LB SageBrushWork PostDefense

Mass Information

Note that only 2 samples were produced using the oven method (0.04% and 10%). The target masses are as follows

50% Se/Sage Sample

Selenium Target (50% Sagebrush Se Mix)	Mass (g)
Outer Front Ni Foil	0.6948
Se Mass	0.51
Outer Se Mass	0.1
Sagebrush Leaves Mass	0.4969

10% Sample

Selenium Target (10% Sagebrush Se Mix)	Mass (g)
Outer Front Ni Foil	0.2783
Se Mass	0.0523
Outer Se Mass	0.0971
Sagebrush Leaves Mass	0.5111

0.1% Se/Sage Sample

Selenium Target (0.1% Sagebrush Se Mix)	Mass (g)
Outer Front Ni Foil	1.1437
Se Mass	0.0559
Outer Se Mass	0.1118
Sagebrush Leaves Mass	50.1080

0.04% Sample

Selenium Target (0.04% Sagebrush Se Mix)	Mass (g)
Outer Front Ni Foil	0.5447
Se Mass	0.0020
Outer Se Mass	0.0992
Sagebrush Leaves Mass	4.9326

Time Cuts

The first step in the PAA process is to identify the time cuts used for the split run. This must be done for all samples (50%,10%,0.1%, and 0.04%).

50% Sage/Se Mixture Time Cuts

The 50% Se/Sage mixture was measure on Detector B (unshielded, so watch the SNR) on 5/24/17 for a total of 2130.540 seconds. The outer pure witness Se was measure first, and sub-run was roughly 300 seconds for the samples of interest, and 60 seconds for the Co-60 flag. The root command used to draw the timing information was

TTree* tree = MPA;

MPA->Draw("evt.Chan:evt.Sec>>hist2","evt.ADCid == 1");

which produced the histogram below

This seems a little sloppy, lets try a 1D histogram instead to see if the cuts are more clear

ROOT Command: MPA->Draw("evt.Sec>>hist","ADCid==1","");

This produced the histogram below

This seems much cleaner and clearly shows the time cuts

The time cuts are

0-300 (Pure Se)

375-440 (Co-60)

450-700 (Mixture)

715-780 (Co-60)

800-1010 (Pure Se)

1055-1150 (Co-60)

1160-1420 (Mixture)

1425-1495 (Co-60)

1500-1800 (Pure Se)

1810-1870 (Co-60)

1880-2100 (Mixture)

10% Sage/Se Mixture Time Cuts

The 10% Se/Sage mixture was measured on Detector A (shielded) on 5/25/17 for a total of 5136.343 seconds. The mixture was measured first, and a sub-run was roughly 300 seconds for the Se samples and 60 seconds for the Co-60 flag. The root commands used were

TTree* tree = MPA;

MPA->Draw("evt.Chan:evt.Sec>>hist2","evt.ADCid == 0");

The time cut information is as follows

0-300 (Mixture)

300-360 (Co-60)

400-640 ( Pure Se)

680-710 (Co-60)

730-1020 (Mixture)

1030-1080 (Co-60)

1100-1360 ( Pure Se)

1400-1440 (Co-60)

1480-1775 (Mixture)

1800-1840 (Co-60)

1875-2150 (Pure Se)

2190-2220 (Co-60)

2250-2550 (Mixture)

2590-2620 (Co-60)

2650-2930 (Pure Se)

2950-3000 (Co-60)

3050-3300 (Mixture)

3390-3350 (Co-60)

3400-3690 (Pure Se)

3700-3750 (Co-60)

3775-4050 (Mixture)

4060-4100 (Co-60)

4120-4400 (Pure Se)

4420-4470 (Co-60)

4480-4770 (Mixture)

4790-4820 (Co-60)

4840-5130 (Pure Se)

0.1% Sage/Se Mixture Time Cuts

The 0.1% Se/Sage mixture was measured on Detector A (shielded) on 5/24/17 for a total of 2130.540 seconds. The mixture was measured first, and a sub-run was roughly 300 seconds for the Se samples and 60 seconds for the Co-60 flag. The root commands used were

TTree* tree = MPA;

MPA->Draw("evt.Chan:evt.Sec>>hist2","evt.ADCid == 0");

which produced the histogram below

This seems a little sloppy, so let's repeat the procedure for the 50% sample

ROOT Command:ROOT Command: MPA->Draw("evt.Sec>>hist","ADCid==0","");

This produced the histogram below

This is again much better than the 2D histogram.

The time cuts are

0-300 (Mixture)

306-340 (Co-60)

376-640 (Pure Se)

650-720 (Co-60)

730-1010 (Mixture)

1020-1050 (Co-60)

1100-1350 (Pure Se)

1400-1460 (Co-60)

1470-1730 (Mixture)

1735-1800 (Co-60)

1804-2140 (Pure Se)

The histogram for the time cuts of the second run is shown below

The time cuts are

0-240 (Outer Se)

245-300 (Co-60)

305-820 (Mixture)

0.04% Sample Time Cuts

The 0.04% Se/Sage mixture was measured on Detector A (shielded) on 5/25/17 for a total of 1711.891 seconds. The mixture was measured first, and a sub-run was roughly 300 seconds for the Se samples and 60 seconds for the Co-60 flag. The root commands used were

TTree* tree = MPA;

MPA->Draw("evt.Sec>>hist2","evt.ADCid == 0");

The histogram representing the time cuts for the first run are shown below

The time cuts for this run are

0-290 (Mixture)

295-360 (Co-60)

370-684 (Pure Se)

The histogram representing the time cuts for the second run are shown below

The time cuts for this run are

0-300 (Mixture)

305-355 (Co-60)

360-650 (Pure Se)

660-735 (Co-60)

740-1020 (Mixture)

The histogram representing the time cuts for the third run are shown below

It would appear that first two time cuts are difficult to determine because the Co-60 flag's counts are on the same order as the sample's, so watch out for this next time! Each run should be roughly 300 seconds for the sample and 60 seconds for the Co-60 flag, so check the histograms to make sure there are no Co-60 lines to correct for this. To double check these time cuts I looked for Cl-34m in the mixture (which according to my 10% analysis was not present in the pure Se sample) and the Co-60 lines that may have overlapped. It seems there is a line near 1773 keV present in the mixture, but the 1332 keV line is missing in the mixture. Keep an eye out.

0-300 (Mixture,145 keV 1173 present | 1332 keV not present,good)

305-350 (Co-60, good)

360-650 (Pure Se, good)

660-710 (Co-60, good)

720-940 (Mixture, good)

1020-1070 (Co-60, good)

1100-1240 (Pure Se, good)

1270-1310 (Co-60, good)

1320-1630 (Mixture, good)

1660-1720 (Co-60, good)

1740-2030 (Pure Se, good)

2040-2120 (Co-60, good)

2130-2420 (Mixture, good)

2430-2490 (Co-60, good)

2500-2800 (Pure Se, good)

2810-2850 (Co-60, good)

2880-3150 (Mixture, good)

3170-3220 (Co-60, good)

3240-3510 (Pure Se, good)

3520-3580 (Co-60, good)

3600-3970 (Mixture, good)

4000-4060 (Co-60, good)

4100-4350 (Pure Se, good)

4370-4420 (Co-60, good)

4450-4710 (Mixture, good)

4730-4780 (Co-60, good)

4800-5080 (Pure Se, good)

5100-5160 (Co-60, good)

5190-5460 (Mixture)

5410-5600 (Co-60)

Below is the histogram representing the time cuts for the 4th run

Below are the time cuts

0-300 (Pure Se)

306-359 (Co-60)

362-818 (Mixture)

Gamma Spectrum Analysis

50% Sample Analysis

Below is the analysis table for the 50% Se/Sage mixture. The 103 keV line of Se-81m corresponds to a channel # of 130. Due to the sloppiness of the spectrum, I will use a linear + Gaussian fitting function and restrict my analysis to 6 channels because there are other energy lines nearby. Below is a sample spectrum for an idea of the resolution of Detector B for this measurement

As a comparison for the constant fit, here is a sample spectrum of the Se/Sage measured by Detector A

	0<t<300
Thin Window Histogram
Signal in Thin Window
Integrated Background
Signal - Background
Runtime (s)
Rate (Hz)
Integral Decay Correction (Hz)
Dead Time (%)
Dead Time Corrected Signal (Hz)
.Dat File Entry For HL Plot

10% Sample Analysis

Below is the analysis table for the 10% Se/Sage mixture. The 103 keV line of Se-81m corresponds to a channel # of 113

	0<t<300	730<t<1020	1480<t<1775	2250<t<2550	3050<t<3300	3775<t<4050	4480<t<4770
Thin Window Histogram
Signal in Thin Window	[math] 6.019 \times 10^5 \pm 775.82[/math]	[math] 4.852 \times 10^5 \pm 696.56 [/math]	[math] 4.161 \times 10^5 \pm 645.06 [/math]	[math] 3.667 \times 10^5 \pm 605.56 [/math]	[math] 2.645 \times 10^5 \pm 514.30 [/math]	[math] 2.451 \times 10^5 \pm 495.08 [/math]	[math] 2.344 \times 10^5 \pm 484.15 [/math]
Integrated Background	[math] 2.956 \times 10^5 \pm 885.1 [/math]	[math] 2.074 \times 10^5 \pm 728.7 [/math]	[math] 1.668 \times 10^5 \pm 653.0 [/math]	[math] 1.47 \times 10^5 \pm 606.0 [/math]	[math] 1.115 \times 10^5 \pm 528.6 [/math]	[math] 1.055 \times 10^5 \pm 418.7 [/math]	[math] 9.935 \times 10^4 \pm 496 [/math]
Signal - Background	[math] 3.063 \times 10^5 \pm 1177.01 [/math]	[math] 2.778 \times 10^5 \pm 1008.07 [/math]	[math] 2.493 \times 10^5 \pm 917.88[/math]	[math] 2.197 \times 10^5 \pm 856.70 [/math]	[math] 1.53 \times 10^5 \pm 737.51 [/math]	[math] 1.396 \times 10^5 \pm 648.39 [/math]	[math] 1.35050 \times 10^5 \pm 693.12 [/math]
Runtime (s)	300	290	295	300	250	275	290
Rate (Hz)	[math] 1021 \pm 3.92 [/math]	[math] 957.93 \pm 3.48 [/math]	[math] 845.08 \pm 3.11 [/math]	[math] 732.33 \pm 2.86 [/math]	[math] 612 \pm 2.95 [/math]	[math] 507.64 \pm 2.36 [/math]	[math] 465.69 \pm 2.39 [/math]
Integral Decay Correction (Hz)	[math] 1052.2 \pm 4.04 [/math]	[math] 986.23 \pm 3.58 [/math]	[math] 870.47 \pm 3.20 [/math]	[math] 754.71 \pm 2.95 [/math]	[math] 627.56 \pm 3.03 [/math]	[math] 521.85 \pm 2.43 [/math]	[math] 479.44 \pm 2.46 [/math]
Dead Time (%)	5.06 +/- 0.39	3.06 +/- 0.30	2.53 +/- 0.31	2.26 +/- 0.33	1.92 +/- 0.26	1.65 +/- 0.34	1.55 +/- 0.18
Dead Time Corrected Signal (Hz)
.Dat File Entry For HL Plot

Background and SNR Information

Below is a plot of the background in a 10 channel window around the short lived half life's energy peak of interest (103 keV). The long lived half live can be measured for at least a year even in a 0.1% by mass concentration, so it is less pressing. The values presented are weighted by the mass of the sage ash.

The fit parameters are

Constant: 4.50734e+00 +/- 2.42037e-03

Slope: -2.31438e-04 +/- 1.05610e-06

Which gives a rough half life of 49.92 +/- 0.23 minutes

Below is the SNR plotted in xmgrace

0.1% Sample Analysis

Below is the analysis table for the 0.1% Mixture, the 103 keV line for Se-81m corresponds to a channel # of 113.

	0<t<300	730<t<1010	1470<t<1730	305<t<820 (Run 2)
Thin Window Histogram
Signal in Thin Window	No Signal Visible	No Signal Visible	No Signal Visible	Possible Signal Visible?
Integrated Background	-	-	-	-
Signal - Background	-	-	-	-
Runtime (s)	300	280	260	515
Rate (Hz)	-	-	-	-
Integral Decay Correction (Hz)	-	-	-	-
Dead Time (%)	-	-	-	-
Dead Time Corrected Signal (Hz)	-	-	-	-
.Dat File Entry For HL Plot	-	-	-	-

0.04% Sample Analysis

	0<t<290	0<t<300 (Run 2)	740<t<1020 (Run 2)
Thin Window Histogram
Signal in Thin Window	No Signal Visible	No Signal Visible	No Signal Visible
Integrated Background	-	-	-	-
Signal - Background	-	-	-	-
Runtime (s)	290	300	280
Rate (Hz)	-	-	-	-
Integral Decay Correction (Hz)	-	-	-	-
Dead Time (%)	-	-	-	-
Dead Time Corrected Signal (Hz)	-	-	-	-
.Dat File Entry For HL Plot	-	-	-	-

Background and SNR Information

Below is the information for the background in the window [109,119] (Channel # here). The data was weighted by both the runtime and the mass of the sage ash.

The fit parameters here are

Constant: 3.42624e+00 +/- 3.71043e-03

Slope: -3.44115e-04 +/- 7.67333e-07

which gives a half life of 33.57 +/- 0.07 minutes.

The SNR plot is shown below

Fall 2018 Possible Sage Irradiation Activity Prediction

Isotope Search link: http://nucleardata.nuclear.lu.se/toi/

For this section I will attempt to identify the most active line within a sagebrush sample. The histograms that follow in this section will be weighted by the mass of the sage that was used for the sample. I will use the 10% Sage/Se mixture because it was processed using the oven method for dehydration. The mass was 0.5111g which gives a weighting factor of 1.9566 [math] g^{-1} [/math] Below is a full spectrum for the time cut of 0 <t< 300 seconds.

It seems the two most prominent lines are around 150 keV and 250 keV, so let's try to study the decay of those first.

144.5 keV Line

Note: the x-axis for the first 2 histograms should be Energy (keV). This line is NOT present in the Pure Se Sample, so it should be a line produced by the sage itself.

	0<t<300	730<t<1020	1480<t<1775	2250<t<2550	3050<t<3300	3775<t<4050	4480<t<4770
Histogram
Signal in Thin Window	3.424 [math] \times 10^4 \pm [/math] 185.04	2.535 [math] \times 10^4 \pm [/math] 159.22	2.037 [math] \times 10^4 \pm [/math] 142.72	1.695 [math] \times 10^4 \pm [/math] 130.19	1.14 [math] \times 10^4 \pm [/math] 106.77	1.154 [math] \times 10^4 \pm [/math] 107.42	1.115 [math] \times 10^4 \pm [/math] 105.59
Integrated Background	1.9628 [math] \times 10^4 \pm [/math] 167.4	1.4035 [math] \times 10^4 \pm [/math] 139.3	1.1473 [math] \times 10^4 \pm [/math] 128.80	9877 [math] \pm [/math] 118.3	7133 [math] \pm [/math] 86.1	6951.7 [math] \pm [/math] 84.0	7182 [math] \pm [/math] 85.4
Signal - Background	1.4612 [math] \times 10^4 \pm [/math] 249.52	1.1315 [math] \times 10^4 \pm [/math] 211.55	8897 [math] \pm [/math] 192.24	7073 [math] \pm [/math] 175.91	4267 [math] \pm [/math] 137.16	4588.3 [math] \pm [/math] 136.36	3968 [math] \pm [/math] 135.80
Runtime (s)	300	290	295	300	250	275	290
Rate (Hz)	48.71 [math]\pm[/math] 0.83	39.02 [math] \pm [/math] 0.73	30.16 [math] \pm [/math] 0.65	23.58 [math] \pm [/math] 0.59	17.07 [math] \pm [/math] 0.55	16.68 [math] \pm [/math] 0.49	13.68 [math] \pm [/math] 0.47

Without any corrections, the half life here is 38.61 [math] \pm [/math] 0.84 minutes. This is likely Cl-34m (32 min half life) produced by a (g,n) reaction on Cl-35 (75.76% natural abundance), which is stable, because a second line characteristic of Cl-34m was found (1176 keV). This could also be produced by a (g,pn) knockout on Ar-36 in air. This is chlorine since using the isotope search with an energy uncertainty of 5 keV and a half life uncertainty of 10 minutes, the only isotope that shared 146 and 1176 keV with branching ratios that made sense was Cl-34m.

9/10/18 Irradiation

The mass information is

Al Cylinder: 26.0249g

Sage Ash (oven method): 2.0913g

Beam off: 18:30

Calibration

Below is the runlist used for the calibration on Detector D

Source	Serial No.	Reference Date	Activiy	Half life	Expected Energies (keV)	Line Seen (Channel No.)	Runtime (s)	Position	File Name	Date Measured
Mn-54	J4-348	8/1/12	9.882 uCi	312.20 days	834.827	835.117	300.601	10	LB_Mn_54_9_10_18_Pos10_DetD	9/10/18
Cs-137	129793	7/1/08	1.066 uCi	30.08 years	661.657	661.887	141.356	10	LB_Cs137_9_10_18_Pos010_DetD	9/10/18
Co-60	129739	07/01/08	1.082 uCi	1925.28 days	1173.228, 1332.492	1173.338, 1332.564	232.521	10	LB_Co60_9_10_18_Pos010_DetD	9/10/18
Ba-133	129790	07/01/08	1.188 uCi	10.551 years	80.9979, 276.3989, 302.8508, 356.0129, 383.8485	81.391, 276.741, 303.166, 356.315, 384.137	250.816	10	LB_Ba133_9_10_18_Pos010_DetD	9/10/18

The calibration coefficients are (according to my fits)

Intercept = -0.370972 +/- 0.616

Slope = 0.490352 +/- 0.000534241

The calibration used at the IAC was

Intercept = 0.272366

Slope = 0.490198

Efficiency

Below is a table of the runlist used for the efficiency on Detector D.

Source	Serial No.	Reference Date	Activiy	Half life	Expected Energies (keV)	Start	Stop	Runtime (s)	Position	File Name	Date Measured
Mn-54	J4-348	8/1/12	9.882 uCi	312.20 days	828.859	12:45	12:50	300.601	10	LB_Mn_54_9_10_18_Pos10_DetD	9/10/18
Mn-54	J4-348	8/1/12	9.882 uCi	312.20 days	828.859	12:52	12:57	305.787	20	LB_Mn_54_9_10_Pos020_DetD	9/10/18
Mn-54	J4-348	8/1/12	9.882 uCi	312.20 days	828.859	12:59:41	113:04	300.734	30	LB_Mn_54_9_10_18_Pos030_DetD	9/10/18
Co-60	129740	07/01/08	10.42 uCi	1925.28 days	1173.228, 1332.492	18:17:35	18:24	409.011	80	LB_Co60_9_10_18_Pos080_DetD	9/10/18
Co-60	129740	07/01/08	10.42 uCi	1925.28 days	1173.228, 1332.492	18:26:11	18:29	201.084	70	LB_Co60_9_10_18_Pos070_DetD	9/10/18

Runlist for 9/10/18 Irradiated Samples

Sample	Date	Start	Stop	Runtime (s)	Position	Detector	% Dead	File Name
Sage Ash	9/10/18	20:31:35	09:26	46507.875	40	Detector D	< 2%	LB_SageAsh_OvenMethod_9_10_18_DetD_002
Sage Ash	9/11/18	14:59:50	10:57	71854.534	40	Detector D	<1%	LB_SageAsh_OvenMethod_9_11_18_DetD_003
Sage Ash	9/12/18	11:01:05		89908.033	20	Detector D	<1%	LB_SageAsh_OvenMethod_9_12_18_DetD_Pos20_001
Sage Ash	9/13/18	12:03:02		73275.295	10	Det D	<1%	LB_SageAsh_OvenMethod_9_13_18_DetD_Pos10_001
Sage Ash	9/14/18	09:26:37	10:41 (9/17/18)		10	Det D	<1%	LB_SageAsh_OvenMethod_9_14_18_DetD_Pos10_001
Sage Ash	9/17/18	10:51:02			10	Det D	<1%	LB_SageAsh_OvenMethod_9_17_18_DetD_Pos10_001
Sage Ash	10/01/18	14:04:00			Face of Detector	Det D	<1%	LB_SageAsh_OvenMethod_10_1_18_DetD_DetFace_002

September Sage+Al Analysis

https://wiki.iac.isu.edu/index.php/MCNP_Sim_of_Jack_Converter

Below is the first measured histogram generated from the file LB_SageAsh_OvenMethod_9_10_18_DetD_002. Note that the Al cylinder and the sage ash were not separated, so there will be some lines from Al present. The histogram shown below is not weighted because there are two different samples in front of the detector at the same time (Al cylinder and sage ash). Once the lines have been identified, the mass will be taken into account

The command lines used in the directory /data/IAC/LB_Thesis_Analysis/Sept2018_SageAshBackground/Samples

.L Eff.C

Eff t

t.Loop(RangeMin,RangeMax);

Below is a histogram of the second measurement taken overnight on 9/11/18

Now let's overlay these two histograms as a function of activity rather than counts to see if there are any lines that have decayed away that could possibly be identified. I did this as Hz vs. 0.5*(Chan)-0.4. The dithering proved to be quite difficult for both histograms.

Below is a table detailing the decaying/decayed lines. The relative rates were calculated using a linear fit plus a Gaussian fit, then the background subtracted activity was found.

Histogram Line	Channel	Energy (keV)	Relative Rate ([math] \frac{A_2}{A_1} [/math])
863	1726.8	846	0
1846	3692	1810	0
2155	4310.8	2113.4	0

Background Analysis

Below is the analysis of the background around the Se line of interest. The histograms were unweighted due to the presence of both the Al cylinder and the sage ash. The data points on the half life plot are weighted by the runtime. The energy window used was [90,130]. The times I concerned myself with spanned 5 half lives of Se (17184 sec) which were split cut into 10 different sets (runtime = 1718.4 sec).

The parameters are as follows

	0<t<1718.4 s	1718.4<t<3436.8 s	3436.8<t<5155.2 s	5155.2<t<6873.6 s	6873.6<t<8592 s	8592<t<10310.4 s	10310.4<t<12028.8 s	12028.8<t<13747.2 s	13747.2<t<15461.6 s	15461.6<t<17180 s
Slope ([math] \alpha [/math])	5.853 [math] \pm [/math] 0.562	5.33 [math] \pm [/math] 0.54	4.981 [math] \pm [/math] 0.532	5.423 [math] \pm [/math] 0.521	6.234 [math] \pm [/math] 0.511	5.155 [math] \pm [/math] 0.503	4.703 [math] \pm [/math] 0.496	4.053 [math] \pm [/math] 0.489	4.49 [math] \pm [/math] 0.49	4.506 [math] \pm [/math] 0.503
Intercept ([math] \beta [/math] )	1051 [math] \pm [/math] 61.9	998.8 [math] \pm [/math] 59.6	974.6 [math] \pm [/math] 58.7	871.7 [math] \pm [/math] 57.4	731.4 [math] \pm [/math] 56.2	796.7 [math] \pm [/math] 55.4	807.3 [math] \pm [/math] 54.6	841 [math] \pm [/math] 53.9	836.8 [math] \pm [/math] 54.5	868.6 [math] \pm [/math] 55.4
Integral from [90,130]	39.45 [math] \pm [/math] 2.04	36.90 [math] \pm [/math] 1.96	35.44 [math] \pm [/math] 1.92	34.18 [math] \pm [/math] 1.89	32.99 [math] \pm [/math] 1.85	31.74 [math] \pm [/math] 1.82	30.83 [math] \pm [/math] 1.80	29.95 [math] \pm [/math] 1.77	30.98 [math] \pm [/math] 1.78	31.76 [math] \pm [/math] 1.82

Now the total background was found by integrating the linear fit function across the region of interest, in other words

[math] f(x) = \int_a^b (\alpha x + \beta)dx [/math]

To find the error in the integral, use the standard error propagation method

[math] \sigma_f = \sqrt{(\frac{\partial f}{\partial \alpha})^2 \sigma_{\alpha}^2 + (\frac{\partial f}{\partial \beta})^2 \sigma_{\beta}^2} [/math]

[math] = \sqrt{[\frac{\partial}{\partial \alpha}(\int_a^b (\alpha x + \beta)dx)]^2 \sigma_{\alpha}^2 + [\frac{\partial}{\partial \beta}(\int_a^b (\alpha x + \beta)dx)]^2 \sigma_{\beta}^2} [/math]

Since the partial derivatives are not taken with respect to the variable of integration and the function is analytic within the region, the derivative may be moved inside the integral. This action yields

[math]\sigma_f = \sqrt{(\int_a^b x dx)^2 \sigma_{\alpha}^2 + (\int_a^b dx)^2 \sigma_{\beta}^2} [/math]

[math] = \sqrt{(\frac{b^2-a^2}{2})^2 \sigma_{\alpha}^2 + (b-a)^2 \sigma_{\beta}^2} [/math]

Below is the initial plot of the background in the region from [90,130]

This plot has some outliers and fluctuations in the background that could be due to the presence of other sources (Dr. Dale was measuring very hot gallium on Det A during my overnight measurement).

10 Channel Analysis

The fits were done in a larger window [90,130] to get enough bins for a good fit, so I should be able to simply change the bounds of the integration to make the correction. There is definitely some randomness within the time cuts which produce bins with data above and below the fit line, which makes this more difficult. With the dithering, the peak on Detector A has a mean value of 103.949 kev, so the window I will analyze on Detector D (calibrated to energy) will be [99,109] keV

0<t<1718.4 s

1718.4<t<3436.8 s

3436.8<t<5155.2 s

5155.2<t<6873.6 s

6873.6<t<8592 s

8592<t<10310.4 s

10310.4<t<12028.8 s

12028.8<t<13747.2 s

13747.2<t<15461.6 s

15461.6<t<17184 s

17184 <t< 18902.4 s

18902.4 <t< 20620.8 s

20620.8<t<22339.2 s

22339.2<t<24057.6 s

24057.6<t<25776 s

25776<t<27494.4 s

27494.4<t<29212.8 s

29212.8 <t< 30931.2 s

30931.2 <t< 32649.6 s

32649.6<t<34368 s

34368<t<36086.4 s

36086.4<t<37804.8

37804.8 <t< 39523.2

39523.2<t<41241.6 s

41241.6 <t< 42960 s

42960<t<44678.4 s

44678.4 <t< 46396.8 s

Slope ([math] \alpha [/math])

5.853 [math] \pm [/math] 0.562

5.33 [math] \pm [/math] 0.54

4.981 [math] \pm [/math] 0.532

5.423 [math] \pm [/math] 0.521

6.234 [math] \pm [/math] 0.511

5.155 [math] \pm [/math] 0.503

4.703 [math] \pm [/math] 0.496

4.053 [math] \pm [/math] 0.489

4.49 [math] \pm [/math] 0.49

4.506 [math] \pm [/math] 0.503

5.101 [math] \pm [/math] 0.496

5.215 [math] \pm [/math] 0.490

4.695 [math] \pm [/math] 0.482

4.685 [math] \pm [/math] 0.477

4.731 [math] \pm [/math] 0.468

4.218 [math] \pm [/math] 0.468

3.95 [math] \pm [/math] 0.459

4.388 [math] \pm [/math] 0.452

4.180 [math] \pm [/math] 0.446

3.512 [math] \pm [/math] 0.442

4.423 [math] \pm [/math] 0.440

4.751 [math] \pm [/math] 0.435

3.695 [math] \pm [/math] 0.431

3.372 [math] \pm [/math] 0.424

3.112 [math] \pm [/math] 0.420

3.784 [math] \pm [/math] 0.415

2.792 [math] \pm [/math] 0.414

Intercept ([math] \beta [/math] )

1051 [math] \pm [/math] 61.9

998.8 [math] \pm [/math] 59.6

974.6 [math] \pm [/math] 58.7

871.7 [math] \pm [/math] 57.4

731.4 [math] \pm [/math] 56.2

796.7 [math] \pm [/math] 55.4

807.3 [math] \pm [/math] 54.6

841 [math] \pm [/math] 53.9

836.8 [math] \pm [/math] 54.5

868.6 [math] \pm [/math] 55.4

769.5 [math] \pm [/math] 54.6

732.8 [math] \pm [/math] 54.0

737.5 [math] \pm [/math] 53.1

715.1 [math] \pm [/math] 52.6

673.8 [math] \pm [/math] 51.6

714.3 [math] \pm [/math] 51.5

701.0 [math] \pm [/math] 50.6

625.5 [math] \pm [/math] 49.8

620.9 [math] \pm [/math] 49.1

676.1 [math] \pm [/math] 48.8

562.8 [math] \pm [/math] 48.4

508.3 [math] \pm [/math] 47.9

600.2 [math] \pm [/math] 47.5

608 [math] \pm [/math] 46.7

623 [math] \pm [/math] 46.3

519.5 [math] \pm [/math] 45.7

618.1 [math] \pm [/math] 45.6

Fit Function Integral from [99,109]

9.67 [math] \pm [/math] 0.50

9.04 [math] \pm [/math] 0.48

8.69 [math] \pm [/math] 0.47

8.35 [math] \pm [/math] 0.46

8.03 [math] \pm [/math] 0.45

7.76 [math] \pm [/math] 0.44

7.54 [math] \pm [/math] 0.44

7.35 [math] \pm [/math] 0.43

7.59 [math] \pm [/math] 0.43

7.78 [math] \pm [/math] 0.44

7.57 [math] \pm [/math] 0.44

7.42 [math] \pm [/math] 0.43

7.13 [math] \pm [/math] 0.42

7.00 [math] \pm [/math] 0.42

6.78 [math] \pm [/math] 0.41

6.71 [math] \pm [/math] 0.41

6.47 [math] \pm [/math] 0.40

6.30 [math] \pm [/math] 0.40

6.14 [math] \pm [/math] 0.39

6.06 [math] \pm [/math] 0.39

5.95 [math] \pm [/math] 0.39

5.83 [math] \pm [/math] 0.38

5.73 [math] \pm [/math] 0.38

5.58 [math] \pm [/math] 0.37

5.51 [math] \pm [/math] 0.37

5.31 [math] \pm [/math] 0.37

5.29 [math] \pm [/math] 0.36

Stats Box Integral

[math] 1.674 \times 10^4 [/math]

[math] 1.565 \times 10^4 [/math]

[math] 1.505 \times 10^4 [/math]

[math] 1.159 \times 10^4 [/math]

[math] 1.401 \times 10^4 [/math]

[math] 1.341 \times 10^4 [/math]

[math] 1.306 \times 10^4 [/math]

[math] 1.292 \times 10^4 [/math]

[math] 1.332 \times 10^4 [/math]

[math] 1.347 \times 10^4 [/math]

[math] 1.313 \times 10^4 [/math]

[math] 1.296 \times 10^4 [/math]

[math] 1.238 \times 10^4 [/math]

[math] 1.197 \times 10^4 [/math]

[math] 1.194 \times 10^4 [/math]

[math] 1.166 \times 10^4 [/math]

[math] 1.134 \times 10^4 [/math]

[math] 1.101 \times 10^4 [/math]

[math] 1.085 \times 10^4 [/math]

[math] 1.064 \times 10^4 [/math]

[math] 1.046 \times 10^4 [/math]

[math] 1.027 \times 10^4 [/math]

9943

9872

9699

9206

9110

Stats Box Activity (Hz)

9.58 [math] \pm [/math] 0.07

9.12 [math] \pm [/math] 0.07

8.76 [math] \pm [/math] 0.07

6.74 [math] \pm [/math] 0.06

8.15 [math] \pm [/math] 0.07

7.80 [math] \pm [/math] 0.07

7.60 [math] \pm [/math] 0.07

7.53 [math] \pm [/math] 0.07

7.75 [math] \pm [/math] 0.07

7.84 [math] \pm [/math] 0.07

7.64 [math] \pm [/math] 0.07

7.54 [math] \pm [/math] 0.07

7.20 [math] \pm [/math] 0.06

6.97 [math] \pm [/math] 0.06

6.95 [math] \pm [/math] 0.06

6.79 [math] \pm [/math] 0.06

6.60 [math] \pm [/math] 0.06

6.41 [math] \pm [/math] 0.06

6.31 [math] \pm [/math] 0.06

6.19 [math] \pm [/math] 0.06

6.09 [math] \pm [/math] 0.06

5.98 [math] \pm [/math] 0.06

5.79 [math] \pm [/math] 0.06

5.74 [math] \pm [/math] 0.06

5.64 [math] \pm [/math] 0.06

5.36 [math] \pm [/math] 0.06

5.30 [math] \pm [/math] 0.06

Corrected Background Measurement

9.58 [math] \pm [/math] 0.09

9.12 [math] \pm [/math] 0.08

8.76 [math] \pm [/math] 0.07

6.74 [math] \pm [/math] 1.61

8.15 [math] \pm [/math] 0.12

7.80 [math] \pm [/math] 0.04

7.60 [math] \pm [/math] 0.06

7.53 [math] \pm [/math] 0.18

7.75 [math] \pm [/math] 0.16

7.84 [math] \pm [/math] 0.06

7.64 [math] \pm [/math] 0.07

7.54 [math] \pm [/math] 0.12

7.20 [math] \pm [/math] 0.07

6.97 [math] \pm [/math] 0.03

6.95 [math] \pm [/math] 0.17

6.79 [math] \pm [/math] 0.08

6.60 [math] \pm [/math] 0.13

6.41 [math] \pm [/math]

6.31 [math] \pm [/math] 0.17

6.19 [math] \pm [/math] 0.13

6.09 [math] \pm [/math] 0.14

5.98 [math] \pm [/math] 0.15

5.79 [math] \pm [/math] 0.06

5.74 [math] \pm [/math] 0.16

5.64 [math] \pm [/math] 0.13

5.36 [math] \pm [/math] 0.05

5.30 [math] \pm [/math] 0.01

This looks like there are two separate half lives present, so split them up and fit.

The fit parameters for the first portion are

Slope: -2.22732e-05 +/- 8.61118e-07

Constant:2.25058e+00 +/- 6.19036e-03

Which gives a half life of 8.47 +/- 0.32 hours

The fit parameters for the second portion are

Constant: 2.24079e+00 +/- 5.78712e-03

Slope: -1.28411e-05 +/- 1.46816e-07

Which gives a half life of 14.99 +/- 0.17 hours

846 keV Line Analysis

Below is the analysis table. The energy window under study is [841,851]

	0<t<7751.3125	7751.3125 <t< 15502.625	15502.325 <t< 23253.9375	23253.9375 <t< 31005.25	31005.25 <t< 38756.5625	38756.5625 <t< 46507.875
Histogram
Signal in Window	1.013 [math] \times 10^5 \pm [/math] 318.28	5.856 [math] \times 10^4 \pm [/math] 241.99	3.427 [math] \times 10^4 \pm [/math] 185.12	2.062 [math] \times 10^4 \pm [/math] 143.60	1.289 [math] \times 10^4 \pm [/math] 113.53	8254 [math] \pm [/math] 90.85
Integrated Background	6040 [math] \pm [/math] 110	4912 [math] \pm [/math] 98	4295 [math] \pm [/math] 91	3739 [math] \pm [/math] 83	3224 [math] \pm [/math] 77	2889 [math] \pm [/math] 72
Signal - Background	9.5260 [math] \times 10 ^4 \pm [/math] 336.75	5.3648 [math] \times 10^4 \pm [/math] 261.08	2.9975 [math] \times 10^4 \pm [/math] 206.28	1.6881 [math] \times 10^4 \pm [/math] 165.86	9666 [math] \pm [/math] 137.18	5365 [math] \pm [/math] 115.92
Runtime (s)	7751.3125	7751.3125	7751.3125	7751.3125	7751.3125	7751.3125
Rate (Hz)	12.29 [math] \pm [/math] 0.04	6.92 [math] \pm [/math] 0.03	3.87 [math] \pm [/math] 0.03	2.18 [math] \pm [/math] 0.02	1.25 [math] \pm [/math] 0.02	0.69 [math] \pm [/math] 0.01

The exponential decay plot is shown below

The fit parameters are

Constant: 2.50880 [math] \pm [/math] 0.00287747

Slope: -7.42478 [math] \pm [/math] 0.0249932 [math] \times 10^{-5} [/math]

Which yields a half life of 2.59 [math] \pm [/math] 0.01 hours, which is within one standard deviation of Mn-56's half life (2.58 hours)

The lines that are characteristic with the highest branching ratios of Mn-56 (1810,2133 keV) are both present in the spectrum. This would lead me to believe it is indeed Mn-56 which is produced by either a proton knockout of Fe-57, or neutron capture on Mn-55.

There is also an 834 keV line present, but due to the long half life of Mn-54, this will take some time to analyze, but remember it is there!

1367.5 keV Line Analysis

There is a line decaying at 1367.5 keV. Let's do an analysis on it to see if the isotope can be identified. The window of analysis is [1362,1372]

	0<t<7751.32 s	7751.32<t<15502.64 s
Histogram
Signal in Window	[math] 7.472 \times 10^4 [/math]	[math] 6.7 \times 10^4 [/math]
Integrated Background	2732 [math] \pm [/math] 44	2145 [math] \pm [/math] 39
Signal - Background
Runtime (s)	7751.32	7751.32	7751.32	7751.32	7751.32	7751.32
Rate (Hz)

Production Optimization

The sage ash has a density of 0.1977 [math] \frac{g}{cm^3} [/math]. To perform this I will use an 8 hour half life from the sage ash/Al sample irradiated on 9/10/18.

8 Hour Half Life (9/10/18)

This section focuses on optimization for the sage/Al cylinder 8 hour half life performed above. The decay constant for that sample was -2.22732e-05 +/- 8.61118e-07 [math] s^{-1} [/math]. The production rate is given by

[math] N(t) = \frac{n_T V_T}{\lambda} \int \sigma (E) \phi(E) dE (1-e^{- \lambda t}) [/math]

For the sage ash, the cross section and the flux are unknown, so reduce this equation to

[math] N_{Sage/Al}(t) = \frac{d_T V_T}{\lambda}(1-e^{- \lambda t}) [/math]

where [math] d_T [/math] is the density of the target and [math] V_T [/math] is the volume of the Al cylinder (assuming the cylinder will be completely filled with sage ash)

[math] V_T = 190.755 cm^3 [/math]

For the selenium, we can compute the number of atoms per unit volume, [math] n_T [/math]. The mass of a single selenium pellet is approximately 0.1g, while the atomic mass is 78.96u. So the number of atoms in a single selenium pellet is [math] 7.62 \times 10^{20} [/math] atoms, which means

[math] n_{Se_T} = 3.812 \times 10^{22} \frac{atoms}{cm^3} [/math]

Using the number of atoms vs. the density yields a highly unphysical result. Try using the density for the selenium as well.

[math] d_{Se_T} = 5 \frac{g}{cm^3} [/math]

The capacitive decline and the differences in half life imply that the production rate will always be higher for the sage ash.