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

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]	393.01 +/- 0.35	0.15
r5826	Na-22	1274	6	145946	[1255:1295]	142.05 +/- 0	0.10
r5827	Na-22	511	7	261117.732	[490:540]	313.60 +/- 0.26	0.12
r5827	Na-22	1274	7	145946	[1255:1295]	114.72 +/- 0	0.08
r5828	Na-22	511	8	260919.264	[490:540]	280.01 +/- 0.25	0.11
r5828	Na-22	1274	8	145836	[1255:1295]	102.59 +/- 0	0.07
r5829	Na-22	511	9	260919.264	[490:540]	233.43 +/- 0.21	0.09
r5829	Na-22	1274	9	145836	[1255:1295]	86.38 +/- 0	0.06
r5830	Na-22	511	10	260919.264	[490:540:]	205.89 +/- 0.17	0.08
r5830	Na-22	1274	10	145836	[1255:1295]	76.40 +\- 0	0.05
r5831	Na-22	511	11	260919.264	[490:540]	173.49 +/- 0.17	0.07
r5831	Na-22	1274	11	145836	[1255:1295]	63.14 +/- 0	0.04
r5832	Na-22	511	12	260919.264	[490:540]	157.73 +/- 0.16	0.06
r5832	Na-22	1274	12	145836	[1255:1295]	57.85 +/- 0	0.04
r5833	Na-22	511	13	260919.264	[490:540]	140.18 +/- 0.12	0.05
r5833	Na-22	1274	13	145836	[1255:1295]	51.74 +/- 0	0.04
r5835	Na-22	511	14	260919.264	[490:540]	124.81 +/- 0.09	0.05
r5835	Na-22	1274	14	145836	[1255:1295]	45.57 +/- 0	0.03
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]