LB Feb 2017 Energy Efficiency Calculations

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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

Cs137 Activity.png

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 [652:672] 339.2 +/- 0.05 0.16
r5871 Ba-133 356 118236.28 [348:364] 286.00 +/- 0.03 0.24
r5820 Na-22 511 260985.42 [490:530] 479.94 +/- 0.42 0,18
r5820 Na-22 1274 145873.0421 [1255:1295] 177.99 +/- 0 0.12
r5896 Mn-54 834 9247.6875 [824:842] 14.93 +/- 0.01 0.16
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

Detector B

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 (0.329 \right )\left ( 0.671 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 8168.083 Hz [/math] for the 81 keV line
= [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. The branching ratio for the 356keV line is 62.05% while the branching ratio for the 81 keV line is 32.9%

= [math]\left (0.329 \right )\left ( 5.1219 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= 62348.8887 Hz [/math] for the 81 keV line
= [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


Run Source Energy (keV) Position Expected Rate (Hz) ROOT Window HpGe Rate (Hz) Detector B Efficiency (%)
Ba133_3.9cm_detB Ba-133 81 3.9cm 8168.083 [76:86] 137.12 +/- 0.6266 1.68
Ba133_3.9cm_detB Ba-133 356 3.9cm 15405.15 [352:360] 191.21 +/- 0.074 1.24
Ba133_4.1cm_detB Ba-133 81 4.1cm 8168.083 [76:86] 137.5 +/- 0.6984 1.68
Ba133_4.1cm_detB Ba-33 356 4.1cm 15405.15 [352:360] 190.44 +/- 0.08 1.24
Ba133_7.9cm_detB Ba-133 81 7.9cm 62348.8887 [76:86] 345.36 +/- 1.32 0.55
Ba133_7.9cm_detB Ba-133 356 7.9cm 117591.1412 [352:360] 494.24 +/- 0.0954 0.42
Ba133_8.1cm_detB Ba-133 81 8.1cm 62348.8887 [76:86] 326.17 +/- 1.20 0.52
Ba133_8.1cm_detB Ba-133 356 8.1cm 117591.1412 [352:360] 482.58 +/- 0.10 0.41
Cs137_3.9cm_detB Cs-137 661 3.9cm 26079.7 [658:666] 182.33 +/- 0.05 0.70
Cs137_4.1cm_detB Cs-137 661 4.1cm 26079.7 [658:666] 175.26 +/- 0.04 0.67
Cs137_7.9cm_detB Cs-137 661 7.9cm 26079.7 [658:666] 64.28 +/- 0.04 0.25
Cs137_8.1cm_detB Cs-137 661 8.1cm 26079.7 [658:666] 65.14 +/- 0.04 0.25
Mn54_3.9cm_detB Mn-54 834 3.9cm 8986.976 [830:838] 54.75 +/- 0.02 0.61
Mn54_4.1cm_detB Mn-54 834 4.1cm 8986.976 [830:838] 52.55 +/- 0.02 0.58
Mn54_7.9cm_detB Mn-54 834 7.9cm 8986.976 [830:838] 18.62 +/- 0.02 0.21
Mn54_8.1cm_detB Mn-54 834 8.1cm 8986.976 [830:838] 17.98 +/- 0.01 0.20
Na22_3.9cm_detB Na-22 511 3.9cm 7541.784 [504:516] 81.74 +/- 0.09 1.08
Na22_3.9cm_detB Na-22 1274 3.9cm 4215.35 [1270:1280] 24.18 +/- 0 0.57
Na22_4.1cm_detB Na-22 511 4.1cm 7541.784 [504:516] 74.71 +/- 0.09 0.99
Na22_4.1cm_detB Na-22 1274 4.1cm 4215.35 [1270:1280] 22.90 +/- 0 0.54
Na22_7.9cm_detB Na-22 511 7.9cm 7541.784 [504:516] 25.55 +/- 0.05 0.34
Na22_7.9cm_detB Na-22 1274 7.9cm 4215.35 [1270:1280] 7.70 +/- 0 0.18
Na22_8.1cm_detB Na-22 511 8.1cm 7541.784 [504:516] 24.88 +/- 0.06 0.33
Na22_8.1cm_detB Na-22 1274 8.1cm 4215.35 [1270:1280] 7.11 +/- 0 0.17
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