An Uncertainty Analysis of Neutron Activation Measurements in Hiroshima and Nagasaki

Neutron activation was measured with two fundamentally different types of detection with different types of errors: counting atoms with radiometric methods (beta or gamma counting) and counting atoms with accelerator mass spectroscopy (AMS). The following discussion focuses first on the general approach to error analysis that is used here, and then on each classification of measurement.

The general approach used here is to begin by exhaustively identifying all the quantities that are measured and the formulas by which investigators use the quantities to calculate results in the terms commonly reported in the literature. There must initially be a thorough consideration of the uncertainty in all the measured *or assumed* values of quantities that are used by investigators to arrive at the final reported result, although some of the quantities may prove to be known with such accuracy and precision that their uncertainty can be ignored in a quantitative treatment. The latter quantities can then be treated as constants. For example, we assume the weighing of samples and standards to be so precise and well calibrated that the associated error is not included in any of the estimates calculated here. But, a volumetric error is typically associated with pipetting microliter quantities of liquids, such as might be used to prepare calibration standards, and this would be a potential contributor to experimental error of some significance if not verified and corrected by weighing.

The objective is to estimate the total uncertainty of each reported result in relation to some presumed true value of interest. *For the purposes of this appendix, the true value of interest is the amount of the neutron activation product nuclide per unit mass of the associated stable target element that existed in the sample being measured at the time of the bombing (ATB) in 1945.* Depending on the measurement method, this value may be stated in units involving ra-

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Appendix B
An Uncertainty Analysis of Neutron Activation Measurements in Hiroshima and Nagasaki
Neutron activation was measured with two fundamentally different types of detection with different types of errors: counting atoms with radiometric methods (beta or gamma counting) and counting atoms with accelerator mass spectroscopy (AMS). The following discussion focuses first on the general approach to error analysis that is used here, and then on each classification of measurement.
The general approach used here is to begin by exhaustively identifying all the quantities that are measured and the formulas by which investigators use the quantities to calculate results in the terms commonly reported in the literature. There must initially be a thorough consideration of the uncertainty in all the measured or assumed values of quantities that are used by investigators to arrive at the final reported result, although some of the quantities may prove to be known with such accuracy and precision that their uncertainty can be ignored in a quantitative treatment. The latter quantities can then be treated as constants. For example, we assume the weighing of samples and standards to be so precise and well calibrated that the associated error is not included in any of the estimates calculated here. But, a volumetric error is typically associated with pipetting microliter quantities of liquids, such as might be used to prepare calibration standards, and this would be a potential contributor to experimental error of some significance if not verified and corrected by weighing.
The objective is to estimate the total uncertainty of each reported result in relation to some presumed true value of interest. For the purposes of this appendix, the true value of interest is the amount of the neutron activation product nuclide per unit mass of the associated stable target element that existed in the sample being measured at the time of the bombing (ATB) in 1945. Depending on the measurement method, this value may be stated in units involving ra-

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tios of numbers of atoms or in units of radioactivity per unit mass of the target element.
Sample-specific activity ATB (August 6 or 9, 1945) is related to the dosimetric quantities of interest for survivor dose in a complicated way. The sample-specific activity ATB is a function of the bomb-related thermal-neutron and epithermal-neutron fluences that existed in the sample ATB. Those fluences are in turn related to the free-field neutron fluences at the same location in a way that depends to some extent on local moderation and absorption of the free-field neutron fluences. Local moderation occurs in the terrain and structures close to the sample and in the sample itself. The free-field neutron fluences are of paramount interest because they are the quantities used to calculate doses to survivors and because they constitute a uniform basis for the comparison of measured values. This appendix does not analyze the uncertainty in the free-field neutron fluences calculated by DS86; they are discussed in Chapter 6 of this report. The relationship between free-field and insample neutron fluences is discussed below in connection with the plotting and fitting of measurements.
For analytical purposes, every measured or assumed value is treated here as a random variable. The difference between a true value and an individual measured value has both a systematic and a random component, corresponding to a mean difference and a standard deviation. The former is commonly characterized as a bias and the latter as a random error. Every experiment is based on methods that are intended to minimize systematic and random errors. Although it is difficult for a retrospective analysis as reported here to obtain sufficient information to identify and provide a useful quantitative estimate of a nonzero bias, every reasonable effort is made to do so. More often, the main quantitative result of this type of analysis is to verify the magnitude of an investigator’s estimated random error or provide a more realistic estimate of the true random error. This type of analysis can also help to identify possible sources of error that cannot be quantified with the information at hand but can be addressed in recommendations for future work.
Another way to look at the uncertainty issue is to focus on the limiting case of measurements that approach the limits of detectability by making generic calculations of limits of detection with accepted formulas based on statistics. For radiation-counting methods, such calculations must be based on assumed nominal values for sample and background counting time, counting efficiency, and the amount of the stable target element present in the sample, which are treated as constants for the purpose of the calculation. Those calculations are useful for illustration and for defining limits below which reported measured results should be treated with particular caution. They also help to define the nature of some important relationships for the lowest-level measurements, relating the comparative sizes of counting-system background, sample background, and calculated or measured sample content from the bomb fluence. These issues are addressed in detail below.

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PROPAGATION OF ERROR
To estimate the uncertainty in the final reported result, sample-specific activity ATB, a propagation-of-error calculation can be based on the equations by which the measured and assumed values of quantities are used by investigators to calculate reported results, incorporating the uncertainty estimates of the individual values involved. The desired result is an estimate of the total uncertainty in the final reported result that is due to all sources combined. For the purpose of this report, standard formulas based on the first-order terms of Taylor-series expansions are used. It should be noted that these formulas tend to underestimate somewhat the variance in the reported values as a function of the available estimates of component uncertainties. The underestimation might not be negligible. As one indication of the potential inadequacy of first-order approximations, it can be noted that a large majority of the major-component uncertainties given by measurers have fractional standard deviations exceeding 10% in one or both components typically reported. To evaluate and improve the estimates of uncertainty in the specific activity ATB, numerical simulations were performed.1 For any individual result, there is generally no reason to believe that errors in the different components are correlated. The resulting propagation-of-error calculations are therefore relatively simple; the formulas used in spreadsheet calculations based on the first-order approximation are given in the sections below. In general, it is noted that for any set of uncorrelated values and estimated standard deviations, say,
X±a,Y±b,Z±c
and any constants mi, the sum or difference formula gives the result
(1)
1
When simplified numerical simulations (multivariate normal with zero covariance) are performed to evaluate the combined error of sample-specific activity as calculated from a radiation counting, it is notable that if any term in the divisor of the equation as it is normally formulated (counting efficiency, result of the stable element assay) begins to exceed about 12–15% coefficient of variation, the error distribution of the specific activity becomes badly skewed upward. That is because such a situation involves a nontrivial probability of a small value close to zero in the divisor of the formula for specific activity, with such small values causing arbitrarily large calculated specific activities. Several of the 152Eu measurements of Shizuma and others (1993) have rather large estimated error in the assay of stable europium as reported by the authors. Of these, two cases may deserve review of the determined stable europium content because the calculated specific activity is considerably larger than other nearby measurements: Sorazaya Shrine, 873-m slant range, 15% estimated SD in stable europium, and Enryu Shrine, 1081-m slant range, 14% estimated SD in stable europium. In addition, it should be noted with regard to all the radiometric neutron-activation measurements in the literature that if there are cases in which the author’s estimates of the error in stable europium and cobalt assays are substantially understated, those measurements might be similarly affected.

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and the product or quotient formula gives
(2)
As a matter of nomenclature, the coefficient of variation σ/μ (standard deviation divided by mean) for a variable of interest may be given herein as a fraction and called a fractional standard deviation, or it may be given as a percentage and simply called a % error. Thus, Equation 1 says that for such formulas as sums, differences, and weighted sums the standard deviations themselves sum in quadrature. Equation 2 similarly says that for products and quotients the fractional standard deviations sum in quadrature.
CORRELATED ERRORS
In addition to the possible effect of correlation of the errors in the component quantities on a single result, another type of correlation must be considered in any application based on more than one measured result: correlation of errors among reported results. Various subsets of measured values, classified at various levels (for example, within the same sample, within a given sampling location, within a given investigator’s laboratory, and within a given range of calendar time), can share the same measured or assumed value for some part of the calculated result, such as a calibration factor, and can therefore be correlated with respect to that factor. Such cases will be discussed in detail.
One might ask whether the measurements at a particular site can tend to share a common bias relative to the true value, that is not due to sharing a common value for something, such as a calibration factor. To the extent that such a covariance might exist, it would most likely be due to an unmeasured covariable that affects the true value for the sample, rather than to an error inherent in the measurement process. Nothing about the site should affect the process, and the properties of the sample should have minimal effect on the measurement process. For example, the sample-specific properties that would affect the counting efficiency, such as the effect of the elemental composition of the sample on its self-absorption of the emitted radiation being measured, are likely to have negligible influence.
However, there might be sample-specific variables that appreciably affect the neutron activation level of the sample for a given incident bomb fluence (such as boron content or water content) that have not been measured or have not been properly incorporated in the calculated value for the sample. Such site-correlated errors are not included in the uncertainty analysis reported here, because they are errors in the calculated value and not the measured one as defined here. However, they do

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need to be considered in fitting curves to the measurements. They are discussed further in the next section.
COMBINED UNCERTAINTY ESTIMATES: 32P MEASUREMENTS OF FAST NEUTRON FLUENCE
The 32P measurements made by Japanese physicists in 1945 (Yamasaki and others 1987) have often been cited in relation to general source term parameters such as yield and height of burst. Because these measurements are at fairly close distances and are used in this manner, it is of some interest to characterize their uncertainty as an aggregate, as well as individually. Unfortunately, characterizing the uncertainty of these measurements in the aggregate, or using them in fitting a model, is difficult to do correctly, because their errors are highly correlated. Even the calculation of a weighted mean for these measurements, for the reasons discussed below, would require a very careful and somewhat complicated approach to propagation of error.
The 32P measurements were very fortuitous, or very well planned, in several respects, including the facts that the measurements were made on essentially pure elemental sulfur of reliably high purity, and the measurements were originally calibrated with a natural radioactive source of good chemical purity, uranium oxide, whose emission rate of beta particles can therefore be accurately predicted. These factors, along with the preservation of the Lauritsen electroscopes used to perform the measurements, allowed a series of careful retrospective studies of factors related to the measurements’ accuracy by Hamada (1983a,b, 1987) and Shimizu and Saigusa (1987). Hamada (1987) estimates a 2% random error in uniformity of sample preparation that relates to a counting efficiency factor, presumably related primarily to the evenness of spreading the powdered sample on the glass plate for counting and the resulting differences in self-absorption of betas. Based on the accuracy quoted by Hamada (1987) for his 32P reference standard and the likely counting error variance of his calibration measurements, it would seem reasonable to estimate that the calibration error should not exceed 5% or so, where the greater error would likely be the counting error of his calibration measurements rather than the accuracy of his standard reference material.
These numbers can be combined with the counting error given by Hamada (1987) in his Table 2 to provide estimates of the errors in individual measurements considered in isolation, which are shown in Table B-1. (The chemical purity of each sample, as it relates to the accuracy of the estimated weight of pure sulfur present in each sample, appears to be high and to have a fractional standard deviation of only a fraction of a % based on Hamada’s data (1987). It is ignored in this calculation.)
These estimates differ very little from those of Hamada, because the larger counting errors do in fact predominate. The fractional standard deviation (FSD’s) of individual measurements are fairly large, up to 53%. Some measurements with even larger errors are not shown in the table, and some measurements for which the azimuth is unknown are also omitted.

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TABLE B-1 Estimates of Errors in Individual Measurements Considered in Isolation
Sample
Counting Interval, min.
Electroscope Reading, div s−1
Activity (Net) dis s−1 Sg−1
Total Error, SD dis s−1 Sg−1
Total Error % FSDa
background
200
0.00124
–
–
A4
40
0.00200
2200
434
20
B5
38
0.00224
2940
441
15
C6
45
0.00154
880
399
45
D12
70
0.00162
1500
442
29
D12
70
0.00178
1140
247
22
E13
95
0.00205
2430
342
14
F14
74
0.00166
1260
335
27
G15
90
0.00167
1370
337
25
G15
90
0.00175
1620
336
21
H7
85
0.00144
630
336
53
aFSD=fractional standard deviation.
An important caveat is that the errors in these measurements are highly correlated. This is because all measurements appear to share a common determination of background, which is an additive error, and a common determination of counting efficiency, which is a multiplicative error. Background in particular was a rather proportionally large error in this experiment. Any effort to use these error estimates in fitting to calculated values should involve a very careful propagation of error formulation that begins by extracting the common error in background. This would require a careful reestimation based on reworking Hamada’s (1987, actually, Roesch’s and Jablon’s) equations (1) through (8) for calculating error in count rate based on error in time to reach a common electrical charge on the electroscope.
INVESTIGATORS’ ESTIMATES OF UNCERTAINTY BASED ON COUNTING STATISTICS
In radiation-counting applications, investigators have almost universally calculated their estimated errors in the radioactivity content of samples on the basis of Poisson counting statistics. With rare exceptions, these appear to be the sole basis of plotted error bars and published estimates that are intended to suggest the precision of measured values. But the raw data of the measurements are generally not available to allow checking of the calculations. For example, in the case of radiometric methods, one would have to obtain at least the
Calendar date(s) when samples were counted.
Lengths of the counting intervals (in detector live time) and counts in the region of interest and background subtracted, for all counts of bomb-fluence samples.
Blanks for background and calibration standards for counting efficiency.

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Although it was the intent of the committee’s questionnaire (see Appendix A) to obtain such information, it was not provided by most investigators.
The most basic aspect of the calculations can be checked in a limited way via a calculation of minimum detectable activity (MDA). If one has estimates of background count rate, counting efficiency, and counting interval for sample and background, an MDA can be calculated and compared to give the sample’s estimated content. Such calculations have the limitation that they assume the counting efficiency and background count rate as fixed constants. The validity of such comparisons is also a function of the extent to which the assumed counting intervals are representative of those used. Calculations of MDA and related quantities are discussed further in later sections.
ESTIMATION OF COMPONENTS OF UNCERTAINTY NOT ESTIMATED BY INVESTIGATORS
Because the method of uncertainty analysis was limited to what could be done with incomplete information, it was necessary that the method be flexible and carefully adapted to each individual situation. In some cases, particular uncertainty components have been estimated on the basis of expert judgment and knowledge of typical standards and practices or by using a carefully considered application of values obtained by other investigators with similar methods. Where such judgments have been made, they are clearly so identified in the following sections, regardless of the magnitude of their effect (sensitivity) on the total uncertainty estimates.
STATISTICAL DISTRIBUTIONS OF ERRORS
A word about statistical distributions is in order. The types of detection methods considered here are counting methods, and their raw results are expected to obey the Poisson distribution. At present it appears that all measurements have sufficient numbers of counts for the Poisson to be well approximated by the Gaussian distribution; therefore, skewness is not a major concern. The counting statistics tend to dominate the uncertainty of the measurements, especially inasmuch as the assays were typically calibrated by comparison with other results of the same (radiation-counting) type applied to standard materials. In the case of radiation measurements, assay of stable-element concentration is another major factor in the reported result. Radiation counting of the activation product radionuclide is a third. Most assays of elemental concentration were also performed with radiation counting after controlled neutron irradiation. Moreover, reported results are usually based on averaging of several measurements, and the central limit theorem supports the distributions of component and overall errors’ being approximately Gaussian.
Statistical distribution does not affect the second-moment properties that define the propagation of error equations, but it does affect the interpretation of a standard deviation in terms of cumulative probability. For example, the construction

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of confidence intervals depends on the type of the assumed underlying error distribution and on the estimated value of its standard deviation. Another important consideration in this particular analysis is that the type of error distribution affects decisions about the type of transformation that should be applied to the variable, if any, to fit curves to the data as a function of distance from the epicenter.
ERROR IN THE INDEPENDENT VARIABLE: DISTANCE FROM THE HYPOCENTER
There is appreciable error in the principal independent variable of interest in all analyses of the measurements: the distance from the burst point (epicenter) of the bomb to the location of the sample. That distance is used as a major input for calculating survivor dose. The standard approach in all dose-calculating systems has necessarily been to assume radial symmetry about the hypocenter (ground zero) of the bomb. Therefore, the free-field value calculated by the dosimetry system—the value for an idealized infinitesimal-volume element of air or tissue suspended 1 m above flat ground—depends only on the radial distance from the epicenter (slant distance) or hypocenter (ground distance).
Most investigators have published estimates of uncertainty in distance with their measurements; among neutron measurements, this information is lacking for only a small portion of the data, mainly values reported in the DS86 final report and earlier source documents. The values that are published by measurers are somewhat subjective and have some unusual attributes. For example, because of the geographical context, investigators have tended to think of the “plus-or-minus” values that they estimate as being something like a maximal credible range, rather than a standard deviation. The plus-or-minus uncertainty values tend to fall mostly in a range from about 3 m to about 30 m, but there are a few values as high as 90 m, for samples for which the measurer knew only that a sample came from a particular large building and could obtain no better information from the collector.
The magnitude of the effect of distance error on calculated neutron activation is a function of two factors: geometry and effective attenuation of the radiation fluence. The effective attenuation of the fluence by interactions in air and on the ground predominates: a relaxation length of 125 m, for example, corresponds to a change in fluence of roughly 25% over 30 m at any distance.
In contrast, at distances of interest in connection with survivor dose, the inverse square effect is small: it changes fluence from a point isotropic source by only about 6% over a slant distance of 30 m at 1 km from the epicenter, and 4% at 1.5 km. The effect is larger at shorter distances of interest for fitting the measurements, such as about 10% at 600 m. For a more extended source, such as the fireball, as might apply to delayed radiation to some extent, the geometrical dependence is closer to the inverse of distance than to the inverse square, and the effect is correspondingly smaller.
Efforts are in progress at RERF to provide improved estimates of map location, distance, and related uncertainty by using geographical information system (GIS)

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software in combination with the extensive source documents available. Distance uncertainty is discussed below in relation to fitting curves to the data.
GRAPHICAL DEPICTION AND FITTING OF CURVES TO THE DATA
Scaling by the Inverse Square of Distance
For purposes of graphical depiction, measurement results stated ATB are plotted against slant distance from the epicenter on a semilogarithmic plot, which is standard in the literature. To facilitate visual comparisons, all values—those calculated by DS86 and those calculated from measurements—are multiplied by the square of slant distance in kilometers. That removes the inverse-square dependence on distance that is universal for radiation emitted isotropically from a point source. Hence, in the absence of attenuation, radiation fluences from such a source, so scaled, would have a perfectly constant fluence. And the fluences of radiation from such a source if subject to exponential attenuation as a function of distance, would fall on a straight line, whose slope is commonly characterized by its inverse in terms of the natural logarithm; the distance subject to attenuation by a factor of 1/e, is commonly called a relaxation length. Any systematic departure from a straight line indicates a departure from one or both of these assumptions: the source is not isotropic or is not of small extent compared with the distances involved, or the attenuation is not effectively an exponential function of distance.
Appropriate DS86-Calculated Values for Comparison with Specific Measurements
To compare measured values with DS86-calculated values, it is necessary to determine appropriate DS86-calculated values. Samples were chosen by investigators to be near the surface of the sampled material in a location with a direct line of sight to the epicenter, with three exceptions:
Samples that were deliberately taken at increasing depths in the material at a given location to measure activities related to depth.
In the case of gamma thermoluminescent dosimetry measurements, samples like the pottery shards from the interiors of houses and buildings or underlying roofing tiles that were chosen with foreknowledge that the results would be questionable and that were prominently so identified as “shielded samples.”
Steel concrete reinforcement rods (“rebar”) located at depths approximating 8 cm in concrete, that were measured in the 1960’s with a specific plan in mind to evaluate factors related to the spectra of incident neutron fluences (Hashizume and others 1967).

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The approach of exclusively measuring surface line-of-sight samples for evaluating neutron activation as related to distance was pursued in the belief that such samples would yield measured values as close as possible to the free-field or free-in-air value at the location in question. That approximation is subject to question. The extent to which a given sample reflects the free-field value at 1 m above flat ground, as a standardized reference value for systematic comparisons of measured values as a function of distance from the bomb, depends on more than its being a surface line-of-sight sample. It also depends on the size, shape, and composition of the structure in which the sample is situated and on the properties of the surrounding terrain.
The situation is further complicated in that DS86 was written to calculate not neutron activation, but rather neutron dose to tissue. Calculating neutron activation, even a free-field value, requires a mathematical convolution of the appropriate neutron-interaction cross-section values with the energy-dependent neutron fluences given by DS86. Such calculations should be done by an expert in any case.
The neutron measurements are in four categories with respect to the DS86-calculated values available for comparison:
Measurements for which detailed calculations based on DS86 neutron fluences have used Monte Carlo or Sn simulations with a model of the structure containing the sample, such as the Sn calculations for the Yokogawa Bridge samples by Oak Ridge National Laboratory (Kerr and others 1990) or the calculations done for the Motoyasu Bridge pillar by Hasai and others (1987).
Measurements for which relatively simple calculations have been done by Scientific Applications International Corp. (SAIC) to account for the shielding effect of materials overlying the sample.
Measurements that have been reviewed by an expert at SAIC (Dr. Egbert) and classified as being well approximated by the free-field value on the basis of expert judgment regarding the nature of the sample location.
Measurements, mostly published since 1997, for which no expert evaluation has been performed and the only value available for comparison is the free-field value.
M/C and C/M Plots vs. Plotting M and C Separately
For purposes of comparing measured and DS86-calculated values as a function of distance, some investigators have preferred simply to plot the ratio of measured to calculated (M/C) or the ratio of calculated to measured (C/M) values. However, that gives no information about the behavior of the two individual quantities as a function of distance. When plotting the quantities separately against distance, it is natural to plot the DS86-calculated free-field values rather than the sample-specific in situ calculated values because the former lie on a continuous

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curve. If the measured values are plotted without modification, their difference from the DS86-calculated free-field values reflects both
The difference between a DS86 free-field value at the indicated distance and a completely calculated DS86-based value for the sample, where the latter includes the effect of local terrain and the shielding due to overlying materials, as would be calculated by a full application of computational methods to the DS86 free-field fluences.
Any difference between the measured value and such a completely calculated value for the sample.
To make plots and fitted values that focus on the discrepancies between measured and DS86-calculated values, we made two key decisions:
Measurements at subsurface depths in the sample material were omitted to minimize the shielding correction between free-field and sample-specific calculated values, and
Plotted and fitted measured values were corrected for the ratio between the DS86 free-field calculated value and the most completely calculated sample-specific DS86 value available. That is, “measured free-field equivalent values” were calculated to remove the effect of shielding and local terrain as much as possible and obtain the free-field value that would presumably be associated with the in situ measured value.
It is emphasized that “measured free-field equivalent values” do not reflect any calculation that is new or different from what has been done before. They merely represent a way of plotting measurements in relation to a continuous curve for the DS86-calculated value as a function of distance for samples that have sample-specific calculated values that differ from the free-field calculated values.
Choice of Functions for Fitting to the Data
The DS86-calculated gamma dose for both cities falls very close to a straight line on a semi-log plot of values scaled by the square of distance: its attenuation is close to exponential, and its effective source size is fairly small relative to all distances on the ground. Some 1/r dependence at shorter distances is to be expected from the distributed nature of such sources as fission products in the fireball and neutron-capture gammas arising from interactions with nitrogen in the air near the explosion. Efforts to estimate coefficients separately for a 1/r dependence and a 1/r2 dependence in fits to the measured values were not successful, apparently because the rate of change in the fitted values due to a 1/r dependence is smaller that due to the exponential attenuation and because of the lack of precision in the measurements. The DS86-calculated neutron activation for both cities shows a small but appre-

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Radionuclide Investigator(s)
60Co Shizuma
60Co Kimura/ Hamada
60Co Kerr
60Co Hashizume/ Maruyama
60Co Okumura/ Shimazaki
Investigator(s)
Shizuma
Shizuma
Nakanishi
Iimoto
Okumura/ Shimazaki
Photon Energy Measured
122 keV +344 keV
344 keV
39−40 keV
39–40 keV
T, seconds
1.00×10–6
1.00×10–6
1.00×10–6
1.00×10–6
B, cts on interval of T sec.
3.42×10–3
1.25×10–3
560
226.6666667
SB
58.45226
35.35534
23.66432
15.05545305
counting efficiency, cps/Bq
0.09
0.04
0.008
0.003
MDC, Bq
3.05×10–3
4.19×10–3
1.41×10–2
2.43×10–2
lowest mg per sample
0.02
0.02
1
1.16
highest MDCsa, Bq/mg
1.53×10–1
2.09×10–1
1.41×10–2
2.10×10–2
highest mg per sample
0.05
0.05
2
1.91
lowest MDCs, Bq/mg
6.11×10–2
8.37×10–2
7.06×10–3
1.27×10–2
HL
13.54
13.54
13.54
13.54
year of measurement
1992
1992
1992
1997
highest MDCsa,ATB, Bq/mg ATB
1.69310
2.32063
0.15670
0.30053
lowest MDCsa,ATB, Bq/mg ATB
0.67724
0.92825
0.07835
0.18252
NOTES: 1. The background for Hamada’s 60Co measurement is based on Kerr’s noted background of about 200 counts per million seconds per 1-keV channel in a 113-cm2, well-shielded HPGe detector (ORNL 6590) and a 6-keV-wide total ROI for the two gamma rays, pending additional information from Hamada. 2. The background for Nakanishi’s 152Eu measurements is based on a crude estimate from Figure 2 of Nakanishi’s 1983 paper in Nature, giving an apparent background of about 60 counts in 118.35 h=140 counts per channel per million seconds, and assuming a four-channel-wide ROI, pending additional information from Nakanishi.
60Co
Calculated MDC and critical level values are shown in Figure B-1. A value of 1 million seconds for both sample and background is used here as a nominal counting time for comparing results among investigators. Some investigators count for somewhat longer, in which case the MDC would decrease as the inverse of the square root of the counting time if sample and background counting times were increased equally. However, determining background by trapezoidal approximation from the sample spectrum itself introduces additional uncertainty. And if background is determined by a separate count with an empty sample chamber, there should be some

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FIGURE B-1 60Co detection limits.

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concern about whether the statistical properties of background count rate were adequately evaluated for such factors as drift in the instrument electronics over long periods and periodic variation due to solar activity. Furthermore, in the case of 60Co counted in recent years in samples from locations far from the hypocenter, there is a nontrivial contribution from cosmic-ray neutrons that increases the total background count rate beyond what is evaluated by either of the two methods above and correspondingly increases the MDC.
ii. 152Eu
Calculated MDC and critical level values are shown in Figure B-2. A value of 1 million seconds is used as a nominal counting time for comparing results among investigators. All the considerations cited above for 60Co also apply to 152Eu except that the cosmic-ray-generated background is not expected to make a significant contribution to experimental error.
iii. 36Cl
AMS results intrinsically report the isotope ratio of 36Cl to chlorine (36Cl/Cl). In this case, there is a system background for a condition of no injected sample that consists of electronic noise in the detectors being used for 36Cl and chlorine, but it is not typically reported. Ratios obtained for blank samples involve a source of stable chlorine of some type, which contains 36Cl at a level defined by the long-term (geological) saturation of the cosmic ray activation in the source material from which the chlorine was taken. Published data on the intrinsic detection limits of the method indicate that it is about 1 atom of 36Cl per 1015 atoms of chlorine (Straume and others 1994). Although that value is not precise or clearly stated from a statistical point of view, it is about one-hundredth of the background levels of interest that appear to exist in unexposed samples. Thus, the situation for 36Cl is different from that of 60Co and 152Eu: the MDC is determined completely by the statistical variation in the background due to cosmic-ray activation.
Calculated Estimates of In Situ Cosmic-ray Production
See Appendix C for a detailed discussion of cosmic-ray neutron fluences.
60Co
Komura and Yousef (1998) give a calculated value of 0.2 dpm/g (3.3× 10−6 Bq/mg) at saturation, on the basis of a flux of 0.008 n/cm2 s, in their 1998 abstract of a presentation at the 41st meeting of the Japan Radiation Research Society (December 2–4, 1998, Nagasaki). That value is also cited by Shizuma and others in their 1998 Health Physics paper.
152Eu
Komura and Yousef give a calculated value of 5 dpm/g (8.3×10−5 Bq/mg), based on a flux of 0.008 n/cm2/s in the 1998 abstract just cited.

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FIGURE B-2 152Eu detection limits.

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Measurements of Samples Far from the Hypocenters or Heavily Shielded Samples
60Co
Kerr and others (1990) measured two samples, one from a surface building and one from a mine. Both had rather meager cobalt content, and the MDC is about 2.4×10−5 Bq/mg as measured for the mine sample and 1.5×10−5 Bq/mg for the surface sample. Shizuma and others (1998) measured a sample from the Army Food Warehouse at 4571 m in Hiroshima. It also had little stable cobalt in the extracted sample, and the MDC was about 3.7×10–4 Bq/mg.
152Eu
Shizuma and others (1992) measured a heavily shielded sample from the basement of the A-bomb Dome, but its MDC was about 0.21 Bq/mg as measured, not nearly low enough to be informative. Shizuma also supplied some results from the Hiroshima Commercial High School at a 2870-m ground distance (Shizuma 2000a). It appears that this sample also had a poor recovery of 1.82 ppm in an enriched sample of 6.75 g, equaling about 0.0123 mg, resulting in an MDC of about 0.341 Bq/mg at time of measurement in 2000, or about 5 Bq/mg ATB in 1945.
Trends in Deep Portions of Cored Samples
60Co
Some early attempts were made to measure depth profiles in steel, for example, the work on Aioi Bridge girders reported by Hoshi and Kato (1987) and the work by Shizuma and others (1992) on structural steel of the A-bomb Dome, but these measurements are far too shallow to approach the asymptote.
152Eu
A thorough review indicates that a total of six cores or samples of a similar nature have been measured in granite or concrete. Of these, two (the Saikou-ji gravestone and the Motoyasu Bridge pillar) are of such small cross section that the effective depth of the deepest samples is not what is indicated by the axial distance on the depth profile. Of the others, none is measured at a depth greater than 37 cm, and no apparent approach to an asymptote is seen in the depth profiles. Two of the cores measured by Shizuma and others (1997) are deep enough to allow measurement at somewhat greater depths (Hiroshima Bank, 62 cm; Shirakami Shrine; 81 cm), but indicates that those deeper slices would fall below the MDC.
36Cl
On the basis of material presented by Tore Straume at the workshop on RERF dosimetry held on March 13–14, 2000, in Hiroshima, measurements deep in concrete appear to approach an asymptote in the vicinity of 100 Bq mg–1 at depths greater than 35 cm. That is consistent with background samples measured in a shielded location at 1700 m and that with other background samples reported by Straume and others (1994).

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Measurements of Laboratory Reagents
60Co
Komura and Yousef (1998) measured laboratory reagents containing large amounts of stable cobalt in a subterranean laboratory, giving very low detection limits. They reported a measured value of 0.21 dpm/g (3.5×10–6 Bq/mg), comparable with calculated values. Shizuma (1999) also measured 60Co in 4 g of CoO with a well-type Ge detector and obtained a much lower value of 7.2×10–7 Bq/mg. It is possible that this sample was not old enough to have reached saturation at background levels in its storage location or was stored in a heavily shielded location.
152Eu
Komura and Yousef (1998) report a value of 1.37 dpm/g (2.3×10–5 Bq/mg) in their measurements on Eu2O3 that is described as “modern” with respect to age (as opposed to before World War II), which is only about one-fourth of the calculated value. Shizuma (1999) reported an even lower value of 4.6×10–6 in 1 g of Eu2O3 reported to be about 25 years old. Again, there are major unresolved questions about the saturation levels of both Eu2O3 samples.
Potential Counting Interferences
Several potential causes of misleading results have been identified by reviewing the literature and interviewing the investigators. The specific possibilities mentioned here are preliminary and require further investigation. Spectral and radiochemical data were taken from the WWW Table of Radioactive Isotopes by Chu, Ekstrom, and Firestone, of the Lawrence Berkeley National Laboratory in the United States and the University of Lund in Sweden at the Internet address http://nucleardata.nuclear.lu.se/nucleardata/toi/index.asp.
Lanthanum X-rays from Photon Interactions in Stable Lanthanum of Sample Matrix
Nakanishi and others have primarily counted 152Eu via the Kα x-rays of samarium that are emitted at 39.522 keV and 40.118 keV. Because of the chemistry of the europium enrichment process and the natural abundance of lanthanum in the lithosphere, the samples are expected to contain large amounts of lanthanum. Lanthanum has Kβ rays at 37.720 keV, 37.801 keV, 38.804 keV, 38.726 keV, and 38.826 keV. All can be produced by interactions of higher-energy photons, such as background photons and photons from 152Eu, with inner-shell electrons in the lanthanum contained in the sample.
138La and 176Lu Relative to 152Eu in the 39 to 40-keV Region
138La and 176Lu are extremely long-lived (over 1010 y) naturally occurring lanthanides that might be expected to accompany 152Eu in chemical separations. Their

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natural isotopic abundances are 0.0902% and 2.59%, respectively. By calculation, natural lanthanum should be about 0.82 Bq/g 138La/La and natural lutetium should be about 52 Bq/g 176Lu/Lu. 138La emits Ba x-rays at 36.304 keV (1.19%), 36.378 keV (3.69%), 37.255 keV (1.16%), and 37.349 keV (0.261%), and five Ce x-rays at 39.17−40.33 keV, all with low spectral abundance under 0.01%. This source of interference is expected to be minor compared with the lanthanum x-rays.
176Lu emits no photons at these precise energies but does emit a number of lower—and higher—energy photons and was specifically identified by Nakanishi as a possible concern, perhaps because of its substantial natural abundance.
212Pb(212Bi) Relative to 152Eu in the 39 to 40-keV Region
212Bi of the thorium series (half-life, 60.55 m) has a 39.9-keV gamma with 1.1% spectral abundance associated with its alpha decay.
223Ra and 234U Relative to 152Eu in the 122 keV Region
223Ra (half-life, 11.435 d), a naturally occurring member of the actinium (4n+3) series, has a gamma ray of 1.2% spectral abundance at 122.319 keV. 234U has a gamma ray of 0.034% spectral abundance at 120.90 keV.
227Ac Relative to 152Eu in the 122-keV Region
227Ac (half-life, 21.773 y) of the actinium series, has a gamma ray of low spectral abundance (0.00213%) at 121.53 keV.
Discussion
In many cases, the uncertainty estimates calculated for this analysis are substantially greater than those published by the authors originally. That is due primarily to the inclusion of terms involving the assay of stable cobalt or europium. Estimates of the precision of the stable cobalt or europium assay based on measures of reproducibility have often been included in publications but have almost never been included in a combined estimate of total uncertainty. The accuracy (as opposed to the precision) of the assays is also of concern, especially in cases involving unenriched samples. The calibration of the assays of stable cobalt or europium in unenriched samples appears to have unexpectedly substantial uncertainty, according to the information that has been obtained to date. Thus, the values estimated here for the uncertainty in the reported values of stable cobalt or europium and the total combined uncertainty of the specific radioactivity per unit mass of stable cobalt or europium, are often considerably larger than might have been suggested previously.
The most important effect of these revised estimates, in a proportional sense, is to increase somewhat the unrealistically low uncertainty that was sometimes estimated for measurements with good counting statistics because of their relatively large radioactivity content.
Table B-3 offers some interesting observations. In all cases, the measurements suggest that the DS86-calculated value is (very roughly) 50% too high at the short-

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est ranges. Interestingly, the initial fitted relaxation lengths are not particularly discrepant compared with DS86. But the measurements clearly display substantially greater curvature than DS86, as quantified by the δ parameter for change in relaxation length per unit slant range. Several selected subsets of the data are shown in the table. They serve mainly to illustrate that the trends are not strongly influenced by the less precise data at longer ranges. For 60Co, three subsets show the effect of omitting successively, in order of decreasing range. The highly discrepant measurements at distances beyond the Yokogawa Bridge; the measurements at the Yokogawa Bridge, for which the fully calculated DS86 values involve a large correction from free-field values because of the unusual nature of the structure in which the samples were constituent; the measurements at 1168 and 1330 m that are thought to be above the MDC but are not completely documented with respect to mg cobalt content.
In the case of 152Eu, essentially all measurements beyond 1200 m are suspect with respect to the MDC, at least pending some additional information on several measurements by Nakanishi and others. However, these more distant measurements do not account for the curvature in the fitted values. There is a difference between the fitted values for the two main groups making measurements, the Nakanishi group and the Shizuma group, but the difference does not appear to be statistically significant.
The Nagasaki measurements, in contrast with those in Hiroshima, do not appear to support statistically a discrepancy with DS86, on the basis of the methods described here that have been applied to them thus far. However, the absence of a discrepancy in Nagasaki is not well established. Some trends in the data are suggestive but do not achieve statistical significance, and the 152Eu analysis in particular is very strongly dependent on a few influential observations at the greatest distances. Showing the absence of an effect amounts to “proving a negative.” The relative paucity of measurements in Nagasaki, particularly at greater distances, is problematic. To a great extent, this lack of longer-range measurements in Nagasaki is driven by the lower overall neutron fluences there. One cannot measure as far from the hypocenter in Nagasaki as in Hiroshima, for a given limit of detection, because the values of neutron activation overall are somewhat lower in Nagasaki.
The low-level measurement situation is different among the three main radionuclides that have been measured for thermal-neutron activation. For 36Cl, the detection limit might be some 2 powers of 10 below the apparent natural background level in materials similar to the samples of interest, which presumably is due to cosmic-ray production over geological time. The natural background level has been measured in several types of relevant sample materials and appears to be reasonably consistent overall with the level that is approached in the deeper portions of large concrete cores. Nevertheless, the limit on detectability of 36Cl attributable to the bomb fluence might prove to be determined by the uncertainty in the sample-specific level of 36Cl due to cosmic-ray production, which has some uncertainty in addition to counting statistics. There is substantial potential variation among samples in the saturation level of the chlorine in the sample, which presumably is due to the geological and hydrological history of the chlorine involved. In concrete

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cores, although the material was presumably homogenized at the time of construction in very recent geological time, so that cosmic background should be homogeneous throughout a concrete pour, many cores are not deep enough to approach an unequivocal asymptote that clearly applies to the concrete in question. In fact, the situation is even more complicated, in that concrete can contain inclusions in the form of rocks, pebbles, and so on, that could dominate the material in a given slice of a core and have a different background level from the concrete itself.
Another source of measurement error in the case of 36Cl is the possible dilution of the stable-chlorine pool by infiltration of rainwater into the sample matrix in situ, which needs further evaluation.
Several types of possible errors are related to the depth profile of 36Cl activation in a concrete core: physical modifications of the exposed surfaces of concrete structures (adding or removing material), which might affect the depth profile near the surface or cause uncertainty in the effective depth of a slice from a core at the time of sampling versus ATB, and unexpected buildup or other unforeseen effects due to the interactions of incident high-energy neutrons near the exposed surface.
In addition, there is an issue of possible error due to production of 36Cl from a competing neutron reaction on potassium. However, the classifications pertaining to depth profile and competing production by the 39K(n,α)36Cl reaction are related to errors in calculated values rather than measured values.
For 60Co, the background samples that have been measured have rather high detection limits, especially because of relatively small content of stable cobalt in the steel samples that were measured. The only available indications of likely natural background levels of this radionuclide in iron and steel come from calculation and from measurements in laboratory reagents that contain large masses of concentrated stable cobalt. These natural background indications are below the levels of interest in the more distant bomb samples by less than a power of 10, and the situation is degrading with each passing year because of the radioactive decay of the 60Co from the bomb fluence.
Thus, natural background levels due to cosmic-ray neutrons appear to be a small but not negligible source of bias in the more distant 60Co measurements. That effect has been evaluated here and an effort has been made to correct for it, but better in situ measurements of background in true environmental samples would be helpful.
All but perhaps one of the reported 60Co measurements appear to lie above the nominal calculated MDCs reported here. (More detail on specific measurements is given in the body of Chapter 3.) If samples contained naturally occurring 60Co at exactly 3.33×10−6 Bq/mg due to cosmic-ray production, this would increase the applicable background count rate by no more than 5%, except for the larger and more distant samples of Shizuma and others (1992), which would see increases up to about 14%. The actual increase in the MDC would depend on the assumed statistical distribution among samples of true values for 60Co due to cosmic-ray production, but the effect would be minor for most cases of interest.

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For 152Eu, there are no relevant background samples at all. Distant samples have not been measured, and the deeper portions of granite cores are too small and too close to some portion of the surface exposed to the bomb fluence to provide an indication of natural background levels in the sample materials of interest. The sample from the basement of the A-bomb Dome building (Shizuma and others 1992) has a detection limit that is insufficient to measure the levels of interest. Again, the only available indications of likely natural background levels of this radionuclide in rocks, concrete, and ceramic tiles come from calculation and from measurements in laboratory reagents that contain large masses of concentrated stable europium. These natural background indications lie below the levels of interest in the more distant bomb samples by at least 2 powers of 10; this suggests that they should not be a significant source of bias in the measurements done to date. However, that has not been confirmed with true background samples of rocks, concrete, and ceramic tiles.
In the case of 152Eu, some of the most distant measurements are close to or below the MDCs calculated here and should be interpreted with caution. That also implies that current methods might not have sufficient precision to provide useful estimates of natural background levels in the sample materials of interest; therefore, it might not be feasible to measure true background levels in sample-type materials. However, it might still be of interest to extract and measure a few large background samples, in order to reduce the MDC for excluding natural background levels further below the range currently being reported in measurements.
There is a possibility that measurements of 152Eu at greater distances are affected by the counting interferences discussed above. It is not yet clear that all the measurements made by Nakanishi and others at 39–40 keV are free of potential bias from these sources. The method described by Shizuma and others (1993) of comparing the results of the 122 and 344-keV regions is intended to address this issue, but it might not have adequate sensitivity to identify all measurements that are affected by the counting interferences in the 122-keV region at these low levels. These issues deserve further attention and clarification.
Finally, substantial issues related to various aspects of quality assurance cannot be quantitatively evaluated here. Any future work should give serious consideration to maximizing the value of this important body of work by following a well-designed program of remeasurements and intercomparisons with stringent data-quality objectives.
SUMMARY AND CONCLUSION
Careful Analysis of the Measurement Data Has Results in Several Important Observations
The uncertainty used to characterize published measurements should be increased somewhat in most cases by calculating a total combined uncertainty for each

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measurement to account for all sources of random error that might have affected final reported values.
Statistical simulations indicate that the dispersion among the measurements, even after correcting some of the measurements for sample composition and local environment using the limited sample-specific calculated values that are currently available, is much too large to be consistent with the estimated uncertainties of the measurements, when those uncertainties are calculated based on propagation of error methods applied to the measurement process. Some of this apparent over-dispersion among the measurements could clearly be reduced by using detailed models of samples and their environs to create more accurate sample-specific calculated values for all of the measurements. However, some of this over-dispersion may also reflect sources of random error in the measurement process that are still unknown.
When the estimated uncertainties are increased to the extent that appears appropriate on the basis of the (admittedly sparse) information available for the present analysis, a discrepancy with DS86-calculated values clearly still remains in Hiroshima.
The data for Nagasaki are to some extent suggestive of a discrepancy, but more measurements are necessary to resolve this issue.
The discrepancy with DS86 in Hiroshima is statistically fairly robust and does not appear to be attributable solely to the less precise measurements made at the greatest distances.
When the measurements are fitted with a model that allows the relaxation length to vary, as should be allowed because of physical considerations, it appears that the initial relaxation length near the hypocenter is close to DS86 values, but the relaxation length increases more rapidly with distance than DS86. That might offer a clue to the nature of the discrepancy.
The 36Cl measurements have several significant, recently discovered complications that must be resolved before they can be subjected to useful analysis.
The 60Co and 152Eu measurements are subject to several important concerns that could be addressed by a program of additional measurements or remeasurements and intercomparisons among laboratories.
Fitting a rapidly changing relaxation length involves an effect at the greater distances of interest in the Hiroshima neutron activation measurements (say, 1000–2000-m slant range) that is similar to fitting a finite asymptote, which might correspond to a “background effect” of some kind; and the two models might not be statistically distinguishable from each other in these data.