LB Feb 2017 Geometric Efficiency Calculations

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]