4.5. Activity determination from several gamma lines¶
In this example of use from the gamma-ray spectrometry, preferentially with high-resolution Germanium detectors, it is assumed that some different radionuclides may occur in the measured source, but the gamma lines (more than one) of that radionuclide for which the activity shall be determined must not interfere with other lines in the spectrum. The case that the activity shall be determined from only a single line, is not considered here, because that can be done with the standard procedure of UncertRadio.
Let the net counting rates \(R_{ni}\) of n gamma lines of the radionuclide be given. From these the activity values \(A_{i}\), in Bq, are calculated with the following equation:
The symbols herein mean:
Symbols
|
Meaning
|
In Windows Dialog
written as
|
\(R_{ni}\)
|
net counting rate of the gamma line at
energy \(E_{i}\), in \(s^{- 1}\)
|
RnetRate or
PeakNetRate
|
\(\epsilon_{i}\)
|
full-energy peak efficiency at energy
\(E_{i}\)
|
effi, eps or epsPeak
|
\({\ p}_{\gamma, i}\)
|
(absolute) emission probability of the
line i
|
pgamm
|
\(f_{att',i}\)
|
self-attenuation correction at energy
\(E_{i}\)
|
fatt
|
\(f_{coinsu,i}\)
|
correction for coincidence summing of a
line at energy \(E_{i}\)
|
fcoinsu
|
The standard uncertainties \(u\left( A_{i} \right)\) of the activities of single lines calculated according to Eq. (4.5.1) are calculated internally in UncertRadio by using the uncertainty propagation for Eq. (4.5.1).
Note: Covariances between the calculated activities \(A_{i}\) are considered. Such covariances e.g. may be inferred by reading efficiency values from the same FEP efficiency curve \(\epsilon(E)\), because their values for different energies are derived from the same identical set of parameters obtained from fitting the curve. Considering this would require the inclusion of the full covariance matrix of these parameters, which however cannot be handled by the program. Instead, single values of the covariance/correlation can be input under the TAB “Values, Uncertainties”.
Description of procedures for calculating a mean
Procedure for calculating Decision threshold and Detection limit for Gamspk1
Invoking the evaluation of several gamma lines
In the text field for equations the following call is used in that place where one otherwise would define the activity A of the counting source:
A = Gamspk1(E, tlive)
Gamspk1 is the name of the procedure being activated with its sub-dialogs which is doing the calculations of the chosen mean. Its parameters are:
E placeholder for the energies of individual gamma lines, in keV; the program automatically attributes values to \(E\)
tlive counting time (duration) (live-time) , in \(s\);
After loading the symbols from the equations they are available to the Gamspk1 function. Within the TAB “Values, uncertainties” a value and its uncertainty must be given for the symbol tlive, but not for E. Of course, instead of E and tlive other symbol names can be used, they only must be defined in the symbol list of the project. These symbols are defined always as “global” variables.
Note
For the source activity A as defined here the decay correction and e.g. a mass or a volume have to be defined in the equations outside of Gamspk1.
Input of values:
for further information about input: Dialog Values from spectrum evaluation
