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

The plots for these efficiency calculations are shown in LB Efficiency Plots Feb 2017

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 [490:540] 485.55 +/- 0.39 0.19
r5825 Na-22 1274 5 145946 [1255:1295] 176.84 +/- 0 0.12
r5826 Na-22 511 6 261117.732 [490:540]
r5826 Na-22 1274 6 145946 [1255:1290]
r5827 Na-22 511 7 261117.732 [490:540]
r5827 Na-22 1274 7 145946 [1255:1295]
r5828 Na-22 511 8 260919.264 [490:540]
r5828 Na-22 1274 8 145836 [1255:1295]
r5829 Na-22 511 9 260919.264 [490:540]
r5829 Na-22 1274 9 145836 [1255:1295]
r5830 Na-22 511 10 260919.264 [490:540:]
r5830 Na-22 1274 10 145836 [1255:1295]
r5831 Na-22 511 11 260919.264 [490:540]
r5831 Na-22 1274 11 145836 [1255:1295]
r5832 Na-22 511 12 260919.264 [490:540]
r5832 Na-22 1274 12 145836 [1255:1295]
r5833 Na-22 511 13 260919.264 [490:540]
r5833 Na-22 1274 13 145836 [1255:1295]
r5835 Na-22 511 14 260919.264 [490:540]
r5835 Na-22 1274 14 145836 [1255:1295]
r5836 Na-22 511 15 260919.264 [490:540]
r5836 Na-22 1274 15 145836 [1255:1295]
r5897 Na-22 511 16 259596.144 [490:540]
r5897 Na-22 1274 16 145096.5316 [1255:1295]
r5898 Na-22 511 17 259596.144 [490:540]
r5898 Na-22 1274 17 145096.5316 [1255:1295]
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