Co-57 Count Rates:
Measured vs. Predicted
Derek Hullinger
23 July 2004
Bottom Line First:
The measurement is about 48% higher than the prediction, which is a much
larger a discrepancy than that seen with the other 3 sources.
Data sets examined:
- arr_x_co57_200_22_030618_6a.fits
- arr_x_co57_200_20_030619_2a.fits
- arr_x_co57_200_20_030619_3a.fits
- arr_x_co57_200_20_030619_8a.fits
- arr_x_co57_200_20_030619_9a.fits
(from /local/data/gcn3c/array_cal_030618/coarse_grid/)
- arr_x_co57_200_21_0_0_030404_1.fits
- arr_x_co57_200_21_0_south45_030405_14.fits
- arr_x_co57_200_21_n25_0_030405_6.fits
- arr_x_co57_200_21_n25_0_030405_9.fits
(from /local/data/gcn3a/array_cal/far_field/)
I) Measured Count Rates (from ground software (gsw) tools):
For each of the above data sets:
- ran batgse2dpi with histmode="window" and only including
counts above 20 keV
example command:
batgse2dpi arr_x_co57_200_20_030619_2a.list
arr_x_co57_200_20_030619_2a.dpi_window
histmode="window"
windows="/home/lhea/derek/windows/20kev.window"
- ran bathotpix to generate a "good map" file for the windowed
dpi
example command:
bathotpix arr_x_co57_200_20_030619_2a.dpi_window
arr_x_co57_200_20_030619_2a.mask2_window
detmask="arr_x_co57_200_20_030619_2a.mask_thresh" chatter=3
arr_x_co57_200_20_030619_2a.mask_thresh is a detector map that
excludes all detectors with fewer than 30 counts
- ran batclean to remove background from the windowed dpi
example command:
batclean arr_x_co57_200_20_030619_2a.dpi_window
arr_x_co57_200_20_030619_2a.dpi_window_clean
arr_x_co57_200_20_030619_2a.src
detmask="arr_x_co57_200_20_030619_2a.mask2_window"
srcclean=YES outversion="bkgcleaned"
By default, counts in the dpi are dead-time corrected (that is, they are
multiplied by exposure/live-time).
Measured Count Rate (For Each Detector):
C: dead-time corrected counts from windowed dpi
(counts*exposure/live_time)
t: exposure time for the data set
(See the IDL routine used to generate
the measured count rate for each detector)
II) Measured Count Rate (From sum_spectra):
For comparison, I also added up the counts/s produced by sum_spectra.
sum_spectra gives the counts/s one would expect in a single
fully-illuminated detector at the center of the array. As in the (II) above,
I added up the counts/s in all channels corresponding to 20 keV and above.
III) Predicted Count Rates:
Predicted Count Rate (For Each Detector):
S:
The number of photons/s of a given energy emitted by the source into 4π
Source used: Co-57-121
According to Nadine’s calibration report (calibhigh.xls):
S122 = 1.41 x 108 photons/s (on 8/18/03)
on 6/19/03, this rate would have been higher by a factor of (1/2)^(-60/272),
or 1.65 x 108 photons/s
S136 = 1.79 x 107 photons/s (on 8/18/03)
on 6/19/03, this rate would have been higher by a factor of (1/2)^(-60/272),
or 2.08 x 107 photons/s
r:
distance from the source to the detector
Photons/s/cm2 incident on a fully-illuminated detector at a
distance r from the source.
fatten,E:
the attenutation of photons of energy E through all passive
materials between the source and the detectors, including air (which turns
out to be a significant attenuator). This attenuation was calculated for
the on-axis case, then it was adjusted for each detector to include the cosine
effect.
Aeff,E:
Effective area of the detector
0.16 cm2 * QE * (Cosine Correction Factor)
QE = the quantum efficiency of a detector at a particular photon energy and
at a particular angle
At 122 keV: QE = 1-exp(-4.655*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 0.61
(for the on-axis case)
At 136 keV: QE = 1-exp(-3.374*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.
x, y, and z are the x-,y-, and
z-distances from the source to the detector
fillum:
fraction of photons that are transmitted through the mask
for fully illuminated detectors, this is 1
for fully masked detectors, this is the tranmission of the photons through the
lead tile
for a partially-illuminated detector, it is a number between the two
the cleaning process removes un-modulated counts, so the prediction must do
that, too. This is done by subtracting from each illumination fraction the transmission of photons through a lead tile onto the center of the array.
(See the IDL routine used to generate
the predicted count rate for each detector)
IV) Results:
These are histograms of the measured count rates (using the gsw tools)
and predicted count rates from all
of the "good" detectors in each run. Only center detectors
are included in the histograms.
black: histogram of measured rates derived from gsw tools
red: histogram of predicted rates
The predicted rates are all systematically lower than
the measured rates. After the plots, there is a table that compares these
rates along with the rates derived from the sum_spectra tool.
arr_x_co57_200_22_030618_6a:
back-of-envelope calculation:
The source is at x=-12.7, y=3.72, z=294.2 (all in cm). For a
fully-illuminated detector directly directly below the source,
r=294.2 cm, QE122=0.61, QE136=0.49,
fatten,122=0.904, fatten,136=0.906,
fillum,122=0.978, fillum,136=0.945,
and the cosine
correction factor is 1.
This would give a count rate
of (1.65 x 108)*/(4*π*294.2*294.2)*(0.16)*(0.61)*(0.904)*(0.978)
= 13.1 counts/s from the 122 keV line and
(2.08 x 107)*/(4*π*294.2*294.2)*(0.16)*(0.49)*(0.906)*(0.945) =
1.3 counts/s from the 136 keV line,
making a total of 14.4 counts/s.
arr_x_co57_200_22_030619_2a:
arr_x_co57_200_22_030619_3a:
arr_x_co57_200_22_030619_8a:
arr_x_co57_200_22_030619_9a:
arr_x_co57_200_21_0_0_030404_1:
arr_x_co57_200_21_0_south45_030405_14:
arr_x_co57_200_21_n25_0_030405_6:
arr_x_co57_200_21_n25_0_030405_9:
The "Max Measured Rate" and the "Max Predicted Rate" columns in
this table show the
count rates that correspond to the "peak" rates
in the histograms. This isn't a perfect way to quantify the maximum rate,
but it's not bad.
- "Summed Rate (from sum_spectra)" is the summed background-subtracted
rate derived from sum_spectra
- "Summed Rate (from dpi)" is the summed background-subtracted rate derived
from the dpi following the exact same procedure as used by
sum_spectra
(This was done to verify that sum_spectra was working properly. The
results should be identical, which they are)
- "Max Measured Rate" is the peak rate in the histogram of measured
rates
- "Max Predicted Rate" is the peak rate in the histogram of predicted
rates
- "Ratio" is the ratio between "Max Measured Rate" and "Max Predicted
Rate"
|
Run ID
|
tan(θ)
|
Summed Rate
(from sum_spectra)
|
Summed Rate
(from dpi)
|
Max Measured
Rate
|
Max Predicted
Rate
|
Ratio
|
|
6a
|
0.045
|
20.9
|
20.9
|
20.5
|
14.3
|
1.43
|
|
2a
|
0.030
|
20.7
|
20.7
|
20.7
|
14.3
|
1.45
|
|
3a
|
0.080
|
20.9
|
20.9
|
20.6
|
14.3
|
1.44
|
|
8a
|
0.068
|
20.7
|
20.7
|
20.7
|
14.3
|
1.45
|
|
9a
|
0.514
|
14.3
|
14.3
|
14.0
|
9.0
|
1.56
|
|
1
|
0.079
|
0.457
|
0.457
|
0.448
|
0.298
|
1.50
|
|
6
|
0.282
|
0.385
|
0.385
|
0.384
|
0.260
|
1.48
|
|
9
|
0.342
|
0.395
|
0.395
|
0.392
|
0.264
|
1.48
|
|
14
|
0.589
|
0.254
|
0.254
|
0.25
|
0.168
|
1.49
|
The maximum measured rates are higher than the predicted rates
by 48% on average (standard deviation: 4%).
The summed rates are a little bit different from the maximum measured rate.
This is to be expected, since they are measures of slightly different
quantities. The summed rate is the mask-weighted sum of all detectors,
flat-fielded to
the center of the array and renormalized, whereas the maximum measured rate
is the maximum of the histogram of rates. One would expect the values to
be close, which they are.
V) Conclusions:
The predicted rates are much farther from the measured rates than in the case
of the other sources (Cd-109, Ba-133, and Am-241).
Every explanation I can think of to explain this would only
serve to explain why the prediction might be too high, not too low.
Things I double-checked:
- The exposure times in the headers are consistent with those in the log
books
- The source quoted has been checked against the log book in the
source cabinet over in building 10
Changes from 16 Jun 2003:
- added effects of transparency of mask tiles (this lowered the prediction
slightly)
Changes from 11 Dec 2003:
- added passive materials to the calculation
- changed cross section used in calculation from total to photoelectric
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