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 =0.114 uCi

= [math]\left (0.99937 \right )\left ( 0.114 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 4215.34 Hz [/math] for the 1274 line

= [math]\left (1.788 \right )\left ( 0.114 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 7541.784 Hz [/math] for the 511 line

Cs-137, 661.660 line, 85.21%, 1.066 uCi on July 1, 2008, half life 30.0 +/- 0.2 yrs, Feb 24, 2017 activity = 0.8727 uCi expected rate for 661 line

= [math]\left (0.8521 \right )\left ( 0.8727 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 26079.7 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 24, 2017 activity =0.2435 uCi

= [math]\left (0.99975 \right )\left ( 0.2435 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 8986.976 Hz [/math] for the 834 line

Ba-133, 1.188 uCi on 07-01-08 with a half life of 10.51 years 62.05% for the 356 line, activity on Feb 24, 2017 is 0.671 uCi

= [math]\left (0.6205 \right )\left ( 0.671 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 15405.15 Hz [/math] for the 356 keV line

There was another Ba-133 source used which had an activity of 9.821 uCi on 4-15-07, using the same half life and the same branching ratio, the activity on Feb 24, 2017 is 5.1219 uCi

= [math]\left (0.6205 \right )\left ( 5.1219 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 117591.1412 Hz [/math] for the 356 keV line

Actual Activities

The method for calculating the actual activities is the same as above and the plots can be found at LB_Efficiency_Plots_Feb_2017