LB Feb 2017 Geometric Efficiency Calculations

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Below are the theoretical calculations for the theoretical decay frequencies


Na-22, 10.19 uCi on July 15, 2013, half life 2.602 +/- 0.002 years, 99.937% for 1274.52 keV line and 178.8 for 511 keV line , activity in Feb 4, 2017 = 3.947 uCi

= [math]\left (0.99937 \right )\left ( 3.947 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145,946 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.947 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 261,117.732 Hz [/math] for the 511 keV line

Now compute the expected rate for February 5, 2017.

The activity on Feb 5, 2017 is 3.944 uCi, so the expected rates for the 2 lines are

= [math]\left (0.99937 \right )\left ( 3.944 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145,836 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.944 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 260919.264 Hz [/math] for the 511 keV line

Now compute the expected rate for February 9, 2017

The activity on Feb 9, 2017 is 3.933 uCi, so the expected rate for the 2 lines are


= [math]\left (0.99937 \right )\left ( 3.933 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145,429.32 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.933 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 260,191.55 Hz [/math] for the 511 keV line

Now compute the expected rate for Feb 12, 2017

The activity on Feb 12, 2017 is 3.924 uCi, so the expected rate for the 2 lines are

= [math]\left (0.99937 \right )\left ( 3.924 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145096.5316 Hz [/math] for the 1274 keV line
= [math]\left (1.788 \right )\left ( 3.924 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 259596.144 Hz [/math] for the 511 keV line

Geometric Efficiencies

Below is a table with the calculated efficiencies

Run Source Energy (keV) Position Expected Rate (Hz) ROOT Window HpGe Rate (Hz) HpGe X-Cool Detector Efficiency (%)
r5825 Na-22 511 5 261117.732 [480:540] 225.5 0.09
r5825 Na-22 1274 5 145946 [1240:1320] 76.09 0.05
r5826 Na-22 511 6 261117.732 [480:540] 223.1 0.09
r5826 Na-22 1274 6 145946 [1232:1320] 75.72 0.05
r5827 Na-22 511 7 261117.732 [480:540] 175.6 0.07
r5827 Na-22 1274 7 145946 [1240:1300] 60.24 0.04
r5828 Na-22 511 8 260919.264 [480:540] 157.2 0.06
r5828 Na-22 1274 8 145836 [1240:1300] 53.69 0.04
r5829 Na-22 511 9 260919.264 [480:540] 132.1 0.05
r5829 Na-22 1274 9 145836 [1220:1340] 46.04 0.03
r5830 Na-22 511 10 260919.264 [480:540:] 115 0.04
r5830 Na-22 1274 10 145836 [1240:1300] 39.83 0.03
r5831 Na-22 511 11 260919.264 [480:540] 96.29 0.04
r5831 Na-22 1274 11 145836 [1240:1300] 32.79 0.02
r5832 Na-22 511 12 260919.264 [480:540] 86.92 0.03
r5832 Na-22 1274 12 145836 [1240:1300] 29.79 0.02
r5833 Na-22 511 13 260919.264 [480:540] 77.48 0.03
r5833 Na-22 1274 13 145836 [1240:1300] 26.73 0.02
r5834 Na-22 511 14 260919.264 [480:540] 68.33 0.03
r5834 Na-22 1274 14 145836 [1240:1300] 23.39 0.02
r5835
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