standard foil technique
particularly if the counting technique includes β or soft-photon events.
6.3 Aluminum and Cadmium Boxes:
6.3.1 One set of foils must be irradiated in cadmium boxes or covers to determine that part of the neutron activation resulting
from absorption of epicadmium neutrons. The cadmium box must be constructed so that the entire foil is surrounded by 1 mm
(0.040 in.) of cadmium. This can be accomplished by using a circular cup-shaped design as shown in Fig. 1. To eliminate
positioning errors, aluminum boxes identical to the cadmium boxes should be used for the “bare” or total neutron activation
measurements. Small-bore cadmium tubing having 1 mm walls is commercially available for use with wires.
7. Materials and Manufacture
7.1 The four materials required for the techniques in this method are cobalt, gold, indium, and dysprosium. These metals are
available commercially in very pure form (at least 99.9 %) and can be obtained in either foil or wire form. Cobalt, gold, indium,
TABLE 3 Resonance Self-Shielding Data for Cobalt Foils
(Reference(Ref (18))
Foil Thickness
G'
res
G
res
(132 eV)
(in.) (cm)
0.0004 0.001018 0.8264 0.864
0.0010 0.00254 0.7000 0.765
0.0025 0.00635 0.5470 0.645
0.0050 0.0127 0.4395 0.561
0.0075 0.01905 0.3831 0.517
0.010 0.0254 0.3476 0.489
0.015 0.0381 0.3028 0.454
0.020 0.0508 0.2744 0.432
E262 − 17
TABLE 4 Thermal and Resonance Self-Shielding Data for Cobalt Wires (Reference(Ref (19))
Wire diameter
Cobalt content
G' (132 eV) G G
res th res
(mass %)
(in.) (cm)
0.050 0.127 0.104 1.00 1.00 1.00
0.050 0.127 0.976 0.95 ± 0.04 0.99 ± 0.01 0.96
0.001 0.00254 100 0.81 ± 0.03 0.99 ± 0.02 0.85
0.005 0.01270 100 0.52 ± 0.02 0.97 ± 0.01 0.62
0.010 0.0254 100 0.42 ± 0.02 0.94 ± 0.01 0.55
0.015 0.0381 100 0.38 ± 0.01 0.92 ± 0.02 0.51
0.020 0.0508 100 0.34 ± 0.01 0.90 ± 0.02 0.48
0.025 0.0635 100 0.32 ± 0.01 0.88 ± 0.03 0.47
TABLE 5 Resonance Self-Shielding Data for Gold Foils
(References(Refs 20 and 21)
Foil Thickness G G (G -G )/G
res res theo exp exp
I (barn)
(cm) (theory) (experiment) (%)
–6
2 × 10 1556.83 0.9936 . . . . . .
–6
4 × 10 1550.04 0.9893 . . . . . .
–6
8 × 10 1577.91 0.9815 . . . . . .
–5
2 × 10 1507.41 0.9621 0.9644 –0.24
–5
4 × 10 1465.83 0.9355 0.9340 +0.16
–5
8 × 10 1398.77 0.8927 0.8852 +0.85
–4
2 × 10 1252.38 0.7993 0.7852 +1.80
–4
4 × 10 1088.91 0.6950 0.6836 +1.66
–4
8 × 10 890.482 0.5683 0.5612 +1.27
–3
2 × 10 628.570 0.4012 0.3952 +1.51
–3
4 × 10 468.493 0.2990 0.3020 –0.99
–3
8 × 10 347.671 0.2219 0.2219 –0.0036
–2
2 × 10 234.983 0.1450 0.1505 –0.35
TABLE 6 Resonance Self-Shielding Data for Gold Wires
(Reference(Ref 22)
Wire Diameter
Average
G
Nominal Average res
(cm)
–3 –3
(10 in.) (10 in.)
0.5 0.505 0.00128 0.703
1.0 0.98 0.00249 0.552
2.0 1.98 0.00503 0.410
4.0 4.05 0.01029 0.302
6.0 6.02 0.01529 0.258
8.0 7.98 0.02027 0.228
10.0 10.01 0.02542 0.208
and dysprosium are also available as an alloy with aluminum, for example NIST Standard Reference Material 953. The alloy
dilutions are useful for extending the range of measurement ofto higher neutron fluences; in the case of indium, the alloy has the
additional advantage of mechanical strength. Pure indium is so soft that it must be handled with extreme care to prevent distortions
in the precision punched foils. The use of alloys results in uncertainties and nonuniformity of alloy concentrations, but reduces the
self-shielding corrections and their uncertainties.
8. Procedure
8.1 Cobalt Method (Radiometric Technique):
8.1.1 Pure cobalt wire, 0.127 mm (0.005 in.) in diameter will conveniently monitor thermal neutron fluences in the range of 10
18 –2
to 10 cm . Cobalt-aluminum alloy wire of the same diameter (0.50 % by weight of cobalt or less) can be used for higher
20 –2
fluences. Burn-up of the target material needs to be considered at fluences above 10 cm . The neutron reaction involved is
59 60 60
Co(n,γ) Co. Co emits two gamma rays per disintegration in cascade with energies of 1.17 and 1.33 MeV having a half-life
60m 60
of 1925.23 days (34). Co is also formed in the reaction, but this isometric state decays to Co by means of a single 0.0586
MeV gamma ray having a half-life of 10.467 min (1635).
8.1.2 The equivalent 2200 m/s thermal fluence rate in which a thin sample of cobalt has been irradiated may be calculated as
follows:
R
s
φ 5 (15)
gσ
E262 − 17
TABLE 7 Self-Shielding Calculations for Indium and Gold Foils (Ref 23)
Natural
Natural indium
gold foil
foil thickness G G G /G G G G /G
res th res th res th res th
thickness
(mg/cm )
(mg/cm )
0.05 0.988 1.000 0.988 0.05 0.994 1.000 0.994
0.1 0.977 1.000 0.977 0.1 0.987 1.000 0.987
0.2 0.959 0.999 0.960 0.2 0.975 1.000 0.975
0.5 0.920 0.998 0.922 0.5 0.950 1.000 0.950
1.0 0.868 0.997 0.870 0.075 0.931 0.999 0.932
2.0 0.796 0.993 0.801 1.0 0.919 0.999 0.920
5.0 0.649 0.987 0.658 2.0 0.867 0.998 0.869
10 0.519 0.976 0.531 3.0 0.828 0.997 0.830
20 0.400 0.956 0.417 5.0 0.763 0.995 0.767
30 0.334 0.939 0.357 7.5 0.698 0.994 0.702
40 0.294 0.924 0.319 10 0.645 0.993 0.650
60 0.243 0.897 0.271 20 0.521 0.985 0.529
100 0.192 0.850 0.226 40 0.410 0.969 0.423
150 0.156 0.800 0.195 60 0.347 0.959 0.362
200 0.134 0.759 0.177 120 0.264 0.930 0.283
250 0.120 0.720 0.167 240 0.202 0.882 0.229
FIG. 1 Side View of Cadmium Box Cross Section
R
φ 5 (15)
gσ
where:
R = reaction rate per target atom,
s
σ = 2200 m/s cross section.
R = reaction rate per target atom,
σ = 2200 m/s cross section,
g = Wescott g factor.
8.1.3 The reaction rate is given by
C exp λt
~ !
w
R 5 (16)
s
εN 12 exp 2λt
~ ~ ~ !!!
0 i
C exp~λt !
w
R 5 (16)
εN 12 exp 2λt
~ ~ ~ !!!
0 i
where:
C = net counting rate of Co in the sample at the time of measurement, corrected for background radiations,
–9 –1 60
λ = decay constant of 4.170 × 10 s corresponding to the half-life of Co of 1925.5 days,
N = original number of atoms of nuclide to be activated (given by the product of the weight in grams of Co in the sample
and Avogadro’s number divided by the atomic weight, 58.9332, in g),
ε = efficiency of the detector for Co radiation in the given geometry,
t = duration of the exposure, and
i
t = elapsed time from the end of the exposure period to the time of counting.
w
8.1.4 When the exposure time is small compared to the 1925.5-day half-life of Co, as is usually the case, we may write
12 exp~2λt !'λt (17)
i i
Eq 15 becomes
φ 5 C exp λt /λt N σ ε (18)
~ !
0 w i 0 0
8.1.5 The fluence over the irradiation period is
Φ5 φ t 5 C exp λt /λN σ ε (19)
~ !
0 i w 0 0
E262 − 17
8.1.6 If the cobalt sample has been activated in a neutron spectrum that is not totally thermalized, then the reaction rate must
be corrected for epithermal neutron activation. This is done by irradiating a similar cobalt sample shielded by cadmium (1 mm
(0.040-in.) thick) and using Eq 13 which yields,
1 gσ f σ w'
0 1 0
Φ5 C 2 C 11 1 (20)
S S DD
B cd
G G I G I
th res 0 res 0
·exp λt /λN gσ ε
~ !
w 0 0
where C and C are the Co counting rates in the bare and cadmium-covered samples, respectively. In practice, the 0.127-mm
B cd
cobalt wire cannot be considered a thin sample. The self-shielding effects of the wire are accounted for by the G and G factors
th res
in Eq 20 (see also Tables 4 and 5). If the cobalt-aluminum alloy (0.50 % by weight of cobalt or less) is being used, no self-shielding
correction factors are needed.
8.1.7 There are two methods for obtaining the detection efficiency for the Co in the sample. The first method uses a
high-pressure ionization chamber, a heavily shielded well-type counter that almost completely surrounds the sample being counted
with an ionization volume, thereby allowing for essentially 4-π geometry to detect the radiation. A voltage placed across the
collecting electrodes generates a current proportional to the number of ions produced, which in turn is proportional to the sample
source strength. Measure the current, expressed as the voltage drop across precision resistors, with a potentiometer. Calibrate the
60 60
chamber for Co with a Co gamma source having a certified activity which is traceable to a National Standard. A calibration
constant S, expressed as disintegrations per second per volt, is thereby obtained. Accordingly, the disintegration rate of the cobalt
wire sample is the product of S multiplied by the voltage reading obtained.
8.1.8 A second method for determining the disintegration rate in the cobalt sample as described in Method E181, makes use of
60 6
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