The andrzej soltan institute for nuclear studies

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Program Tukan8k
Peak shape calibration
2.5.2
Peak shape calibration is calculated using data pairs: peak position – Fwhm. If
automatic peak search command was executed before, then table of data is filled
automatically by data pairs: peak position - peak half width. The command is
executed in the same way as in the case of 
energy calibration
 with only one
difference, that you have a choice between two types of calibration equations:
polynomial: 
square root of polynomial: 
where for both types, equation degree can be from zero to three.
Calibration – general principles
Energy calibration
Efficiency calibration
Efficiency calibration
2.5.3
Efficiency calibration is calculated using data pairs: energy – efficiency. Correct
efficiency calibration requires sure identifaction of the energetic lines in
calibration spectrum and calculating detector effectivity for each line. Detector
efficiency is a ratio of counts under the line peak to gamma-ray photons with
corresponding energy emited from source. This quantity strongly depends on
energy and measurement geometry.
Calibration fitting function in this case is an exponent of polynomial of logarithm:
where: y – efficiency, x - energy value in [keV], qi – i-th coefficient of equation, i –
polynomial degree (can be chosen from 0 to 6).
Detection efficiency (see 
Efficiency calculation
) is calculated based on
parameters of calibration peaks and data comming from libraries of  standards or
could be input directly from keyboard
Calibration – algorithms
Energy calibration
Peak shape calibration
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TUKAN 8k
Efficiency of detection
2.5.4
Determination of the efficiency requires: data coming from calibration source
measurement with correct peak recognition and data coming from certificate of
the source given by the producer of the source.
where
: 
 
e[E]
- efficiency fo the detector for energy E
N
- number of netto counts in peak (netto area)
Ig 
- line intensify (or quantum efficiency)
tm
- time of measurement (lifetime) in seconds
Ad
- nuclide activity given by formula:
where:
 
Ao
-activity of the standard according to the certificate (in Bq)
Td
- date and time of the measurement with additional lifetime of
measurement (in seconds)
T0
- date and time coming from the certificate (in seconds)
T1/2
- nuclide half-lifetime in seconds
Given formulae have been applied in program to
 detection efficiency calculation
 
and to calculation of the parameters of the calibration curve.
Efficiency calibration
Przeprowadzanie kalibracji wydajnościowej
2.6
Mathematical analysis – algorithms
The program calculates peak parameters (in spectrum area selected by markers)
directly from experimental data ("on-line" model) or after fitting them by selected
function. The first method is used in "on-line" analysis, the program automatically
performs calculations after every marker's movement or after every data refresh
of 
live spectrum
. In the second method (available in ANALYSIS module only) the
process started activated on request using the mathematical model selected
earlier.
„on-line” peak parameters calculation
Mathematical models of peak analysis
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Program Tukan8k
The peak table that is a result of the spectrum analysis is created using the ROI
table. It means that every peak of interest must be included in ROI structure. The
ROI table may be created manually or automatically as a result of "peak search"
command. ROI table together with data describing measurement are displayed in
REPORT module. It can be examined there, edited and printed.
Peak analysis 'on-line'
2.6.1
The method of peak parameters calculation described below is defined in the
program as „no fit function" model and is given attribute „f0".
Model f0 
– „on-line" model of peak parameters calculation
Peak parameters are calculated using number of counts in channels between the
markers. The channels, at which markers are placed are also taken into account.
Depending on the options set in 
program configuration
, for calculation pure
counts in channel or net counts delivered after subtraction of background
calculated for selected peak are used.
Peak background – defined by linear function laying between interpolated
channels of beginning and end of area. Interpolation is calculated for three
external channels and the one on which the marker is set.
Calculated peak parameters:
Integral – calculated by summing counts in all channels laying within peak
boundaries
Area – computed as a sum of net counts in a peak:
where BL an average count number in 3 channels laying to the left of a peak, BR
an average count number in 3 channels laying to the right of a peak
Ctr. – peak position calculated using the net counts with a weighted average
method using "on_line" metod
Fwhm – peak half width calculated using the net counts. The program calculates
the position of two channels laying on a half of peak height on a left and on a
right of peak's side – their subtraction defines Fwhm value.
Fwtm - peak width calculated for 1/10 of its height calculated with the method
similar to Fwhm
All peak parameters are calculated in channel unit and recalculated to energy
values later on.
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