LB Det A Dead Time

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

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{A_{Measured}}{A_{Theory}} [/math]