Publication Date: 4/1/74
    Pages: 7
    Date Entered: 1/5/93
    Title: Nondestructive Uranium-235 Enrichment Assay by Gamma-Ray Spectrometry
    April 1974
    U.S. ATOMIC ENERGY COMMISSION
    REGULATORY GUIDE
    DIRECTORATE OF REGULATORY STANDARDS
    REGULATORY GUIDE 5.21
    NONDESTRUCTIVE URANIUM-235 ENRICHMENT ASSAY
    BY GAMMA-RAY SPECTROMETRY
A. INTRODUCTION
    Section 70.51, "Material Balance, Inventory, and Records
    Requirements," of 10 CFR Part 70, "Special Nuclear Material," requires,
    in part, that licensees authorized to possess at any one time more than
    one effective kilogram of special nuclear material (SNM) determine the
    material unaccounted for (MUF) and its associated limit of error (LEMUF)
    for each element and the fissile isotope for uranium contained in
    material in process. Such a determination is to be based on
    measurements of the quantity of the element and of the fissile isotope
    for uranium.
    The majority of measurement techniques used in SNM accountability
    are specific to either the element or the isotope but not to both. A
    combination of techniques is therefore required to determine the MUF and
    LEMUF by element and by fissile isotope for uranium. Passive gamma-ray
    spectrometry is a nondestructive method for measuring the enrichment, or
    relative concentration, of the fissile isotope U-235 in uranium. As
    such, this technique is used in conjunction with an assay for the
    element uranium in order to determine the amount of U-235.
    This guide details conditions for an acceptable U-235 enrichment
    measurement using gamma-ray spectrometry, and prescribes procedures for
    operation, calibration, error analysis, and measurement control.
B. DISCUSSION
    The alpha decay of U-235 to Th-231 is accompanied by the emission
    of a prominent gamma ray at 185.7 keV (4.3 x 10(4) of these 185.7-keV
    gamma rays are emitted per second per gram of U-235). The relatively
    low energy and consequent low penetrating power of these gamma rays
    implies that most of those emitted within the interior of the material
    are absorbed within the material itself. These thick(1) materials
    therefore exhibit a 185.7-keV gamma ray activity which approximates the
    activity characteristic of an infinite medium; i.e., the activity does
    not depend on the size or dimensions of the material. Under these
    conditions, the 185.7-keV activity is directly proportional to the U-235
    enrichment. A measurement of this 185.7-keV activity with a suitable
    detector forms the basis for an enrichment measurement technique.
    The thickness of the material with respect to the mean free path
    of the 185.7-keV gamma ray is the primary characteristic which
    determines the applicability of passive gamma-ray spectrometry for the
    measurement of isotope enrichment. The enrichment technique is
    applicable only if the material is thick. However, in addition to the
    thickness of the material, other conditions must be satisfied before the
    gamma-ray enrichment technique can be accurately applied. An
    approximate analytical expression for the detected 185.7-keV activity is
    given below. This expression has been separated into several individual
    terms in order to aid in identifying those parameters which may
    interfere with the measurement. Although approximate, this relationship
    can be used to estimate the magnitude of interfering effects in order to
    establish limits on the range of applicability and to determine the
    associated uncertainties introduced into the measurement. This
    relationship is:
    ----------
    (1) "Thick" and "thin" are used throughout this guide to refer to
    distances in relation to the mean free path of the 185.7 keV gamma ray
    in the material under consideration. The mean free path is the
    1/e-folding distance of the gamma-ray flux or, in other terms, the
    average distance a gamma ray traverses before interacting.
    ----------
    (Due to database constraints, this equation is not included. Please
    contact LIS to obtain a copy.) A derivation of this expression, as well as other necessary
    background information relevant to this guide, may be found in the
    literature. (2) As evident in Eq. 1, the activity (C) is proportional
    to the enrichment (E) but is affected by several other characteristics
    as well.
    Material Thickness Effects
    In order for Eq. 1 to be applicable, it is necessary that the
    material be sufficiently thick to produce strong attenuation of
    185.7-keV gamma rays. To determine whether this criterion is met, it is
    useful to compare the actual thickness of the material with a
    characteristic length x(o), where x(o) is defined as that thickness of
    material which produces 99.5% of the measured 185.7-keV activity, i.e.,
    (Due to database constraints, this equation is not included. Please
    contact LIS to obtain a copy.)----------
    (2) L. A. Kull, "Guidelines for Gamma-Ray Spectroscopy
    Measurements of U-235 Enrichment," BNL-50414, July 1973.
    ----------
    Calculated values of x(o), the critical distance, for several
    common materials are given in Table 1.
    (Due to database constraints, Tables 1 and 2 are not included. Please
    contact LIS to obtain a copy.)----------
    (3) Values of the mass attenuation coefficient, mu, may be found
    in J. H. Hubbell, "Photon Cross Sections, Attenuation Coefficients, and
    Energy Absorption Coefficients From 10 keV to 100 GeV," NSRDS-NBS 29,
    1969.
    ----------
    Note: Other nondestructive techniques are capable of detecting SNM
    distributed within a container. The enrichment technique, however, is
    inherently a surface measurement. Therefore, the "sample" observed
    i.e., the surface, must be representative of all the material in the
    container. In this respect the enrichment measurement is more analogous
    to chemical analysis than other NDA techniques.
    Material Composition Effects
    If the gamma-ray measurement is to be dependent only on the
    enrichment, the term related to the composition of the matrix should be
    approximately equal to one, i.e.,
    (Due to database constraints, this equation is not included. Please
    contact LIS to obtain a copy.) Calculated values of this quantity for common materials are given
    in Table 1. The deviation of the numbers in Table 1 from unity indicate
    that a bias can be introduced by ignoring the difference in material
    composition.
    Inhomogeneities in matrix material composition, uranium density,
    and uranium enrichment within the measured volume of the material (as
    characterized by the depth x(o) and the collimated area A) can produce
    changes in the measured 185.7-keV activity and affect the accuracy of an
    enrichment calculated on the basis of that activity. There is a small
    to negligible effect on the measurement accuracy due to variations in
    the content of low-atomic-number (Z<30) matrix materials. Care should
    be exercised, however, in applying this technique to materials having
    high-atomic-number matrices (Z>50) or materials having uranium
    concentrations less than approximately 75%. Inhomogeneities in uranium
    density will also produce small to negligible effects on the accuracy if
    the matrix is of low-atomic-number elements. Significant inaccuracies
    can arise, however, when the uranium enrichment itself can be expected
    to vary throughout the sample.
    The above conclusions about the effects of inhomogeneities are
    based on the assumption that the thickness of the material exceeds the
    critical distance, x(o), and that the inhomogeneities exist within this
    depth. In the case of extremely inhomogeneous materials such as scrap,
    the condition of sufficient depth may not always be fulfilled, or
    inhomogeneities may exist beyond the depth x(o); i.e., the "sample" is
    not representative. Therefore, this technique is not applicable to such
    inhomogeneous materials.
    Container Wall Effects
    Variations in the thickness of the container walls can
    significantly affect the activity measured by the detector. The
    fractional change in the measured activity deltaC/C due to a small
    change deltad in the container wall thickness can be expressed as
    follows:
    (Due to database constraints, this equation is not included. Please
    contact LIS to obtain a copy.) Calculated values of DeltaC/C, corresponding to a change in
    container thickness Deltad of 0.0025 cm, for common container materials,
    are given in Table 2.
    Therefore, the container wall thickness should be known, e.g., by
    measuring an adequate number of the containers before loading. In some
    cases an unknown container wall thickness can be measured using an
    ultrasonic technique and a simple correction applied to the data to
    account for attenuation of the 185.7-keV gamma rays (see eq. 5).
    Commercial equipment is available to measure wall thicknesses ranging
    from about 0.025 to 5.0 cm to relative accuracies of approximately 1.0%
    to 0.1%, respectively.
    Area and Geometrical Efficiency
    The area of the material viewed by the detector and the
    geometrical efficiency are variables which may be adjusted, within
    limits, to optimize a system. It is important to be aware that once
    these variables are fixed, changes in these parameters will affect the
    results of the measurement.
    It is also important to note that the placement of the material
    within the container will affect the detected activity. The material
    should fill the volume of the container to a certain depth, leaving no
    void spaces between the material and the container wall.
    Net Detector Efficiency
    Thallium-activated sodium iodide, NaI(TI), scintillation detectors
    and lithium-drifted germanium, Ge(Li), solid-state detectors have been
    used to perform these measurements. The detection systems are generally
    conventional gamma-ray spectrometry systems presently commercially
    available in modular or single-unit construction.
    The following factors influence detector selection and the control
    required for accurate results.
1. Background
    a. Compton Background. This background is predominately
    produced by the 765-keV and 1001-keV gamma rays of Pa-234m, a daughter
    of U-238. Since, in most cases, the Compton background behaves smoothly
    in the vicinity of the 185.7-keV peak, it can be readily subtracted,
    leaving only the net counts in the 185.7-keV full-energy peak.
    b. Overlapping Peaks. The observable peak from certain gamma
    rays may overlap that of the 185.7-keV peak due to the finite energy
    resolution of the detector; i.e., the difference in energies may be less
    than twice the FWHM.(4) This problem is common in enrichment
    measurements of recently separated uranium from a reprocessing plant.
    The peak from a strong 208-keV gamma ray from U-237 (half-life of 6.75
    days) can overlap the 185.7-keV peak when an NaI detector is used.
    Analytical separation of the two unresolved peaks, i.e., peak stripping,
    may be applied. An alternative solution is to use a Ge(Li) detector so
    that both peaks are clearly resolved.
    The U-237 activity present in reprocessed uranium will depend on
    the amount of Pu-241 present before reprocessing and also on the time
    elapsed since separation.
    c. Ambient Background. The third source of background
    originates from natural sources and from other uranium-bearing materials
    located in the vicinity of the measuring apparatus. This last source
    can be particularly bothersome since it can vary with time within wide
    limits depending on plant operating conditions.
2. Count-Rate Losses. Calculation of the detector count rates for
    purposes of making dead time estimates requires that one calculate the
    total count rate, not only that due to U-235. Total count rate
    estimates for low-enrichment material must therefore take into account
    the relatively important background from U-238 gamma rays. If other
    radioactive materials are present within the sample, their contributions
    to the total count rate must also be considered.
    Count-rate corrections can be made by determining the dead time or
    by making measurements for known live-time(5) intervals. The pile-up or
    overlap of electronic pulses is a problem which also results in a loss
    of counts in the full-energy peak for Ge(Li) systems. A pulser may be
    used to monitor and correct for these losses. Radiation which provides
    no useful information can be selectively attenuated by filters; e.g., a
    one-millimeter-thick cadmium filter will reduce x-ray interference,
    eliminating this source of count-rate losses.
    ----------
    (4) FWHM - full width of the spectrum peak at half its maximum
    height.
    ----------
3. Instability in Detector Electronics. The gain of a
    photomultiplier tube is sensitive to changes in temperature, count rate,
    and magnetic field. Provision can be made for gain checks and/or gain
    stabilization for enrichment measurement applications. Various gain
    stabilizers that automatically adjust the system gain to keep a
    reference peak centered between two preset energy limits are available.
C. REGULATORY POSITION
    Passive gamma-ray spectrometry constitutes an acceptable means for
    nondestructively determining U-235 enrichment, if the following
    conditions are satisfied:
    Range of Application
1. All material to be assayed under a certain calibration should be
    of similar chemical form, physical form, homogeneity, and impurity
    level.
2. The critical distance of the material should be determined. Only
    those items of the material having dimensions greater than this critical
    distance should be assayed by this technique.
3. The material should be homogeneous in all respects on a
    macroscopic(6) scale. The material should be homogeneous with respect
    to uranium enrichment on a microscopic(6) scale.
4. The containers should all be of similar size, geometry, and
    physical and chemical composition.
    System Requirements
1. NaI(T1) scintillation detectors having a resolution of FWHM <16%
    at the 185.7-keV peak of U-235 are generally adequate for measuring the
    enrichment of uranium containing more than the natural (0.71%) abundance
    of U-235. Crystals with a thickness of @@ 1.25 cm are recommended for
    optimum efficiency. If other radionuclides which emit significant
    quantities of gamma radiation in an energy region E = 185.7 keV plus or
    minus FWHM at 185.7 keV are present:
    ----------
    (5) "Live time" means that portion of the measurement period
    during which the instrument can record detected events. Dead time refers
    to that portion of the measurement period during which the instrument is
    busy processing data already received and cannot accept new data. In
    order to compare different data for which dead times are appreciable,
    one must compare counts measured for equal live-time periods.
    (actual measurement period) - (dead time) = live time
    (6) Macroscopic refers to distances greater than the critical
    distance; microscopic to distances less than the critical distance.
    ----------
    a. A higher-resolution detector, e.g., Ge(Li), should be used,
    or
    b. A peak stripping procedure should be used to subtract the
    interference. In this case, data should be provided to show the range
    of concentration of the interfering radionuclide, and the accuracy and
    precision of the stripping technique over this range.
2. The detection system gain should be stabilized by monitoring a
    known reference peak.
3. The system should measure live time or provide a means of
    determining the count-rate losses based on the total counting rate.
4. Design of the system should allow reproducible positioning of the
    detector or item being assayed.
5. The system should be capable of determining the gamma-ray activity
    in at least two energy regions to allow background subtraction. One
    region should encompass 185.7 keV, and the other region should be above
    this but not overlapping. The threshold and width of the regions should
    be adjustable.
6. The system should have provisions for filtering low-energy
    radiation which could interfere with the 185.7-keV or background
    regions.
    Data Reduction
1. If the total counting rate is determined primarily by the
    185.7-keV gamma ray, the counting rate should be restricted (absorbers,
    decreased geometrical efficiency) below those rates requiring
    correction. The system sensitivity will be reduced by these measures
    and, if no longer adequate, separate calibrations should be made in two
    or more enrichment regions.
    If the total counting rate is determined primarily by events other
    than those due to 185.7-keV gamma rays, counting rate corrections should
    be made.
2. To determine the location and width of the 185.7-keV peak region
    and the background region(s), the energy spectrum from each calibration
    standard (see Calibration, next section) should be determined and the
    position of the 185.7-keV peak and neighboring peaks noted. The
    threshold and width of each energy region should then be selected to
    avoid including any neighboring peaks, and to optimize the system
    stability and the signal-to-background ratio.
3. The net response attributed to 185.7-keV gamma rays should be the
    accumulated counts in the peak region minus a multiple of the counts
    accumulated in a nearby background region(s). A single upper background
    region may be monitored or both a region above the peak region and one
    below may be monitored.
    If only an upper background region is monitored, the net response, R,
    should be given by
    R = G--bB
    where G and B are the gross counts in the peak region and the background
    region, respectively, and b is the multiple of the background to be
    subtracted. This net response, R, should then be proportional to the
    enrichment, E, given by
    E = C(1) R = C(1)(G--bB)where C(1) is a calibration constant to be determined (see Calibration,
    next section). The gross counts, G and B, should be measured for all
    the standards. The quantities G/E should then be plotted as a function
    of the quantities B/E and the slope of a straight line through the data
    determined. This slope is b, the multiple of the upper background
    region to be subtracted, i.e.,
    G/E = b(B/E) + 1/C(1)The data from all the standards should be used in determining this
    slope.
    If both an upper and a lower background are monitored, the counts
    in each of these regions should be used to determine a straight line fit
    to the background. Using this straight line approximation, the area or
    number of counts under this line in the peak region should be subtracted
    from the gross counts, G, to obtain the net response. An adequate
    technique based on this principle is described in the literature.(7)Calibration(8)1. Calibration standards should be obtained by:
    a. Selecting items from the production material. A group of
    the items selected should, after determination of the gamma-ray
    response, be measured by an independent, more accurate technique
    traceable to, or calibrated with, NBS standard reference material, e.g.,
    mass spectrometry. The other items should be retained as working
    standards.
    ----------
    (7) G. Gunderson, I. Cohen, M. Zucker, "Proceedings: 13th Annual
    Meeting, Institute of Nuclear Materials Management," Boston, Mass.
    (1972) p. 221.
    (8) None of the calibration techniques or data reduction
    procedures exclude the use of automated direct-readout systems for
    operation. The procedures described in this guide should be used for
    adjustment and calibration of direct-readout instruments.
    ----------
    b. Fabricating standards which represent the material to be
    assayed in chemical form, physical form, homogeneity, and impurity
    level. The U-235 enrichment of the material used in the fabrication of
    the standards should be determined by a technique traceable to, or
    calibrated with, NBS standard reference material, e.g., mass
    spectrometry.
2. The containers for the standards should have a geometry,
    dimensions, and composition which approximate the mean of these
    parameters in the containers to be assayed.
3. The values of enrichment for the calibration standards should span
    the range of values encountered in normal operation. No less than three
    separate standards should be used.
4. Each standard should be measured at a number of different
    locations, e.g., for a cylinder, at different heights and rotations
    about the axis. The mean of these values should be used as the response
    for that enrichment. The dispersion in these values should be used as
    an initial estimate of the error due to material and container
    inhomogeneity.
5. The data from the standards, i.e., the net response attributed to
    185.7-keV gamma rays and the known uranium enrichment, should be used to
    determine the constants in a calibration function by a weighted
    least-squares technique.
    Operations
1. The detection system and counting geometry (collimator and
    container-to-detector distance) should be identical to those used in
    calibration.
2. The data reduction technique and count-rate loss corrections, if
    included, should be identical to those used in calibration.
3. Data from all measurements should be recorded in an appropriate
    log book.
4. At least two working standards should be measured during each
    eight-hour operating shift. The measured response should be compared to
    the expected response (value used in calibration) to determine if the
    difference exceeds three times the expected standard deviation. If this
    threshold is exceeded, repeat measurements should be made to verify that
    the response is significantly different and that the system should be
    recalibrated.
5. All containers should be agitated, or the material mixed in some
    manner, if possible, prior to counting. One container from every ten
    should be measured at two different locations. Other items may be
    measured at only one position. (If containers are scanned to obtain an
    average enrichment, the degree of inhomogeneity should still be measured
    by this method.) The difference between the measurements at different locations
    should be used to indicate a lack of the expected homogeneity. If the
    two responses differ by more than three times the expected standard
    deviation (which should include the effects of the usual or expected
    inhomogeneity), repeat measurements should be made to verify that an
    abnormal inhomogeneity exists. If the threshold is exceeded, the
    container should be rejected and investigated to determine the cause of
    the abnormal inhomogeneity.(9)6. In the event that all containers are not filled to a uniform
    height, the container should be viewed at a position such that material
    fills the entire volume viewed by the detector. The procedure for
    determining the fill of the container should be recorded, e.g., by
    visual inspection at the time of filling and recording on the container
    tag.
7. The container wall thickness should be measured. The wall
    thickness and location of the measurement should be indicated, if
    individual wall thickness measurements are made, and the gamma-ray
    measurement made at this location. If the containers are nominally
    identical, an adequate sampling of these containers should be
    representative. The mean of the measurements on these samples
    constitutes an acceptable measured value of the wall thickness which may
    be applied to all containers of this type or category.
8. The energy spectrum from a process item selected at random should
    be used to determine the existence of unexpected interfering radiations
    and the approximate magnitude of the interference. The frequency of
    this test should be determined by the following guidelines:
    a. At least one item in any new batch of material.
    b. At least one item if any changes in the material processing
    occur.
    c. At least one item per material balance period.
    If an interference appears, either a higher-resolution detector
    must be acquired or an adequate peak stripping routine applied. In both
    cases additional standards which include the interfering radiations
    should be selected and the system recalibrated.
    ----------
    (9) The difference may also be due to a large variation in wall
    thickness.
    ----------
9. No item should be assayed if the measured response exceeds that of
    the highest enrichment standard by more than twice the standard
    deviation in the response from this standard.
    Error Analysis
1. A least-squares technique should be used to determine the
    uncertainty in the calibration constants.
2. The measurement-to-measurement error should be determined by
    periodically observing the net response from the standards and repeating
    measurements on selected process items. Each repeat measurement should
    be made at a different location on the container surface, at different
    times of the day, and under differing ambient conditions.(10) The
    standard deviation should be determined and any systematic trends
    corrected for.
    ----------
    (10) The statistical error due to counting (including background)
    and the errors due to inhomogeneity, ambient conditions, etc. will be
    included in this measurement-to-measurement error.
    ----------
3. The item-to-item error due to the uncertainty in wall thickness
    should be determined. The uncertainty in the wall thickness may be the
    standard deviation about the mean computed from measurements on randomly
    selected samples, or it may be the uncertainty in the thickness
    measurement of individual containers. This uncertainty in wall
    thickness should be multiplied by the effect of a unit variation in wall
    thickness on the measured 185.7-keV response to determine this component
    uncertainty.
4. Item-to-item errors other that those measured, e.g., wall
    thickness, should be determined by periodically (see guidelines in
    paragraph 8. of the Operation Section) selecting an item and determining
    the enrichment by an independent technique traceable to, or calibrated
    with, NBS standard reference material. A recommended approach is to
    adequately sample and determine the U-235 enrichment by calibrated mass
    spectrometry. In addition to estimating the limit of error from these
    comparative measurements, the data should be added to the data used in
    the original calibration and new calibration constants determined.
    9