Version 3.2

Cascade Summing

Correction

Gamma Spectroscopy Software Solutions

ISOCS ™ - LabSOCS ™

Version 4.2

Monica Gattinoni

Summing Effects Definition

� Random Summing– loss of observable peak area as a function increasing count rate– independent of energy, sample-to-detector distance, number of

nuclides in the sample– correctable with the use of a pulser or a stationary reference

source� Cascade Summing (True Coincidence Summing)

– loss or gain of observable peak area as a function of nuclide decay scheme and geometry

– independent of count rate– different effect for different gamma energies of even the same

nuclide

Distance Result, 22% Detector

• Example of coincidence summing effect for some of the Eu-152 gamma lines as a function of sample - detector distance using a small 22% relative efficiency detector. Note the almost 50% loss of area for peak 244 keV at

close distances.0 5 10 15

0.5

1

1.5

Source - Detector Distance (cm)

Rat

io o

f Obs

erve

d vs

. Cor

rect

Pea

k A

rea

244 keV

1085 keV

1112 keV

Simple Coincidence Theory

� With no coincidence, the rate of pulses for peakγ1 is n = Ap1ε1where A = activity, p1 = emission probability ofγ1, and ε1 = peak efficiency at E1

� With coincidence, the rate of pulses in peak γ1 isn* = Ap1ε1-Ap1ε1εt2where εt2 is the probability of observing a count due to γ2 emitted at energy E2 anywhere in the spectrum, i.e. the total efficiency at energy E2.

� The correction is C = n/n* = 1/(1-εt2)� Need to calibrate for total efficiency, or a

combination of peak efficiency and peak-to-total efficiency, which can be used to calculate the total efficiency.

γ1

γ2

Co-60

Ni-60

Total efficiency vs. Peak efficiency

• Total efficiency: ratio of all counts in the spectrum to the gamma rays emitted by the source

• Peak efficiency: ratio of all counts in the photopeak(at the emission energy) to the gamma rays emitted by the source.

• P/T ratio is the Peak Efficiency divided by the Total Efficiency.

0 100 200 300 400 500 60020

30

50

100

200

300

500

1,000

Total efficiency

Peak efficiency

Peak-to-Total Calibration

• The inherent P/T-ratio– for all practical purposes, does not depend on

the source-to-detector distance– it has been shown that for HPGe detectors up

to about 80% relative efficiency the use of the intrinsic P/T-calibration during the integration of the coincidence correction factor produces sufficiently accurate results.

P/T ratio is essentially independent of sample position relative to the detector

7

6

5

4

3

1 2

1 2 3 4 5 6 7

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

Model: ConstantChi 2 = 0.00303a�-1.614

Model: ConstantChi 2 = 0.00103a�-1.224

Mapping of P/T-ratio around detector(no separation)

Zn Mn

ln(P

/T)

Position of point around end cup

Empirical Peak -to-Total Curve

100 1000

-2,0

-1,8

-1,6

-1,4

-1,2

-1,0

-0,8

-0,6

-0,4

-0,2

20% Canberra, 1997

18% ORTEC, 1995

20% Canberra, 2000

P/T

Rat

io (

Ln)

Energy, keV

Cascade Summing effects

Efficiency calibration is also effected

Br-82, Sand Matrix, 15% detector

0.85

0.9

0.95

1

1.05

1.1

1.15

0 500 1000 1500 2000Energy (keV)

Rat

io to

Cor

rect

Act

ivity

Corrected Activity

Uncorrected Activity

Coincidence Correction for Voluminous Sources

• The inherent P/T-ratio is a constant value (geometry independent):

• But our sample has a certain geometry, so the peak efficiency is different• We use LABSOCS to calculate for us the

PEAK EFFICIENCY for the used geometry• Based on the above formula, the

TOTAL efficiency can next be calculated as follows:

(E)Constant (E) Efficiency Total

(E) EfficiencyPeak =

(E) Efficiency Total(E)Constant

(E) EfficiencyPeak =

Coincidence Correction forVoluminous Sources

• divide source into 2n voxels• place point source into each voxel in

random location• compute efficiency at that point in space• divide by inherent P/T ratio• calculate the coincidence correction

factor• do this for all voxels and totalize• repeat with 2n+1 voxels• continue doubling until no further

change in coincidence correction factor• repeat for all energies and sources

source volume

generic attenuators 1 & 2

sample container

source attenuation correction pathway

collimator attenuation correction pathways

collimator

detector

point sources

Conclusion

• Approximate detector characterization is acceptable to use for cascade summing corrections when the detector specific characterization is not available, at least above about 120 keV.

• Genie 2000 (S501C) will be shipped with a selected range of detector characterizations, enabling the effectiveCoincidence Summing Correction for the vast majority of cases.

Cascade Summing Correction

CascadeSummingCorrection

P/TCalibration

GeometryDescription

NID Results

CorrectedNID

Results

P/T (Peak to Total) Calibration

P/T calibration curve

241Am

109Cd

54Mn

137Cs

113Sn

65Zn

P/T (Peak to Total) Calibration

Genie 2000

• Pre loaded P/T calibrations per detector type.– Either do a detector specific P/T calibration

– Or use one of the pre-loaded files

Geometry Description

GeometryComposer

GeometryDescription

(*.GEO)

Geometry Composer

Geometry Composer

Cascade Summing Correction

• 1. Perform P/T Calibration (only once for eachdetector) – or use a pre-loaded one.

• 2. Define counting geometry and select similardetector from supplied LabSOCS templates

• 3. Perform Cascade Summing Correctionduring NID

Cascade Summing Correction

Nuclide Id Energy Yield Activity Activity Coinc

Name Confidence (keV) (%) (Bq /Filt) Uncertainty Corr

K-40 0.946 1460.81* 10.67 1.037731E+00 6.206464E-01 miss

Co-60 0.947 1173.22* 100.00 9.617665E+00 3.544436E-01 0.949

1332.49* 100.00 9.375374E+00 3.637913E-01 0.946

Se-75 0.982 96.73* 3.41 1.564261E+01 1.424260E+00 free

121.11* 16.70 1.444366E+01 7.741458E-01 0.909

136.00* 59.20 1.326770E+01 7.399303E-01 0.907

198.60* 1.45 1.772982E+01 3.722104E+00 0.869

264.65* 59.80 1.353332E+01 6.656023E-01 0.901

279.53* 25.20 1.414516E+01 7.395598E-01 0.930

303.91 1.32

400.65* 11.40 2.288417E+01 1.124830E+00 1.531

Kr-85 0.972 513.99* 0.43 1.820692E+03 5.812067E+01 miss

Ba-133 0.949 79.62 2.55

81.00* 33.00 5.994030E+00 5.042487E-01 0.912

276.40* 6.90 5.584701E+00 6.266892E-01 0.931

302.84* 17.80 6.196358E+00 5.741855E-01 0.962

356.01* 60.00 5.427056E+00 3.817154E-01 0.966

free = No coincidence correction required.

miss = Nuclide energy was not found in the coincidence library.

Distance Effect

• To correct/avoid for coincidence summing you could move the sample further away from the detector.

• If you move a 5 cm diameter x 1 cm high disk source from being on the end cap to 15 cm away to eliminate true coincidence effects the MDA will increase by a factor 22.

• To reach the same MDA you are able to achieve at the end cap you must count the sample at 15 cm for 500 times longer!

Real examples, pointsource

• XTRa, GX4018, Pointsource– Pointsource at contact

• Co-60: 21% correction

– Pointsource at 2 cm• Co-60: 8% correction

– Pointsource at 5 cm• Co-60: 3% correction

Real examples, filter paper

• XTRa, GX4018, filter paper– Filter at contact

• Co-60: 17,5% correction

– Filter at 2 cm• Co-60: 7% correction

– Filter at 5 cm• Co-60: 3% correction

Real examples, Beaker

• XTRa, GX4018, Beaker– Beaker at contact

• Co-60: 7,5% correction

– Beaker at 2 cm• Co-60: 3,5% correction

– Beaker at 5 cm• Co-60: 1,85% correction

Overview

XTRa, GX4018, b01166, Co-60, % loss

Pointsource Filter Beaker0 cm 21 17,5 7,52 cm 8 7 3,55 cm 3 3 1,85

NEW Cascade Summing v3.2Total efficiency automatically calculated

• Now TE can be calculated internally [P/T method still retained].

Using a characterizeddetector the Peak-to-Total calibration is no longer needed

• Total Efficiency algorithms include corrections for build-up.

• Calibration sources are no longer required in order to take advantage of the Genie2K’s cascade summing corrections.

• CSC results are better

NEW Cascade Summing v3.2Total efficiency automatically calculated

NEW Cascade Summing v3.2

• Correcting for gamma-gamma, X ray-and positron annihilation-gamma summing effects

• Expansion of the library to include 200 nuclides (over 2050 lines).

NEW Cascade Summing v3.2Nuclear Data Automatically

extracted from ENSDF

Measured Activity of a filter paper on the detector endcap

without and with Canberra CSC

Cascade Summing Correctionwith Characterized Detector

Other LabSOCS Benefits

When calibration source is different density then sample

Sample is different Z than standard

3D Geometry Composer

LabSOCS and Traditional Efficiency Calibration agreement

Custom General Purpose Beaker Editor

Lab-ISOCS IUE for automated Sensitivity and uncertainty analyses

Lab-ISOCS IUE for automated Sensitivity and uncertainty analyses

ISOCSIIn Situ Object Counting System

ISOCS Application Example

Geometry Composer :

•Characterized detector

•User-selected collimator

•H-Beam with external contamination