Block Calibration Count Rates:
Measured vs. Predicted

Derek Hullinger
15 Jun 2004

Bottom Line First:

¹⁰⁹Cd runs: measurements match predictions to within 1% or so
¹³³Ba runs: measurements are about 6% higher than predictions
²⁴¹Am runs: measurements are about 13% higher than predictions
⁵⁷Co runs: measurements are about 33% higher than predictions

Data sets examined:

²⁴¹Am:

blk_6_am241_200_20_0_0_021127_1.fits.gz
blk_6_am241_200_20_0_0_021201_1.fits.gz
blk_6_am241_200_20_15_0_021128_1.fits.gz
blk_6_am241_200_20_30_0_021127_1.fits.gz
blk_6_am241_200_20_30_0_021202_1.fits.gz
blk_6_am241_200_20_45_0_021127_1.fits.gz
blk_6_am241_200_20_60_0_021127_1.fits.gz
blk_6_am241_200_20_60_0_021202_1.fits.gz

¹³³Ba:

blk_6_ba133_200_20_0_0_021128_1.fits.gz
blk_6_ba133_200_20_0_0_021202_1.fits.gz
blk_6_ba133_200_20_30_0_021201_1.fits.gz
blk_6_ba133_200_20_60_0_021201_1.fits.gz

¹⁰⁹Cd:

blk_6_cd109_200_20_0_0_021203_1.fits.gz
blk_6_cd109_200_20_15_0_021203_1.fits.gz
blk_6_cd109_200_20_30_0_021128_1.fits.gz
blk_6_cd109_200_20_45_0_021202_1.fits.gz
blk_6_cd109_200_20_60_0_021202_1.fits.gz

⁵⁷Co:

blk_6_co57_200_20_0_0_021126_1.fits.gz
blk_6_co57_200_20_0_0_021126_2.fits.gz
blk_6_co57_200_20_0_0_021126_3.fits.gz
blk_6_co57_200_20_15_0_021202_1.fits.gz
blk_6_co57_200_20_30_0_021128_1.fits.gz
blk_6_co57_200_20_45_0_021202_1.fits.gz
blk_6_co57_200_20_60_0_021128_1.fits.gz
blk_6_co57_200_20_60_0_021202_1.fits.gz

(from /local/data/gris1h/block_cal/Block_6/raw/)

Procedure (Measurement):

For each of the above data sets:

changed the value of the BLOCK_ID keyword to 11 (the correct value) in every extension (so that batgse2dpi would apply the correct window ranges)

created a list file with the name of the fits file in it

example command:

ls blk_6_am241_200_20_0_0_021127_1.fits.gz > blk_6_am241_200_20_0_0_021127_1.list

ran batgse2dpi to generate a dpi of the file

example command:

batgse2dpi blk_6_am241_200_20_0_0_021127_1.list blk_6_am241_200_20_0_0_021127_1.dpi histmode=window windows="/home/lhea/derek/windows/24kev.window"

for the ²⁴¹Am runs, I used a window from 24 keV to the end of the channel range.
for the ¹³³Ba runs, I used a window from 17 keV to 90 keV.
for the ¹⁰⁹Cd runs, I used a window from 17 keV to the end of the channel range.
for the ⁵⁷Co runs, I used a window from 20 keV to the end of the channel range.

divided each value in the dpi by the maximum exposure time recorded in the dpi to produce a rate in counts/livetime
(the exposures differ by very little from sandwich to sandwich)

Procedure (Prediction):

Predicted Count Rate (For Each Detector):

²⁴¹Am:

¹³³Ba:

¹⁰³Cd:

⁵⁷Co:

S: The number of photons/s emitted by the source into 4π

The values were taken from Nadine’s calibration report (calibhigh.xls), adjusted to what they would have been at the time the measurements were taken

Example:

¹⁰⁹Cd has a half-life of 462.6 days. On 6/27/03, Nadine calibrated the Cd-109-158 source and found that it was emitting 1.93 × 10⁶ photons/s at 22 keV (in 4π). On 12/02/02, this rate would have been larger by a factor of 2^(207/462.6), or 2.63 × 10⁶ photons/s.

For each data set, these values were calculated anew (though, usually, the difference in activity from day to day was negligible).

r: Distance from the source to the detector

Photons/s/cm² incident on a fully-illuminated detector at a distance r from the source.

f_atten: Fraction of photons that pass through passive materials on the way to the detector

A_eff: Effective area of the detector

0.16 cm² * QE * (Cosine Correction Factor) * (fraction of depositions above threshold, where applicable)

QE = the quantum efficiency of a detector at a particular photon energy and at a particular angle

²⁴¹Am lines:

26 keV: QE = 1-exp(-54.3*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
33 keV: QE = 1-exp(-174.*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
60 keV: QE = 1-exp(-36.2*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
¹³³Ba lines:

31 keV: QE = 1-exp(-107*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
35 keV: QE = 1-exp(-152*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
53 keV: QE = 1-exp(-49.9*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
80 keV: QE = 1-exp(-15.7*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 0.96 (for the on-axis case)

¹⁰⁹Cd lines:

22 keV: QE = 1-exp(-89.6*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
25 keV: QE = 1-exp(-62.9*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1 (for the on-axis case)
88 keV: QE = 1-exp(-12.0*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 0.91 (for the on-axis case)

⁵⁷Co lines:

122 keV: QE = 1-exp(-4.66*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 0.61 (for the on-axis case)
136 keV: QE = 1-exp(-3.37*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 0.49 (for the on-axis case)

The Cosine Correction Factor is:
cos(atan(sqrt(x*x+y*y)/z))+
min(0.15,0.05*abs(z/x))*cos(atan(sqrt(y*y+z*z)/x))+
min(0.15,0.05*abs(z/y))*cos(atan(sqrt(x*x+z*z)/y))

The edge model included in this factor only applies to non-leading-edge detectors. For that reason, only center detectors are used in the comparison.

Fraction of depositions above threshold:
The ¹³³Ba 31 keV and 35 keV photons have escape peaks that lie below the cutoff used in the analysis. Based on monte carlo simulations, 13.5% of all 31 keV photoelectric depositions result in escape peaks and 21% of all 35 keV photoelectric depositions result in escape peaks. These escape peak depositions should be excluded from the prediction.

x, y, and z are the x-,y-, and z-distances from the source to the detector

See the IDL routines used to generate the predicted count rates for each detector: Am runs
Ba runs
Cd runs
Co runs

Results:

I plotted the histograms of the measured and the predicted count rates for each data set, excluding "edge" detectors, noisy detectors, and dead detectors. Shown below are some representative plots from each source.

black: histogram of measured rates
red: histogram of predicted rates

Following the plots for each particular source is a table which displays the average measured and predicted count rate for each run and the ratio between the two.

²⁴¹Am

blk_6_am241_200_20_0_0_021201_1
(source at θ=0°)

blk_6_am241_200_20_45_0_021127_1
(source at θ=45°)

The "Measured Average" and the "Predicted Average" columns in this table show the averages of the histograms.
"Ratio" is the ratio between the two.

Run	Measured Average	Predicted Average	Ratio
blk_6_am241_200_20_0_0_021127_1	1.76	1.56	1.13
blk_6_am241_200_20_0_0_021201_1	1.77	1.56	1.13
blk_6_am241_200_20_15_0_021128_1	1.78	1.55	1.14
blk_6_am241_200_20_30_0_021127_1	1.63	1.40	1.16
blk_6_am241_200_20_30_0_021202_1	1.63	1.40	1.16
blk_6_am241_200_20_45_0_021127_1	1.33	1.15	1.16
blk_6_am241_200_20_60_0_021127_1	0.96	0.82	1.17
blk_6_am241_200_20_60_0_021202_1	0.96	0.82	1.17

The measured rates are higher than the predicted rates by 13% at normal incidence.

This is very different from the results of the array calibrations, for which the measured rates are lower by about 70%

¹³³Ba

blk_6_ba133_200_20_0_0_021128_1
(source at θ=0°)

blk_6_ba133_200_20_60_0_021201_1
(source at θ=60°)

Run	Measured Average	Predicted Average	Ratio
blk_6_ba133_200_20_0_0_021128_1	2.06	1.95	1.06
blk_6_ba133_200_20_0_0_021202_1	2.07	1.95	1.06
blk_6_ba133_200_20_30_0_021201_1	1.90	1.75	1.09
blk_6_ba133_200_20_60_0_021201_1	1.11	1.03	1.08

The measured rates are about 6% higher than the predicted rates at normal incidence.

This very different from the results of the array calibrations, for which the measured rates are lower by 5 - 10%

¹⁰⁹Cd

blk_6_cd109_200_20_0_0_021203_1
(source at θ=0°)

blk_6_cd109_200_20_45_0_021202_1
(source at θ=45°)

Run	Measured Average	Predicted Average	Ratio
blk_6_cd109_200_20_0_0_021203_1	3.99	4.00	1.00
blk_6_cd109_200_20_15_0_021203_1	3.86	3.99	0.97
blk_6_cd109_200_20_30_0_021128_1	3.67	3.59	1.02
blk_6_cd109_200_20_45_0_021202_1	2.96	2.95	1.00
blk_6_cd109_200_20_60_0_021202_1	2.05	2.10	0.98

The measured rates and the lower rates agree to within less than 1% at normal incidence.

This matches the results of the array calibrations, for which the measured rates agreed with the predicted rates quite well.

⁵⁷Co

blk_6_co57_200_20_0_0_021126_2
(source at θ=0°)

blk_6_co57_200_20_45_0_021202_1
(source at θ=45°)

Run	Measured Average	Predicted Average	Ratio
blk_6_co57_200_20_0_0_021126_1	2.52	1.88	1.33
blk_6_co57_200_20_0_0_021126_2	2.50	1.88	1.33
blk_6_co57_200_20_0_0_021126_3	2.51	1.88	1.33
blk_6_co57_200_20_15_0_021202_1	2.47	1.92	1.29
blk_6_co57_200_20_30_0_021128_1	2.38	1.84	1.30
blk_6_co57_200_20_45_0_021202_1	2.12	1.68	1.27
blk_6_co57_200_20_60_0_021128_1	1.74	1.38	1.26
blk_6_co57_200_20_60_0_021202_1	1.73	1.38	1.25

The measured rates are higher than the predicted rates by 33% at normal incidence.

This different from the results of the array calibrations, for which the measured rates are lower by about 20%

Conclusions:

The difference between measurement and prediction for the ¹⁰⁹Cd runs is negligible.
For ¹³³Ba, the measurement is higher by 6%.
For ²⁴¹Am, the measurement is higher by 13%.
For ⁵⁷Co, the measurement is higher by 33%.

An interesting trend is that as the energy of the dominant line increases, so does the discrepancy.

Changes from 29 Jan 2004:

excluded ¹³³Ba 31 keV and 35 keV escape peaks from prediction

Changes from 12 Jan 2004:

included attenuation from passive materials in calculation
used photoelectric cross section for CZT instead of total cross section
(this matters for the ⁵⁷Co lines)

Return to main BAT response page
Return to Home Page of Derek Hullinger

Block Calibration Count Rates: Measured vs. Predicted

Derek Hullinger 15 Jun 2004

Bottom Line First:

Data sets examined:

Procedure (Measurement):

For each of the above data sets:

Procedure (Prediction):

Predicted Count Rate (For Each Detector):

241Am:

133Ba:

103Cd:

57Co: