783620H / 1013 6. ANALYSIS METHODS
The absorption table values can be constructed from mass attenuation coefficients or by ratioing unattenuated spectrum results with attenuated spectrum results. The ratio method is difficult to apply to the internal absorption correction because of the difficulty in obtaining appropriate spectra.
The mass attenuation coefficients are available from many sources. For mixtures not listed in the table, use the molecular weight fractions to obtain an average attenuation coefficient. For example, for water, multiply the hydrogen coefficient by 2.016, the oxygen coefficient by 16 and divide the sum by 18.016.
The table will contain the attenuation coefficients for the absorber being used. The x-factor, which you enter, is in inverse units of the attenuation coefficient. If the coefficient is entered in cm
2
/g, then the factor must be in g/cm
2
, which is the density (g/cm
3
) times the thickness of the sample.
The linear attenuation coefficients can also be used. In this case the input factor will be the thickness. It might be more convenient to use the linear attenuation coefficients so that the input factor can be directly related to the sample.
To use the ratio of two spectra, take at least two spectra with and without the absorber. It is not necessary that the peaks be listed in the library, only that the peaks be defined in the spectra. The half-life of any nuclide used should be very long compared to the time of measurement of both spectra, so that decay corrections will not have to be made. The program calculates the ratio of the peak areas from the absorber-in and absorber-out analysis output files. This will give a table of energies (peak energies) and multipliers. The program now stores the natural log of the multipliers to obtain a table of energies and coefficients. The coefficients are divided by the thickness of the absorber (Length, entered on the Corrections tab, Fig. 142, p. 162), so that the factor you have entered is the sample thickness.
6.10.6.3. Example — Ratio Method
The following is an example of calculating the absorption factor using the ratio of two spectra.
The results of the spectrum analysis without an absorber is shown in Fig. 250. The
154
Eu peaks are used because they are distributed over the range of interest.
The results with an absorber are shown in Fig. 251. The intensity (activity) columns from both figures have been transferred to Table 10, which also shows the ratio of the two sets of intensities and the logarithm of the ratio.
The logarithm values and the energies were entered into the absorption table. The absorption file records were saved in the “absorber-in” spectrum.
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GammaVision
®
v7 (A66-BW) 783620H / 1013
The spectrum was energy and efficiency calibrated using the point source (SRM 4275). The results of the analysis of the three conditions (no absorber, uncorrected absorber, and corrected absorber) are shown in Table 11.
NUCLIDE PEAK CENTROID BACKGROUND NET AREA INTENSITY UNCERT FWHM
CHANNEL ENERGY COUNTS COUNTS CTS/SEC 1 SIGMA % keV
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
EU-154
EU-154
205.56
42.83
600.95
123.08
EU-154 1216.09
247.92
EU-154 1240.28
252.83
21567.
3702.
2387.
842.
81517.
63228.
7803.
66.
81.52
63.23
7.80
.07
.56
.46
1.93
77.62
1.386s
1.096
1.172
.431s
EU-154 2909.92
591.69
EU-154 3516.06
714.71
EU-154 3558.06
723.24
EU-154 4296.98
873.20
EU-154 4902.96
996.19
EU-154 4944.77 1004.67
EU-154 6273.55 1274.35
EU-154 7860.55 1596.44
1386.
1248.
1344.
920.
869.
987.
77.
4.
3309.
258.
11503.
5748.
4710.
7712.
10292.
296.
3.31
.26
11.50
5.75
4.71
7.71
10.29
.30
3.67
47.25
1.45
2.21
2.33
1.81
1.02
6.21
1.490
1.071s
1.577
1.631
1.685
1.841
2.028
1.297s
s Peak fails shape tests.
D Peak area deconvoluted.
Fig. 250. No Absorber Analysis.
NUCLIDE PEAK CENTROID
CHANNEL ENERGY
BACKGROUND
COUNTS
NET AREA
COUNTS CTS/SEC
INTENSITY UNCERT
1 SIGMA %
FWHM keV
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
EU-154
EU-154
205.11
42.74 13258.
600.85
123.06
4562.
EU-154 1215.85
247.88
EU-154 1244.33
253.66
2402.
1757.
27358.
40707.
5359.
208.
27.36
40.71
5.36
.21
1.12
.68
2.56
43.82
1.407s
1.090
1.230
.317s
EU-154 2910.12
591.73
EU-154 3517.08
714.92
EU-154 3558.02
723.23
EU-154 4296.72
873.15
EU-154 4903.03
996.20
EU-154 4944.84 1004.69
EU-154 6273.41 1274.33
EU-154 7860.54 1596.44
1334.
1205.
1185.
602.
718.
799.
85.
0.
2679.
278.
8792.
4686.
3682.
6249.
8654.
256.
2.68
.28
8.79
4.69
3.68
6.25
8.65
.26
4.42
38.89
1.47
2.01
2.62
2.00
1.13
6.25
1.569
.354s
1.628
1.697
1.690
1.824
2.100
1.780s
s Peak fails shape tests.
D Peak area deconvoluted.
Fig. 251. Absorber-In Analysis.
All three isotopes in the sample are affected by the correction (see columns 3 and 4). The
154
Eu and
125
Sb are corrected to the no-absorber value. The
155
Eu activity is not corrected enough because all the lines used in the analysis of
155
Eu are below the lowest energy in the absorption
288
