LB DetLimits Thesis

Analysis

The detection limit was found by using "fixed fit" activity values ([math] A_{Fixed} [/math]) (half life curves with the slope forced to be the accepted half life) and its associated error (|Data Fit - Fixed Fit|). Once those values have been found, then an average value was taken between irradiations with similar beam times. Normalization constants were found for the two averaged values for the activity by computing

[math] Normalization = \frac{A_{Avg}}{A_{Fixed}} [/math]

Once the average was found, the next step was to normalize the activities to the longest beam time with

[math] A_{t_{Norm}} = A_{Fixed} \times \frac{(1-e^{-\lambda_{el} \times t_{Norm}})}{(1-e^{-\lambda_{el} \times t_{irr}})} [/math]

Where [math] t_{Norm} [/math] is the longest irradiation time and [math] t_{irr} [/math] is the actual irradiation time.

If [math] A_{Fixed} [/math] was not normalized to the longest beam time (as it was the longest beam time) the following ratio was computed

[math] \frac{A_{Fixed}\times m_{Se}}{A_{Ref}/m_{ref}} [/math]

If [math] A_{t_{Norm}} [/math] was found, then the ratio was computed as

[math] A_{Fixed}\times m_{Se}}{A_{Ref}/m_{ref}} \times [/math]

50% Excluded

For this analysis, begin by using the first measurement of the Se-75 line and using the standard exponential decay equation to correct it and its error back to the time of beam off. Below is a table of the Se-75 (120d) corrected measurements as well as the front nickel foils and the Mn-54 data for each measurement.

Sample	Activated (total beam time)	Counted	Fully Thesis Corrected Rate @ 1st Measurement (Hz)	Decay Corrected Activity
10% Se/Soil Mixture	5/23/17 and 5/24/17 (83 min)	07/18/17 (16:25:44)	3109.68 [math] \pm [/math] 95.39	4280.08 [math] \pm [/math] 131.29
10% Se/Soil Pure Witness selenium	5/23/17 and 5/24/17 (83 min)	8/1/17 (16:05:51)	4161.29 [math] \pm [/math] 127.63	6210.50 [math] \pm [/math] 190.48
10% Se/Soil Front Inner Ni Foil	5/23/17 (1h)	5/23/17 (15:52:21)	385955 [math] \pm [/math] 23488.8	425064.36 [math] \pm [/math] 25868.95
10% Se/Soil Mixture Mn-54	5/23/17 (1h)	07/18/17 (16:25:44)
1% Sample Se/Soil Mixture	5/23/17 (1h)	6/23/17 (16:39:03)	2233.33 [math] \pm [/math] 68.52	2675.24 [math] \pm [/math] 82.08
1% Sample Se/Soil Pure Witness selenium	5/23/17 (1h)	7/20/17 (16:39:46)	3840.86 [math] \pm [/math] 117.81	5379.43 [math] \pm [/math] 165.00
1% Sample Se/Soil Front Inner Ni Foil	5/23/17 (1h)	5/23/17 (17:59:39)	261461 [math] \pm [/math] 16045.7	293170.78 [math] \pm [/math] 17991.71
0.1% Sample Se/Soil Mixture	5/23/17 (30 min)	6/19/17 (18:25:18)	849.46 [math] \pm [/math] 26.07	993.59 [math] \pm [/math] 30.49
0.1% Sample Se/Soil Pure Witness Selenium	5/23/17 (30 min)	07/25/17 (16:32:52)	834.41 [math] \pm [/math] 25.61	1201.58 [math] \pm [/math] 36.88
0.1% Sample Se/Soil Front Inner Ni Foil	5/23/17 (30 min)	5/24/17 (14:25:39	118412 [math] \pm [/math] 7280.06	197670.18 [math] \pm [/math] 12152.98

Mn-54 Efficiency

A calibrated Mn-54 source was used to find the efficiency of an 834 keV line. The source was serial #J4-348, which had an activity of 9.882 [math] \mu Ci [/math] on 8/01/12, so the activity on 4/18/17 was

[math] A(4/18/17) = 9.882 \times e^{-2.57 \times 10^{-8} * 148694400} = 0.22 \mu Ci [/math]

Now converting to Hz gives

[math]\left (0.999760 \right )\left ( 0.22 \times 10^{-6} \mbox{Ci} \right) \left (\frac{ (3.7 \times 10^{10} \mbox{Hz}}{\mbox{Ci}} \right)= (8138.05 \pm 3\%) Hz [/math]

Source	Energy (keV)	Position	Expected Rate (Hz)	ROOT Window (keV)	HpGe Rate (Hz)	HpGe Detector A Efficiency (%)
Mn-54 (J4-348)	834	10cm (Det A)	8138.05 [math] \pm [/math] 3\%	[829,839]	25.87 [math] \pm [/math] 0.28	0.32 [math] \pm [/math] 0.01