LB Feb 2017 Energy Efficiency Calculations

Theoretical Activities

Na-22, 10.19 uCi on July 15, 2013, half life 2.602 +/- 0.002 years, 99.937% for 1274.52 and 178.8 for 511 line , activity in Feb 4, 2017 =3.945 uCi

= [math]\left (0.99937 \right )\left ( 3.945 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 145873.0421 Hz [/math] for the 1274 line

= [math]\left (1.788 \right )\left ( 3.945 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 260985.42 Hz [/math] for the 511 line

Cs-137, 661.660 line, 85.21% * 9.067 uCi on May 1, 2005, half life 30.0 +/- 0.2 yrs, Feb 4, 2017 activity = 6.915 uCi expected rate for 661 line

= [math]\left (0.8521 \right )\left ( 0.891 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 218014.0455 Hz [/math]

Mn-54, 9.882 uCi on August 1, 2012, half life =312.20 +/- 0.07 days, 99.975% intensity on 834.826 , Feb 12, 2017 activity = 0.25 uCi

= [math]\left (0.99975 \right )\left ( 0.25 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 9247.6875 Hz [/math] for the 834 line

Co-60, 9.080 uCi July 15, 2013, half life 5.271 +/- 0.001 years, 99.0 % for 1173.237 and 99.9824 % for 1332.501, Feb 4, 2017 activity=5.68 uCi

= [math]\left (0.99 \right )\left ( 5.68 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 208058.4 Hz [/math] for the 1173 line

= [math]\left (0.999824 \right )\left ( 5.68 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 210123.0118 Hz [/math] for the 1332 line

Ba-133, 9.821 uCi on 04-15-07 with a half life of 10.51 years 62.05% for the 356 line,

= [math]\left (0.6205 \right )\left ( 5.15 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 118236.28 Hz [/math] for the 356 keV line

Actual Activites

This is an example of the method that will be used to find the activities in the calibrated source's spectra

The line of interest in Cs-137 the 661.7 line.

Using the program BackgroundSubtract.C in /data/IAC/Se/Feb_2017_Efficiency/Energy_Efficiency and the root command

BackgroundSubtract("r5818.root","r5891.root",412,3369);

The 661.7 keV line can be seen

Note that the range along the x-axis is [640:680] and the integral is 208.3.

Taking the ratio of the rate seen in the detector and the theoretical rate calculated above, one can arrive at a detector efficiency of 0.7%

The rest of the data is on the wiki page

LB_Efficiency_Plots_Feb_2017

Energy Efficiencies

Below is a table with the calculated efficiencies

Run	Source	Energy (keV)	Expected Rate (Hz)	ROOT Window	HpGe Rate (Hz)	HpGe X-Cool Detector Efficiency (%)
r5818	Cs-137	661.7	218014.0455	[640:680]	208.3	0.0955
r5871	Ba-133	356	118236.28	[340:376]	150.6	0.1274
r5820	Na-22	511	260985.42	[480:540]	278.6	0.1067
r5820	Na-22	1274	145873.0421	[1220:1320]	95.89	0.0657
r5896	Mn-54	834	9247.6875	[800:860]	7.611	0.0823
r5822	Co-60	1173	208058.4	[1140:1200]	159.1	0.0765
r5822	Co-60	1332.5	210123.0118	[1300:1360]	134.7	0.0641

Theoretical Activities

Na-22, 1.146 uCi on July 1, 2008, half life 2.602 +/- 0.002 years, 99.937% for 1274.52 and 178.8% for 511 line , activity in February 24, 2017 =0.082 uCi

= [math]\left (0.99937 \right )\left ( 1.196 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 44,224 Hz [/math] for the 1274 line

= [math]\left (1.788 \right )\left ( 1.196 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 79122.6 Hz [/math] for the 511 line

Cs-137, 661.660 line, 85.21% * 1.066micro Ci on July 1, 2008, half life 30.0 +/- 0.2 yrs, March 31, 2016 activity = 0.891micro Ci expected rate for 661 line

= [math]\left (0.8521 \right )\left ( 0.891 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 28091.2 Hz [/math]

Mn-54, 11.77 microCi on July 1, 2008, half life =312.20 +/- 0.07 days, 99.975% intensity on 834.826 , March 31, 2016 activity =0.02328micro Ci

= [math]\left (0.99975 \right )\left ( 0.02328 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 861.1 Hz [/math] for the 834 line

Co-60, 10.42micro Ci July 1, 2008, half life 5.271 +/- 0.001 years, 99.0 % for 1173.237 and 99.9824 % for 1332.501, March 31, 2016 activity=3.759micro Ci

= [math]\left (0.99 \right )\left ( 3.759 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 137692.17 Hz [/math] for the 1173 line

= [math]\left (0.999824 \right )\left ( 3.759 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 139058.52 Hz [/math] for the 1332 line

Ba-133, 9.821 uCi on 04-15-07 with a half life of 10.51 years 62.05% for the 356 line,

= [math]\left (0.6205 \right )\left ( 5.15 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 118236.28 Hz [/math] for the 356 keV line