Status of the Dosimetry for the Radiation Effects Research Foundation (DS86) (2001) / Chapter Skim
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Appendix B: An Uncertainty Analysis of Neutron Activation Measurements in Hiroshima and Nagasaki
Appendix B: An Uncertainty Analysis of Neutron Activation Measurements in Hiroshima and Nagasaki
Pages 123-168
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From page 123... ...
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 (ATBJ in 1945. Depending on the measurement method, this value may be stated in units involving ra123
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From page 124... ...
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.
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From page 125... ...
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.
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From page 126... ...
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)
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From page 127... ...
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.
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From page 128... ...
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.
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From page 129... ...
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.
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From page 130... ...
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.
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From page 131... ...
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.
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From page 132... ...
Such calculations should be done by an expert in any case. The neutron measurements are in four categories with respect to the DS86calculated 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)
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From page 133... ...
· 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 samplespecific DS86 value available.
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From page 134... ...
Otherwise, there can be no discussion of parameters, such as relaxation length. To provide a basis for such comparisons, a decision was made to fit curves to the scaled DS86 free-field calculated values and scaled measured values corrected for cosmic background and for the ratio of the freefield value to the most completely calculated sample-specific in situ value available.
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From page 135... ...
That is, among measurements of the same estimated relative precision, stated as estimated coefficient of variation (same value of y/x) , the second factor is constant, and the weights are inversely proportional to the squares of the measured values.
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From page 136... ...
is the fitted curve according to Equation 1 evaluated at the same slant range as x. Therefore, with constant relative measurement precision, each residual has an influence on the fitted curve equal to the proportion of the measured value that the residual represents, regardless of whether the measured value is a large one or a small one.
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From page 137... ...
As noted above, RERF is making continuing efforts to reduce this source of error. Correlated Errors In producing fitted curves, it would be desirable to take account of all covariance among measurements, especially that known to exist among measurements that share factor or factors, such as a measured value of stable cobalt or europium, a calibration factor for counting efficiency, or a calibration factor for the assay of stable cobalt or europium.
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From page 138... ...
If one or more of these variables takes on identical values for all measurements in the set, as arises when the same calibration factor is used for more than one measured value say Ui =u,c~ui =~u,Vi =V,~vi =Ov, p |
From page 139... ...
.U21 (15) i=p It appears that some minor variation of this formula is sufficient for all the radiometric results, in that the investigators' methods are such that subsets of reported values at the same site share either the first, the second and third, or all three of these: · The calibration factor for counting efficiency.
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From page 140... ...
Radiometric methods quantify the neutron activation product nuclide, 60Co or i52Eu, in terms of its radioactive emissions by counting gamma or beta emissions in the sample per unit time. The number of emissions can be corrected by subtracting a background to obtain a net count rate and is then divided by the appli
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From page 141... ...
The mass-related value m is the raw result of the assay of the mass of cobalt or europium in the sample in such units as count rate of an activation radionuclide after neutron irradiation or units of absorption in atomic absorption spectroscopy, and Sib is a calibration factor for that assay; the product of m and Crib is expressed in milligrams. Finally, Ellis the applicable counting efficiency in counts s-i Bq-i, and HL is the half-life of 60Co (5.2714 yr)
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From page 142... ...
or has been simultaneously estimated from the spectrum of the sample itself by means of a trapezoidal approximation based on the count rates in channels adjacent to the region of interest for a given photon energy range. Counting of system background was generally not determined with prepared blank samples intended to simulate the radiation-scattering properties of the sample material, but this is not a major concern; in fact, it would have been difficult to simulate the radiation-scattering properties of the samples with materials assured not to contain any detectable sources of radiation in the energy regions)
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From page 143... ...
For all those reasons, considerable uncertainty exists in the comparative saturation levels of bomb-fluence samples and laboratory reagents, but the former are likely to be more saturated overall. A "best currently available" estimate of cosmic-ray background, corrected for decay to reflect investigators' decay correction to ATE, was subtracted from the measured values for plotting and fitting herein.
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From page 144... ...
REVISED UNCERTAINTY ESTIMATES (60Co AND Lieu) Background and Net Count Rate As noted above, it was not possible to check investigators' estimates of uncertainty based on counting statistics, because of the inability to obtain the raw data.
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From page 145... ...
Calibration of Counting Efficiency The best approach to estimating the error in the calibration of counting efficiency Ellis to break it down into two components: · The error in the radioactivity content of the calibration standard as stated by its supplier and the error in the measured value obtained for that standard material with the investigator' s equipment. · The differences caused by differences in the geometry of the bomb-fluence samples and the calibration source.
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From page 146... ...
In other cases, such as assay by neutron activation analysis (NAA) , the uncertainty was apparently based on the Poisson counting statistics of the radiation from the activation-product nuclide in the irradiated sample.
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From page 147... ...
In some cases, it was not the emissions from the decay of the ground-state isomer of i52Eu that were measured, but the emissions from isomeric transition of a short-lived metastable state, namely the i52Eu state with a half-life of 9.311 h (Shizuma and others 1993~. The complicated neutron activation production and decay schemes of the europium isotopes and their isomers, including i54Eu and i52Eu, and the related potential interferences in their spectra in various energy regions of interest require careful assay.
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From page 148... ...
measured 60Co in enriched steel samples and assayed stable cobalt by the calorimetric method, and they reported uncertainty estimates that are clearly based on reproducibility among replicate measurements. A reproducibility-based estimate of "< 5%" was given.
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From page 149... ...
Pending additional information, a calibration error of 5% is used here in addition to the error estimates given by the authors for stable europium. · Okumura and Shimasaki (1997)
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From page 150... ...
The calibration error for counting efficiency was estimated in two separate parts, source-detector geometry and other; "other" includes the accuracy of the radioactive solution used as a standard. These errors and the reproducibility-related errors given by the authors for stable cobalt or europium content must be combined with the counting-statistics errors attributed by the authors to count-rate results to obtain a more realistic estimate of total experimental error.
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From page 151... ...
Some of this over-dispersion, however, might also reflect sources of random error in the measurement process that are still unknown. Issues Related to Background, Spurious Signal, and Detection Limits The presence of background is a sine qua non of radiometric measurements and is of particular interest in the type of low-level measurement that is necessary for neutron activation products from the atomic bombs in Hiroshima and Nagasaki.
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From page 152... ...
The MDC that actually applies to a given sample with respect to bomb fluence is defined by the total background count rate that applies to that sample, including background from cosmic-ray activation and other possible sources. To obtain some generic values for the analysis of the various radiometric methods, it is assumed that sample and background are counted for equal intervals, that type I and type II error rates are set at 5%, and that the following formula is therefore applicable, as defined in NUREG 1507 (1995~: MDC=3+4-65sB B KT where SB is the standard deviation of the background count (for a nonradioactive sample)
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From page 153... ...
For the present purpose, it is felt that MDCs derived from the assumption of a separate background count and equal counting intervals, which roughly equate to a trapezoidal approximation using equal numbers of channels in the emitted photon and background regions of interest, are still representative. For two representative amounts of recovered stable element that might be present in the sample, a minimum detectable specific activity in the form of a concentration, denoted MDCSa, is then calculated in units of becquerals per milligram of the target element present in the sample on the basis of the measures involved (sample weight, elemental composition, and fraction of the element recovered in an enrichment process)
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From page 154... ...
Those amounts do not have at least a 95% probability of giving a count exceeding the Lc (that is, the type I error rate might be marginally acceptable, but the type II error rate, where it is of concern, is not acceptable.) Furthermore, there is additional uncertainty in the calibration of counting efficiency and, more notably, in the assayed value of the sample's content of the target element.
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From page 155... ...
detector (Kerr and others 1990) On the basis of a cross calibration involving the counting of a sample before and after chemical enrichment, the applicable counting efficiency was stated as 3.99 + 0.24% that is, 0.040 cps/Bq for the paired large (300-mm diameter by 200-mm thick)
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From page 156... ...
The counting efficiency is documented in the paper as 0.002938 cpslBq. On the basis of a background-sample spectrum provided by Iimoto, the background count rate is about 12 counts/channel in 1.8 x 106 s, or about 227 counts per million seconds in the noted 34-channel region of interest.
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From page 157... ...
A revision of these MDCs in the case of 60Co to account for natural 60Co from cosmic-ray production, is discussed below: TABLE B-4 Detection Limits for Thermal Neutron Activation Measurements in Hiroshima and Nagasaki 6oco 6oco 6oco Radionuclide 6oco Kimura/ 6oco Hashizume/ Okumura/ Investigator(s) Shizuma Hamada Kerr Maruyama Shimazaki Photon Energy 1173 keV 1173 keV 1173 keV beta coincidence Measured + 1332 keV + 1332 keV + 1332 keV 0-318 keV (25-250 keV window)
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From page 158... ...
cts on interval 3.42 x 10-3 1.25 x 10-3 560 226.6666667 of T sec. SB 58.45226 35.35534 23.66432 15.05545305 counting efficiency, 0.09 0.04 0.008 0.003 cps/Bq MDC, Bq 3.05 x 10-3 4.19 x 10-3 1.41 x 10-2 2.43 x 10-2 lowest mg per 0.02 0.02 1 1.16 sample highest MDCsa, 1.53 x 10-i 2.09 x 10-i 1.41 x 10-2 2.10 x 10-2 Bq/mg highest mg per 0.05 0.05 2 1.91 sample lowest MDCs, 6.11 x 10-2 8.37 x 10-2 7.06 x 10-3 1.27 x 10-2 Bq/mg HL 13.54 13.54 13.54 13.54 year of measurement 1992 1992 1992 1997 highest MDCsa,ATB, 1.69310 2.32063 0.15670 0.30053 Bq/mg ATE lowest MDCsa,ATB, 0.67724 0.92825 0.07835 0.18252 Bq/mg ATE NOTES: 1.
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From page 160... ...
Published data on the intrinsic detection limits of the method indicate that it is about 1 atom of 36C1 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.
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From page 162... ...
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-i 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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From page 163... ...
They reported a measured value of 0.21 dpm/g (3.5 x 10-6 Bq/mg) , comparable with calculated values.
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From page 164... ...
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.
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From page 165... ...
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 36C1 attributable to the bomb fluence might prove to be determined by the uncertainty in the samplespecific level of 36C1 due to cosmic-ray production, which has some uncertainty in addition to counting statistics.
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From page 166... ...
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.
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From page 167... ...
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.
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From page 168... ...
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.
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