ASTM C1726/C1726M-10(2018)

Standard Guide for Use of Modeling for Passive Gamma Measurements

SIGNIFICANCE AND USE
5.1 The following methods assist in demonstrating regulatory compliance in such areas as safeguards (Special Nuclear Material), inventory control, criticality control, decontamination and decommissioning, waste disposal, holdup and shipping.  
5.2 This guide can apply to the assay of radionuclides in containers, whose gamma-ray absorption properties can be measured or estimated, for which representative certified standards are not available. It can be applied to in situ measurements, measurement stations, or to laboratory measurements.  
5.3 Some of the modeling techniques described in the guide are suitable for the measurement of fall-out or natural radioactivity homogenously distributed in soil.  
5.4 Source-based efficiency calibrations for laboratory geometries may suffer from inaccuracies due to gamma rays being detected in true coincidence. Modeling can be an advantage since it is unaffected by true coincidence summing effects.
SCOPE
1.1 This guide addresses the use of models with passive gamma-ray measurement systems. Mathematical models based on physical principles can be used to assist in calibration of gamma-ray measurement systems and in analysis of measurement data. Some nondestructive assay (NDA) measurement programs involve the assay of a wide variety of item geometries and matrix combinations for which the development of physical standards are not practical. In these situations, modeling may provide a cost-effective means of meeting user’s data quality objectives.  
1.2 A scientific knowledge of radiation sources and detectors, calibration procedures, geometry and error analysis is needed for users of this standard. This guide assumes that the user has, at a minimum, a basic understanding of these principles and good NDA practices (see Guide C1592/C1592M), as defined for an NDA professional in Guide C1490. The user of this standard must have at least a basic understanding of the software used for modeling. Instructions or further training on the use of such software is beyond the scope of this standard.  
1.3 The focus of this guide is the use of response models for high-purity germanium (HPGe) detector systems for the passive gamma-ray assay of items. Many of the models described in this guide may also be applied to the use of detectors with different resolutions, such as sodium iodide or lanthanum halide. In such cases, an NDA professional should determine the applicability of sections of this guide to the specific application.  
1.4 Techniques discussed in this guide are applicable to modeling a variety of radioactive material including contaminated fields, walls, containers and process equipment.  
1.5 This guide does not purport to discuss modeling for “infinite plane” in situ measurements. This discussion is best covered in ANSI N42.28.  
1.6 This guide does not purport to address the physical concerns of how to make or set up equipment for in situ measurements but only how to select the model for which the in situ measurement data is analyzed.  
1.7 The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in non-conformance with the standard.  
1.8 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.  
1.9 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.

General Information

• Status: Published
• Publication Date: 31-Mar-2018
• ICS: 17.240 - Radiation measurements
• Technical Committee: C26 - Nuclear Fuel Cycle
• Drafting Committee: C26.10 - Non Destructive Assay

Relations

• Replaces: ASTM C1726/C1726M-10 - Standard Guide for Use of Modeling for Passive Gamma Measurements
• Effective Date: 01-Apr-2018
• Refers: ASTM C1673-10a(2018) - Standard Terminology of C26.10 Nondestructive Assay Methods
• Effective Date: 01-Apr-2018
• Refers: ASTM C1673-10ae1 - Standard Terminology of C26.10 Nondestructive Assay Methods
• Effective Date: 01-Nov-2010
• Refers: ASTM C1673-10a - Standard Terminology of C26.10 Nondestructive Assay Methods
• Effective Date: 01-Nov-2010
• Refers: ASTM C1490-04(2010) - Standard Guide for the Selection, Training and Qualification of Nondestructive Assay (NDA) Personnel
• Effective Date: 01-Oct-2010
• Refers: ASTM C1673-10 - Standard Terminology of C26.10 Nondestructive Assay Methods
• Effective Date: 01-Jun-2010
• Refers: ASTM C1673-07e1 - Standard Terminology of C26.10 Nondestructive Assay Methods
• Effective Date: 01-Jun-2007
• Refers: ASTM C1673-07 - Standard Terminology of C26.10 Nondestructive Assay Methods
• Effective Date: 01-Jun-2007
• Refers: ASTM C1490-04 - Standard Guide for the Selection, Training and Qualification of Nondestructive Assay (NDA) Personnel
• Effective Date: 01-Feb-2004
• Refers: ASTM C1490-01 - Standard Guide for the Selection, Training and Qualification of Nondestructive Assay (NDA) Personnel
• Effective Date: 10-Jan-2001
• Referred By: ASTM C1592/C1592M-21 - Standard Guide for Making Quality Nondestructive Assay Measurements
• Effective Date: 01-Apr-2018

Overview

ASTM C1726/C1726M-10(2018), "Standard Guide for Use of Modeling for Passive Gamma Measurements," provides comprehensive guidance on the application of mathematical modeling to support passive gamma-ray measurement systems. Developed by ASTM International, this standard targets nondestructive assay (NDA) professionals who require reliable methods for assay and calibration in situations where physical standards are not practical. By leveraging modeling, users can enhance regulatory compliance in areas such as nuclear safeguards, inventory and criticality control, decontamination, waste disposal, and material holdup.

Passive gamma measurements, when coupled with robust models, serve as an essential tool for quantifying radioactivity in a variety of contexts. This standard is particularly relevant when certified reference standards are unavailable, or when complex sample geometries and matrix compositions impede conventional calibration techniques.

Key Topics

• Mathematical Modeling for Gamma Measurements: The standard explains how models based on physical principles support the calibration and data analysis activities associated with passive gamma-ray detection systems.
• Assay of Complex Samples: Guidance is provided for containers, process equipment, contaminated fields, and irregular source geometries where the absorption properties can be reasonably estimated or measured.
• Techniques and Methods: The guide reviews multiple modeling techniques, such as:
  • Generalized Geometry Holdup
  • Far-Field Approximation
  • Voxel-Intrinsic Efficiency
  • Radiation Transport Code Method
  • Hybrid Monte Carlo Transport Approach
• Measurement Geometry and Detector Types: While focusing on high-purity germanium (HPGe) detector systems, the guide’s principles can also apply to sodium iodide and lanthanum halide detectors.
• Calibration and Uncertainty: Emphasis is placed on understanding the limitations of physical calibration in the presence of true coincidence summing, and how modeling compensates for such effects.
• Validation and Quality Assurance: Importance is placed on verifying model accuracy through experimental validation and cross-checking with reference standards or alternative analytical techniques where feasible.

Applications

• Regulatory Compliance: Demonstrates methods for compliance with nuclear safeguards, criticality safety, inventory management, waste management, decontamination, and decommissioning regulations.
• Nondestructive Analysis: Facilitates measurement of radioactive materials in situations where destructive sampling is impractical, costly, or unsafe.
• Waste Characterization: Suitable for the in situ measurement and laboratory analysis of radioactive waste in containers of varied geometries and matrices, including applications in nuclear facilities and environmental remediation.
• Holdup Measurement: Helps quantify nuclear material retained in process equipment, a critical aspect of facility closure and material accountability.
• Measurement Optimization: Supports detector selection, calibration, and efficiency determination, enabling tailored measurement strategies matched to specific item types and geometries.

Related Standards

• ASTM C1490: Guide for the selection, training, and qualification of NDA personnel.
• ASTM C1592/C1592M: Guide for quality in nondestructive assay measurements.
• ASTM C1673: Terminology of NDA methods.
• ANSI N42.28: Standard for calibration of germanium detectors for in situ gamma-ray measurements.

Practical Value

Applying ASTM C1726/C1726M-10(2018) allows organizations and professionals to:

• Achieve cost-effective, high-quality gamma-ray measurements when physical calibration standards are not available.
• Account for complex geometries, matrix effects, and detector characteristics through validated mathematical models.
• Enhance accuracy and reliability in critical NDA applications, such as nuclear material safeguard, waste characterization, and environmental monitoring.
• Ensure compliance with international standards and regulatory requirements in nuclear safety, security, and environmental protection.

By following this guide, NDA practitioners are equipped with scalable, scientifically sound approaches for passive gamma measurements and benefit from the flexibility and rigor needed for modern nuclear measurement challenges.

Keywords: passive gamma measurements, nondestructive assay, mathematical modeling, calibration, HPGe detector, efficiency, radioactive waste assay, radiation transport, gamma spectroscopy, regulatory compliance.

Standards Content (Sample)

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: C1726/C1726M − 10 (Reapproved 2018)
Standard Guide for
Use of Modeling for Passive Gamma Measurements
This standard is issued under the fixed designation C1726/C1726M; 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 1.6 This guide does not purport to address the physical
concerns of how to make or set up equipment for in situ
1.1 This guide addresses the use of models with passive
measurements but only how to select the model for which the
gamma-ray measurement systems. Mathematical models based
in situ measurement data is analyzed.
on physical principles can be used to assist in calibration of
1.7 The values stated in either SI units or inch-pound units
gamma-ray measurement systems and in analysis of measure-
are to be regarded separately as standard. The values stated in
ment data. Some nondestructive assay (NDA) measurement
programs involve the assay of a wide variety of item geom- each system may not be exact equivalents; therefore, each
system shall be used independently of the other. Combining
etries and matrix combinations for which the development of
physical standards are not practical. In these situations, mod- values from the two systems may result in non-conformance
with the standard.
eling may provide a cost-effective means of meeting user’s
data quality objectives.
1.8 The values stated in inch-pound units are to be regarded
as standard. The values given in parentheses are mathematical
1.2 A scientific knowledge of radiation sources and
conversions to SI units that are provided for information only
detectors, calibration procedures, geometry and error analysis
and are not considered standard.
isneededforusersofthisstandard.Thisguideassumesthatthe
user has, at a minimum, a basic understanding of these
1.9 This international standard was developed in accor-
principles and good NDA practices (see Guide C1592/
dance with internationally recognized principles on standard-
C1592M),asdefinedforanNDAprofessionalinGuideC1490.
ization established in the Decision on Principles for the
The user of this standard must have at least a basic understand-
Development of International Standards, Guides and Recom-
ing of the software used for modeling. Instructions or further
mendations issued by the World Trade Organization Technical
training on the use of such software is beyond the scope of this
Barriers to Trade (TBT) Committee.
standard.
2. Referenced Documents
1.3 The focus of this guide is the use of response models for
2.1 ASTM Standards:
high-purity germanium (HPGe) detector systems for the pas-
C1490 GuidefortheSelection,TrainingandQualificationof
sive gamma-ray assay of items. Many of the models described
Nondestructive Assay (NDA) Personnel
in this guide may also be applied to the use of detectors with
C1592/C1592M Guide for Making Quality Nondestructive
different resolutions, such as sodium iodide or lanthanum
Assay Measurements (Withdrawn 2018)
halide. In such cases, an NDA professional should determine
C1673 Terminology of C26.10 Nondestructive Assay Meth-
the applicability of sections of this guide to the specific
ods
application.
2.2 Other Standard:
1.4 Techniques discussed in this guide are applicable to
ANSI N42.28 Performance Standard for the Calibration of
modeling a variety of radioactive material including contami-
Germanium Detectors for In Situ Gamma-Ray Measure-
nated fields, walls, containers and process equipment.
ments
1.5 This guide does not purport to discuss modeling for
3. Terminology
“infinite plane” in situ measurements. This discussion is best
3.1 See Terminology C1673.
covered in ANSI N42.28.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
This guide is under the jurisdiction ofASTM Committee C26 on Nuclear Fuel Standards volume information, refer to the standard’s Document Summary page on
Cycle and is the direct responsibility of Subcommittee C26.10 on Non Destructive the ASTM website.
Assay. The last approved version of this historical standard is referenced on
Current edition approved April 1, 2018. Published May 2018. Originally www.astm.org.
approved in 2010. Last previous edition approved in 2010 as C1726/C1726M – 10. Available from American National Standards Institute (ANSI), 25 W. 43rd St.,
DOI: 10.1520/C1726_C1726M-10R18. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1726/C1726M − 10 (2018)
4. Summary of Guide being detected in true coincidence. Modeling can be an
advantage since it is unaffected by true coincidence summing
4.1 Passive gamma-ray measurements are applied in con-
effects.
junction with modeling to nondestructively quantify radioac-
tivity.
6. Procedure
4.1.1 Modeling may be used to (1) design and plan the
6.1 Modeling may lead to a bias if any of the measurement
measurements, (2) establish instrument calibration, (3) inter-
parameters do not match the physical characteristics of the
pret the data acquired, (4) quantify contributions to the
item.Uncertaintiesintheitemparametersofthefollowingmay
measurementuncertainty, (5)simulatespectra,and (6)evaluate
lead to a bias:
the effectiveness of shielding.
6.1.1 Matrix distribution is homogenous throughout the
4.1.2 Various models commonly use analytical, numerical
container,
integration and radiation transport approaches. This guide
6.1.2 Hidden containers,
provides a brief review of several approaches to help the user
6.1.3 Matrix identification,
select a suitable method and apply that method appropriately.
6.1.4 Container fill heights,
4.1.3 Modeling makes use of knowledge of the measure-
6.1.5 Mass attenuation coefficients,
ment configuration including the shape, dimensions and mate-
6.1.6 Matrix density,
rials of the detector, collimator, and measurement item content.
6.1.7 Detector parameters, and
4.1.4 The exact geometry may be approximated in the
6.1.8 Physical distribution of radioactivity.
model. The degree of approximation acceptable is assessed on
6.2 If the quantity of nuclear material is “infinitely thick” to
a case by case basis.
the emitted gamma rays, measurement results will be biased.
4.1.5 Process knowledge may be required to provide infor-
This hazard is common when measuring items containing large
mation about inner containers, intervening absorbers, matrix
quantities of heavy elements (for example, thorium, uranium,
materials or which radionuclides are present.
or plutonium) or items with highly attenuating matrices.
4.1.6 The models make use of basic physical interaction
Alternate NDAassay methods are recommended if this condi-
coefficients. Libraries and data sets must be available.
tion exists.
4.1.7 Models are typically used to: (1) account for field of
6.3 Self attenuation, commonly present in lumps of actinide
view and geometry effects, (2) account for matrix attenuation,
material, will bias results low unless lump corrections are
(3) account for container wall and other absorbers, (4) model
computed.
detectors, (5) transfer calibrations from one configuration to
6.4 The Generalized Geometry Holdup Method must be
another, (6) bound the range of assay values due to variations
calibrated with the collimator attached to the detector. If the
in modeling representation parameters, (7) iteratively refine
detector recess changes from the calibration position, the
assessments and decision making based on comparisons with
results will be biased.
observations.
6.5 Absorber foils that are used to reduce count rate must be
4.1.8 Scans may be performed using low-resolution, por-
table gamma-ray detectors (for example, NaI) to identify the included in the model.
location of activity and assist with the modeling.
6.6 Attenuation corrections for very thick items may be
4.1.9 Measurement uncertainties are estimated based on
somewhat compromised by coherent scattering, which may not
uncertainties of the assumptions of the model.
be accurately modeled by attenuation calculations.
5. Significance and Use 7. Method Descriptions
Five commonly used methods are described. These include:
5.1 The following methods assist in demonstrating regula-
(1) Generalized Geometry Holdup, (2) Far-field
tory compliance in such areas as safeguards (Special Nuclear
Approximation, (3) Voxel Intrinsic Efficiency, (4) Radiation
Material), inventory control, criticality control, decontamina-
Transport Code, and (5) Hybrid Monte Carlo.
tion and decommissioning, waste disposal, holdup and ship-
7.1 Generalized Geometry Holdup—The method represents
ping.
items as a point, line, or area (1). Three method calibrations
5.2 This guide can apply to the assay of radionuclides in
are obtained from one set of calibration measurements. Point
containers, whose gamma-ray absorption properties can be
sources of the same material as that to be measured are often
measured or estimated, for which representative certified
used for the calibration. Measurements and calibrations are
standards are not available. It can be applied to in situ
made with a collimator attached. Additional attenuation cor-
measurements, measurement stations, or to laboratory mea-
rection factors are needed for a complete analysis.The detector
surements.
calibrations remain the same for all measurements, but attenu-
ation correction factors will vary with the specific measure-
5.3 Some of the modeling techniques described in the guide
ment. Results are typically reported in units of mass.
are suitable for the measurement of fall-out or natural radio-
activity homogenously distributed in soil.
5.4 Source-based efficiency calibrations for laboratory ge-
The boldface numbers in parentheses refer to a list of references at the end of
ometries may suffer from inaccuracies due to gamma rays this standard.
C1726/C1726M − 10 (2018)
7.1.1 Advantages of this method are: 7.1.4 Calibration—Point sources, representative of the
7.1.1.1 The detector efficiency is easily determined; three material, m , being measured, are positioned in off-axis posi-
o
different types of geometry calibrations are performed concur- tions and the peak count rate is determined at each location.
rently. The activity of each location can be used to represent the
7.1.1.2 Any cylindrical collimator could be used. activity/unit area of the area within the concentric ring, a. See
i
7.1.1.3 Typically, only point sources are used. Fig. 1. This information is integrated to obtain calibration
7.1.1.4 Additional geometry corrections do not require use constants for point, line, and area configurations.
of half-life or gamma ray yields.
7.2 Far-field Approximation—This method is used for the
7.1.2 Disadvantages of this method are:
calculation of activity in well-defined geometries (2). The
7.1.2.1 Some holdup items being measured may not have
method assumes that the matrix attenuation correction for the
geometries that simulate points, lines, or areas. However, the
item being measured can be estimated using a far-field matrix
errors introduced by these assumptions are often small com-
correction approximation. Additional correction factors are
pared to other errors.
needed for other types of attenuation and geometry. Templates
7.1.2.2 The model assumes uniform concentration and dis-
may be prepared that match parameters of the items being
tribution of radioactive material. The uncertainties due to these
measured and the positioning of the detector during the
assumptions can be mitigated by taking multiple overlapping
measurement. Geometry and attenuation correction factors are
measurements (subject to time constraints) and judicial mea-
computed from the information supplied by the templates.This
surement placement.
model can be used for many shapes. Usually measurements are
7.1.2.3 The calibration applies only to the exact detector-
made with a collimator to provide detector shielding and
collimator configuration used during the calibration.
directional response.The detector calibration remains the same
7.1.2.4 Special nuclear material licenses may be required
for all measurements, but attenuation and geometry correction
for the calibration sources.
factors will vary with the specific measurement. Results are
7.1.3 Typical applications include uranium and plutonium
reported in activity, concentration, or mass units.
holdup.
7.2.1 Advantages of this method are:
7.2.1.1 The detector efficiency is easily determined.
7.2.1.2 The calibration can be applied to any gamma-
emittingradionuclidewithintheenergyrangeofthecalibration
In a gaseous diffusion plant there are many items that contain holdup and
source and the validity of the correction factors.
cannot be measured as points, lines or areas.Two examples are converters and pipes
7.2.1.3 Models can be constructed for cylinders, boxes,
in pipe galleys. In order to have a large enough standoff for pipes to meet the criteria
for lines, several pipes in the galley are usually within the field-of-view. Converters
point sources, and disc geometries.
are typically measured from outside cell housings, which places the detector several
7.2.1.4 Detector collimation is incorporated in the model
feet away. Because the converters have a large diameter (from 1.2 m to 2.7 m for the
and does not affect the detector calibration.
sizes that can be reliably measured by gamma), pulling back far enough to make
them line sources would place several converters into the field-of-view, and then
7.2.2 Disadvantages of this method are:
they would not be long enough to meet the line source definition. In addition, the
internal structure of converters is too complex to model them as point, line, or area.
FIG. 1 Detector Position for Calibration
C1726/C1726M − 10 (2018)
7.2.2.1 The model does not apply to the analysis of activity obtain that information, a point-source calibration must be
in a non-uniform condition (for example, activity in soil in an performed at a fixed distance from the face of the detector.
exponential distribution).
7.4 Radiation Transport Code Methods—Radiation trans-
7.2.2.2 The calibration does not apply to close-up
port codes typically use the Monte Carlo method to track the
geometries, where the far-field approximation for matrix at-
motion of radiation through matter interaction by interaction.
tenuation does not apply, or very large items (for example,
Comprehensive Monte Carlo radiation transport codes such as
infinite planes).
MCNP (4), GEANT (5), CYLTRAN (6), and EGS4 (7) allow
7.2.2.3 Correction factors assume incoming gamma rays are
energy deposition in the sensitive volumes of gamma ray
parallel to the detector axis and, therefore, have reduced
detectors to be computed given the material description and
accuracy for the off-axis portion of activity.
source distribution of the measurement situation. This method
7.2.3 Typical applications include modeling of cylinders,
of computing efficiencies is absolute in the sense that the cross
boxes, points and discs with specific dimensions.
sections of the primary photons and all subsequent secondary
7.2.4 Calibration—Typically, a radionuclide point source,
photons are tracked based on detailed calculations of the
with activity traceable to national standards, is positioned at a
fundamental physical process taking place. These interaction
fixed distance from the detector. This source needs to encom-
cross-sections are derived from values stored in a National
pass the energy range of gamma-rays that may be used for the
database. The ultimate accuracy is dependent upon the validity
analysis. Detector efficiencies are then obtained as a function
of the transport model for gamma spectroscopy, the proper
of energy at the distance used for calibration. Typical calibra-
utilization of the code, accurate cross-sections, and an accurate
tion distances range from 20 to 40 cm [7.9 to 15.7 in.].
and detailed model of the detector and the radioactive source.
Calibrations are performed with the source on the detector axis
Models are prepared that match parameters of the items being
so that photons enter only the circular face of the detector.
measured and the positioning of the detector during the
7.3 Voxel-Intrinsic Effıciency—The model (3) is typically measurement. The transport code determines the true detection
efficiency, which may then be used by automated or manual
calibrated with a point source or sources as the far-field
method, but the far-field algorithm for matrix attenuation is not techniques for activity determination. It is especially helpful
for unusually complicated measurement geometries. None of
used. Instead, the attenuation of each voxel is computed and
the overall activity is computed accordingly. The detector is these codes were developed for the purposes of accurate
efficiency calibration of gamma spectroscopy detectors.
character
...