The German standard DIN 25482-5, published in 1993, is equivalent to the in-ternational standard ISO 11929-3. It describes briefly the evaluation of high res-olution γ ray spectrometry measurements. It is required that neighbouring γ lines are more than four times the full width at half maximum (FWHM) apart and the background around a peak can be described by a linear function, other-wise DIN 25482-2 has to be used. The standard neglects any influence of sample treatment, acquisition geometry, weighing, system instabilities and more. Fur-thermore, it is assumed that any factors needed to convert a measured count rate to a sample activity are known to a high precision, so that their uncertainties can be neglected. The data acquisition time has to be small in comparison to the (ef-fective) half life of the nuclide of interest to fulfil the prerequisite of a constant activity. Moreover, it is implied that the detector signals, registered in the spec-trum, are independent Poisson processes so that the sum of counts within a range of channels is Poisson distributed as well. Since only sums of channel contents are used, which are together usually in the order of at least 100, the Poisson tribution is approximated in the calculations of DIN 25482-2 by the Gaussian dis-tribution. (Compare [DIN93, ISO00].) According to Blobel and Lohrmann [BL12]
this approximation is sufficient for expectation values µ larger than 10, except far away from the maximum of the Poisson distribution. As a result, the approxima-tion by a Gaussian distribuapproxima-tion can be problematic in case of low statistics like short measuring periods in low background systems.
An ROI within a spectrum is denoted in DIN 25482-5 with B and has a width of b. The two regions to determine the background within the ROI are indi-cated with A1 and A2, have a width of l and should be located next to the left and right edges of region B. Although it is recommended by the standard to choose the regions A1 and A2next to the edges of the ROI B, DIN 25482-5, sup-plement 1 [DIN97] shows several options to shift both regions for background determination in case tails of neighbouring peaks reach into the regions, which is not allowed. The gross counts within the ROI are denoted with NB (red area in Figure 4.2) and the background integrals with N1 and N2 (green areas). The calculated background within the ROI is denoted with N0(shaded area).
Energy / keV
430 432 434 436 438
Counts
0 50 100 150 200 250 300
350
A
1B A
2l b l
N
1N
BN
0N
2Figure 4.2.: Regions, widths and integrals used in DIN 25482-5 to determine the net peak area Nn. The gross counts NB (red area) within the ROI, background integrals Ni with i = 0, 1 and background N0 within the ROI (shaded area) are marked. (Spectrum shows the 433.94 keV peak of108mAg found in a silver glue sample assayed for 496 h.)
According to DIN 25482-5 the conditions for the width b of an ROI are
1×FWHM<b <3×FWHM (4.2)
b ≥4 channels
and recommends 2.5×FWHM for non dominant background. The width of the background regions l can be defined under the boundary condition
b <2 l <10 b
⇔ 1
10 < b
2 l <1 . (4.3)
The FWHM at the energy of the peak is taken from calibration data or neighbour-ing, well defined peaks. (Compare [DIN93].)
In the case the regions Ai can be chosen adjoining to the ROI, the background N0within region B can be simply calculated as
N0 = (N1+N2) b
2 l , (4.4)
which can be understood as the trapezoid shown in Figure 4.2 as the shaded area.
The net area of the peak is then calculated as
Nn = NB−N0 (4.5)
In case the regions Aihave to be shifted, Equation (4.4) has to be modified to take the different distances to the ROI into account by introducing different weights for the two background integrals N1and N2. (Compare [DIN93].)
Based on these quantities, the acquisition time t and the quantile k1−α of the Gaussian distribution for the type I error probability α, the decision threshold can be calculated according to DIN 25482-5 as
R∗n = k
The detection limit is a priori calculated from a measurement similar to the one of interest according to DIN 25482-5 as
R]n = (k1−α+k1−β)
with k1−β being the corresponding (single sided) quantile of a Normal distri-bution to the type II error probability β. The standard recommends to chose α = β = 0.025, which means to correctly accept the null hypothesis Rn = R0 in 97.5 % of all cases, if there is actually no contribution of the effect of interest in the spectrum. (Compare [DIN93].)
In case the measured count rate Rn is higher than the decision threshold R∗n, a net effect is declared as detected and the result can be converted to an activity of the sample. Only in this case DIN 25482-5 lays down to calculate a confidence interval to the obtained value with the boundaries
Rn±k1−γ/2 recom-mended to chose γ = 0.05. In case the measured count rate Rn does not exceed the decision threshold R∗n, the effect of interest is just classified as not detected.
(Compare [DIN93].) DIN 25482-5 does not include the calculation of upper limits.
Due to the approximation of the Poisson distribution by a Gaussian distribu-tion, the standard does in addition define some conditions in that the real decision
error possibilities can differ from the desired probabilities α and β. In case the ra-tio b/2l is chosen as 1 and low counts can be expected, Equations (4.7) and (4.8) are applicable to the widest input range.
A major drawback of DIN 25482-5 is that it does not define any methods to cor-rect for peaks already present in the background spectrum. It is only possible to evaluate peaks in an acquired spectrum in case there is no peak found at the same energy in the background spectrum or the peak of interest is high in comparison to the corresponding background peak so that the latter is negligible.