LB Det A Dead Time

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Due to the difficulty in getting the activity ratios to match the expected values, I decided to investigate the dead time of the detector in use (Detector A). Below is a table of values used to generate the plot. This will also give the reader a good idea of what the dead times are for certain count rates.

Count Rate (Hz) % Dead
129.47 +/- 7.84 0.24 +/- 0.10
154.33 +/- 10.36 0.29 +/- 0.11
194.83 +/- 8.36 0.41 +/- 0.11
253.69 +/- 14.05 0.51 +/- 0.18
257.11 +/- 11.24 0.53 +/- 0.14
338.8 +/- 11.68 0.65 +/- 0.15
477.61 +/- 15.06 0.84 +/- 0.16
619.3 +/- 10.56 1.34 +/- 0.18
680.83 +/- 17.5 1.33 +/- 0.23
807.37 +/- 15.85 1.55 +/- 0.18
889.6 +/- 16.22 1.65 +/- 0.34
1051.33 +/- 26.74 1.92 +/- 0.26
1213.93 +/- 23.62 2.26 +/- 0.33
1389.45 +/- 24.75 2.53 +/- 0.31
1628.47 +/- 17.17 3.06 +/- 0.30
2084.6 +/- 33.77 3.95 +/- 0.42
2576.5 +/- 31.53 5.06 +/- 0.39
3058.20 +/- 35.62 5.87 +/- 0.54
3362.13 +/- 23.12 6.59 +/- 0.43
4067.2 +/- 45.37 8.18 +/- 0.66
4564.37 +/- 61.94 9.09 +/- 0.60
5511.6 +/- 64.60 10.86 +/- 0.85


Below is a plot of the data

LB DeadTimevsCountRate DetA.png


Improved Measurement

Since the initial measurement of the dead time had a high error associated with the fluctuating of the count rate, a different measurement was made to try and minimized the error. This measurement was taken by using Ba-133 sources on detector A at the IAC. The source was placed at some position in front of the detector, then data was collected. For the next run the source was moved closer to the detector. A larger source was used as well in this manner to try and reach the higher dead times. The measurement gives the number of counts seen in some solid angle. I will compare this with theory by using the fact that the solid angle can be written as

[math] \Omega = \frac{Area}{r^2} [/math]

We can also calculate the theoretical activity of the source. Using this we can find a theoretical rate of photons incident in the solid angle, or

[math] R_{Theory} = A_{Theory} \times \Omega [/math]

Once the theoretical rate has been found, take a ratio between the measured rate and the theoretical rate to get the percent dead time, or

[math] Percent Dead = \frac{R_{Measured}}{R_{Theory}} [/math]


The source information was as follows:

The smaller source used was a 0.9671 uCi source with a reference date of January 1st, 2007 and serial number 1219-33-2

The larger source used was a 10.54 uCi source with a reference date of July 1, 2008 and serial number 129791.

Theoretical Activities

To find the theoretical activities of the sources, we must find the activity on the date that the measurement was taken. The half life of Ba-133 is 10.51 years, or 3836.15 days, which gives a decay constant of

[math] \lambda = \frac{\ln{2}}{t_{\frac{1}{2}}} = \frac{\ln{2}}{3836.15} = 1.80688237 \times 10^{-4} Days^{-1} [/math]

For the smaller source, the number of days between the date printed on the source and the date of measurement, which was December 5, 2017 is 3991 days. By using the decay equation, the activity on the date of the measurement is

[math] A_0 \times e^{-\lambda \times t} = 0.9671 \times e^{-\lambda \times 3991} = 0.4702 \mu Ci \rightarrow 17397 Hz [/math]

For the larger source, the number of days between the date printed on the source and the date of the measurement, which was December 5, 2017 is 3444 days. By using the decay equation, the activity of the source on the day of measurement is

[math] A_0 \times e^{-\lambda \times t} = 10.54 \times e^{-\lambda \times 3444} = 5.6570 \mu Ci \rightarrow 209307.65 Hz [/math]

Below is a table of information about the measurements that were made along with the theoretical rate within the solid angle. The Area of the detector face is 54.1061 [math] cm^2 [/math]

Run Distance from Detector (cm) Number of Histogram Entries Runtime (seconds) [math] R_{Measure} (Hz) [/math] Solid Angle (sterradians) [math] R_{Theory} [/math] [math] \frac{R_{Measured}}{R_{Theory}} [/math]
DetA_DeadTime_90cm 90 10036 +/- 100.180 365.632 27.448 +/- 0.274 0.00668 116.211 0.2362 +/- 0.0024
DetA_DeadTime_85cm 85 7824 +/- 88.453 276.940 28.252 +/- 0.319 0.00749 130.304 0.2168 +/- 0.0024
DetA_DeadTime_80cm 80 5040 +/- 70.993 168.989 29.824 +/- 0.420 0.00845 147.005 0.2029 +/- 0.0029
DetA_DeadTime_75cm 75 5020 +/- 70.196 165.028 30.419 +/- 0.425 0.00962 167.359 0.1818 +/- 0.0025
DetA_DeadTime_70cm 70 5037 +/- 70.972 157.465 31.988 +/- 0.451 0.01104 192.063 0.1665 +/- 0.0023
DetA_DeadTime_65cm 65 5051 +/- 71.070 143.480 35.204 +/- 0.495 0.01281 222.856 0.1580 +/- 0.0022
DetA_DeadTime_60cm 60 5035 +/- 70.958 135.545 37.146 +/- 0.524 0.01503 261.477 0.1421 +/- 0.0020
DetA_DeadTime_55cm 55 5036 +/- 70.965 124.963 40.300 +/- 0.568 0.01789 311.232 0.1295 +/- 0.0018
DetA_DeadTime_50cm 50 6955 +/- 83.397 163.809 42.458 +/- 0.509 0.02164 376.471 0.1128 +/- 0.0014
DetA_DeadTime_45cm 45 5079 +/- 71.267 99.950 50.815 +/- 0.713 0.02671 464.673 0.1094 +/- 0.0015
DetA_DeadTime_40cm 40 5048 +/- 71.049 91.293 55.294 +/- 0.781 0.03381 588.193 0.0940 +/- 0.0013
DetA_DeadTime_35cm 35 5262 +/- 72.540 79.486 66.200 +/- 0.913 0.04417 768.425 0.0862 +/- 0.0012
DetA_DeadTime_30cm 30 5078 +/- 71.601 61.545 82.509 +/- 1.163 0.06011 1045.734 0.0789 +/- 0.0011
DetA_DeadTime_25cm 25 5848 +/- 76.472 53.951 108.395 +/- 1.417 0.08657 1506.058 0.0720 +/- 0.0009
DetA_DeadTime_20cm 20 5380 +/- 73.348 35.239 152.672 +/- 2.081 0.13527 2353.292 0.0649 +/- 0.0013
DetA_DeadTime_15cm 15 6078 +/- 77.962 24.858 244.509 +/- 3.136 0.24047 4183.457 0.0584 +/- 0.0007
DetA_DeadTime_10cm 10 5380 +/- 73.348 11.665 461.209 +/- 6.288 0.54106 9412.821 0.0490 +/- 0.0007
DetA_DeadTime_30cm_LargerSource 30 32989 +/- 181.629 40.822 808.118 +/- 4.4493 0.06012 12583.5759 0.0642 +/- 0.0004
DetA_DeadTime_25cm_LargerSource 25 11424 +/- 106.883 9.895 1154.522 +/- 10.802 0.08657 18119.7633 0.0637 +/- 0.0006
DetA_DeadTime_20cm_LargerSource 20 60557 +/- 246.083 37.121 1631.341 +/- 6.629 0.13527 28313.0458 0.0576 +/- 0.0002
DetA_DeadTime_15cm_LargerSource 15 57329 +/- 239.434 22.402 2559.101 +/- 10.688 0.24047 50332.2106 0.0508 +/- 0.0002
DetA_DeadTime_10cm_LargerSource 10 48392 +/- 219.982 10.354 4673.749 +/- 21.246 0.54106 113247.997 0.0413 +/- 0.0002

Note that these do not match with previous measurements or make intuitive sense. Something is off here.

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