LB DetLimits Thesis

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. Note the Mn-54 analysis was weighted by the mass of the soil.

Sample	Activated (total beam time)	Counted	Fully Thesis Corrected Rate @ 1st Measurement (Hz)	[math] A_{Beam Off} [/math]
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)	15.63 [math] \pm [/math] 0.56	17.67 [math] \pm [/math] 0.63
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
1% Sample Se/Soil Mixture Mn-54	5/23/17 (1h)	6/23/17 (16:39:03)	9.38 [math] \pm [/math] 0.39	10.05 [math] \pm [/math] 0.42
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
0.1% Sample Se/Soil Mn-54	5/23/17 (30 min)	6/19/17 (18:25:18)	9.38 [math] \pm [/math] 0.33	9.96 [math] \pm [/math] 0.35

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

Activity Ratio Plots

Below are plots of the activity ratio of the Se/Soil mixture and specific activity of the pure selenium pellet as a reference material. The plots also have no restrictions on the equation of the line.

Following the analysis in Nate's thesis, the initial concentration should be the intercept on the x-axis, which is

[math] \frac{0.054558 \pm 0.004056}{0.122961 \pm 0.006568} = (0.44 \pm 0.04)\% [/math]

This is much more physical than previous answers, but I was able to detect Se-75 at a 0.1% level. Let's try some other reference materials

Below is a plot where the activity ratio was taken using Ni-57 as a reference material. This was the front inner Nickel foil

This is not very physical because the graph implies that the initial concentration in the soil was 19.18%, but there were no Se-75 lines observed in a pure soil sample, so this cannot be true

Finally let's try Mn-54 as a reference material as it was internal to the sample.

Now find the initial concentration by finding the x-intercept.

[math] \frac{15.320237 \pm 0.742753}{16.456772 \pm 0.694779} = (0.93 \pm 0.06)\% [/math]