Difference between revisions of "LB 170063 Nickel Information With Dead Time"

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Below is a table with thin windows, original windows, and expanded windows for the nickel on sample 170063
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Below is a table with thin windows, original windows, and expanded windows for the nickel on sample 170063. The thin window method can be found at [[LB Thesis Thin Window Analysis]].
−
 
 
 
{| border="3"  cellpadding="5" cellspacing="0"
 
{| border="3"  cellpadding="5" cellspacing="0"
 
|| || 5/25/17 || 5/26/17 || 5/27/17|| 5/29/17 || 5/30/17 || 5/31/17 || 6/1/17 ||   
 
|| || 5/25/17 || 5/26/17 || 5/27/17|| 5/29/17 || 5/30/17 || 5/31/17 || 6/1/17 ||   
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||Position on Detector A (cm) || 50 || 30 || 20 || 20 || 10 || 10 || 10  
 
||Position on Detector A (cm) || 50 || 30 || 20 || 20 || 10 || 10 || 10  
 
|-
 
|-
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||Efficiency (Percent) || 0.017000 +/- 0.000002 || 0.042200 +/- 0.000005 || 0.084700 +/0.000007 || 0.084700 +/0.000007 || 0.310000 +/- 0.000003  
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||Efficiency (Percent) || 0.017000 +/- 0.000002 || 0.042200 +/- 0.000005 || 0.084700 +/0.000007 || 0.084700 +/0.000007 || 0.310000 +/- 0.000003 || 0.310000 +/- 0.000003  || 0.310000 +/- 0.000003 
 +
|-
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||Signal in thin Window With Efficiency || 307941176.5 +/- 3864757.4 || 231895734.6 +/- 741812.3 || 139905549 +/- 406587.1067 || 55985832.4 +/- 257137.3 || 23580645.2 +/- 87216.4 || 17719354.8 +/- 75603. 4 || 10877419.4 +/- 59235.6
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|-
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||Integrated Background with Efficiency || 3877647.1 +/- 101177.5 || 3372857.1 +/- 60953.7 || 3804014.2 +/- 46990.42 || 584179.5 +/- 17709.6 || 465161.3 +/- 8451.6 || 274064.5 +/- 6387.1 || 13897.7 +/- 4516.1
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|-
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||Background Subtracted Signal || 304063529.4 +/- 3866081.6 || 228522877.5 +/- 744312.3 || 136101534.8 +/- 409293.5 || 55401652.9 +/- 257746.4 || 23115483.9 +/- 87624.9 || 17445290.3 +/- 75872.7 || 10863521.7 +/- 59407.5 
 
|-
 
|-
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||Signal in thin Window With Efficiency ||  
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||Runtime (s) || 301.337 || 301.322 || 327.734 || 300.228 || 272.845 || 300.691 || 306.858
 
|-
 
|-
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||Background Subtracted Signal ||  
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||Rate (Hz) || <math> 1.009048 \times 10^6 \pm 1.2829 \times 10^4 </math> || <math>7.58401 \times 10^5 \pm 2.470 \times 10^3</math> ||<math> 4.15280 \times 10^5 \pm 1.248 \times 10^3 </math> || <math>1.84531 \times 10^5 \pm 8.58 \times 10^2 </math>||<math> 8.4720 \times 10^4 \pm 3.2115 \times 10^2</math> ||<math> 5.8017 \times 10^4 \pm 2.5233 \times 10^2 </math>|| <math> 3.5402 \times 10^4 \pm 1.9360 \times 10^2 </math>
 
|-
 
|-
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||Runtime (s)
+
||True Rate (Integral Method) (Hz) || <math>1.040020 \times 10^6 \pm 1.3222 \times 10^4 </math> ||<math> 7.81679 \times 10^5 \pm  2.5458 \times 10^3</math> ||<math> 4.29155 \times 10^5 \pm 1.290 \times 10^3 </math> || <math> 1.90175 \times 10^5 \pm 8.8425 \times 10^2 </math>||<math> 8.7072 \times 10^4 \pm 3.29 \times 10^2 </math> || <math> 5.9793 \times 10^4 \pm 2.59 \times 10^2 </math> || <math> 3.6508 \times 10^4 \pm 2.00 \times 10^2 </math>
 
|-
 
|-
−
||Rate (Hz)
+
||Number of Entries in Histogram || 566090 || 1015134 || 1428804 || 541498 || 984165 || 761238 ||494039
 +
|-
 +
||<math> \frac{Entries}{Runtime} </math> || 1878.59 || 3368.93 || 4359.64 || 1803.62 || 3607.05 || 2531.63 || 1609.99
 +
|-
 +
|| Percent Dead ||3.95 +/- 0.42 || 6.59 +/- 0.43 || 9.09 +/- 0.60 || 3.95 +/- 0.42 || 6.59 +/- 0.43 || 5.06 +/- 0.39 || 3.06 +/- 0.3
 +
|-
 +
||True Rate (Hz) || <math> 1.082790 \times 10^6 \pm 1.4557 \times 10^4 </math> || <math> 8.36825 \times 10^5 \pm 4.764 \times 10^3 </math> || <math> 4.72065 \times 10^5 \pm 3.332 \times 10^3</math> || <math> 1.97995 \times 10^5 \pm 1.322 \times 10^3</math>  || <math> 9.3214 \times 10^4 \pm 5.59 \times 10^2</math> || <math> 6.2979 \times 10^4 \pm 3.62 \times 10^2 </math> ||<math> 3.7660 \times 10^4 \pm 2.33 \times 10^2 </math>
 +
|-
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||Backtracked Signal (For Consistency) || || 
 +
|-
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||.dat file entry || 13.90 +/- 0.01 || 13.64 +/- 0.01 ||  13.06 +/- 0.01 || 12.20 +/- 0.01 || 11.44 +/- 0.01 || 11.04 +/- 0.01|| 10.54 +/- 0.01
 
|-
 
|-
 
|}
 
|}
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 +
We can also trace these signals back in time to make sure that they somewhat match up with the previous signal that was seen.
 +
 +
Below is a plot that was made to help find the half life and the initial activity of the sample
 +
 +
[[File:170063 NickelFoil HLPlot DeadTimeCorrected.png|200px]]
 +
 +
from here we can see that
 +
 +
<math> Slope = 5.63921 \times 10^{-6} \pm 1.75557 \times 10^{-8} </math>
 +
 +
and the intercept is given by
 +
 +
<math> 13.9333 \pm 0.00643596 </math>
 +
 +
By exponentiating the intercept, we can find the activity of the nickel foil at the time of the first measurement, which is
 +
 +
<math> 1.125007 \times 10^6 \pm 7.240 \times 10^3 </math>
 +
 +
Now note that this measurement was taken 8 minutes after the selenium samples were measured. So we must correct the activity back 8 minutes.
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 +
<math> A_0 = 1.125007 \times 10^6 \times e^{5.40845 \times 10^{-6} \times 480} = 1.127931 \times 10^6 Hz </math>
 +
 +
<math> \sigma_{A_0} = 7240 \times e^{5.40845 \times 10^{-6} \times 480} = 7258.82 Hz </math>

Latest revision as of 22:02, 6 December 2017

Below is a table with thin windows, original windows, and expanded windows for the nickel on sample 170063. The thin window method can be found at LB Thesis Thin Window Analysis.

5/25/17 5/26/17 5/27/17 5/29/17 5/30/17 5/31/17 6/1/17
Thin Window 170063 NickelSpectrum 5 25 17 ThinWidnow.png 170063 NickelSpectrum 5 26 17 ThinWindow.png 170063 NickelSpectrum 5 27 17 ThinWindow.png 170063 NickelSpectrum 5 29 17 ThinWindow.png 170063 NickelSpectrum 5 30 17 ThinWindow.png 170063 NickelSpectrum 5 31 17 ThinWindow.png 170063 NickelSpectrum 6 1 17 ThinWindow.png
Original Window 170063 NickelSpectrum 5 25 17 OGWindow.png 170063 NickelSpectrum 5 26 17 OGWindow.png 170063 NickelSpectrum 5 27 17 OGWindow.png 170063 NickelSpectrum 5 29 17 OGWindow.png 170063 NickelSpectrum 5 30 17 OGWindow.png 170063 NickelSpectrum 5 31 17 OGWindow.png 170063 NickelSpectrum 6 1 17 OGWindow.png
Original Background 329.6 +/- 8.6 708.3 +/- 12.8 1611 +/- 19.9 247.4 +/- 7.5 721 +/- 13.1 424.8 +/- 9.9 215.4 +/- 7.0
Integrated Background 659.2 +/- 17.2 1416.6 +/- 25.6 3222 +/- 39.8 494.8 +/- 15 1442 +/- 26.2 849.6 +/- 19.8 430.8 +/- 14
Signal in Thin Window 52350 +/- 228.80 97860 +/- 312.83 118500 +/- 344.24 47420 +/- 217.76 73100 +/- 270.37 54930 +/- 234.37 33720 +/- 183.63
Position on Detector A (cm) 50 30 20 20 10 10 10
Efficiency (Percent) 0.017000 +/- 0.000002 0.042200 +/- 0.000005 0.084700 +/0.000007 0.084700 +/0.000007 0.310000 +/- 0.000003 0.310000 +/- 0.000003 0.310000 +/- 0.000003
Signal in thin Window With Efficiency 307941176.5 +/- 3864757.4 231895734.6 +/- 741812.3 139905549 +/- 406587.1067 55985832.4 +/- 257137.3 23580645.2 +/- 87216.4 17719354.8 +/- 75603. 4 10877419.4 +/- 59235.6
Integrated Background with Efficiency 3877647.1 +/- 101177.5 3372857.1 +/- 60953.7 3804014.2 +/- 46990.42 584179.5 +/- 17709.6 465161.3 +/- 8451.6 274064.5 +/- 6387.1 13897.7 +/- 4516.1
Background Subtracted Signal 304063529.4 +/- 3866081.6 228522877.5 +/- 744312.3 136101534.8 +/- 409293.5 55401652.9 +/- 257746.4 23115483.9 +/- 87624.9 17445290.3 +/- 75872.7 10863521.7 +/- 59407.5
Runtime (s) 301.337 301.322 327.734 300.228 272.845 300.691 306.858
Rate (Hz) [math] 1.009048 \times 10^6 \pm 1.2829 \times 10^4 [/math] [math]7.58401 \times 10^5 \pm 2.470 \times 10^3[/math] [math] 4.15280 \times 10^5 \pm 1.248 \times 10^3 [/math] [math]1.84531 \times 10^5 \pm 8.58 \times 10^2 [/math] [math] 8.4720 \times 10^4 \pm 3.2115 \times 10^2[/math] [math] 5.8017 \times 10^4 \pm 2.5233 \times 10^2 [/math] [math] 3.5402 \times 10^4 \pm 1.9360 \times 10^2 [/math]
True Rate (Integral Method) (Hz) [math]1.040020 \times 10^6 \pm 1.3222 \times 10^4 [/math] [math] 7.81679 \times 10^5 \pm 2.5458 \times 10^3[/math] [math] 4.29155 \times 10^5 \pm 1.290 \times 10^3 [/math] [math] 1.90175 \times 10^5 \pm 8.8425 \times 10^2 [/math] [math] 8.7072 \times 10^4 \pm 3.29 \times 10^2 [/math] [math] 5.9793 \times 10^4 \pm 2.59 \times 10^2 [/math] [math] 3.6508 \times 10^4 \pm 2.00 \times 10^2 [/math]
Number of Entries in Histogram 566090 1015134 1428804 541498 984165 761238 494039
[math] \frac{Entries}{Runtime} [/math] 1878.59 3368.93 4359.64 1803.62 3607.05 2531.63 1609.99
Percent Dead 3.95 +/- 0.42 6.59 +/- 0.43 9.09 +/- 0.60 3.95 +/- 0.42 6.59 +/- 0.43 5.06 +/- 0.39 3.06 +/- 0.3
True Rate (Hz) [math] 1.082790 \times 10^6 \pm 1.4557 \times 10^4 [/math] [math] 8.36825 \times 10^5 \pm 4.764 \times 10^3 [/math] [math] 4.72065 \times 10^5 \pm 3.332 \times 10^3[/math] [math] 1.97995 \times 10^5 \pm 1.322 \times 10^3[/math] [math] 9.3214 \times 10^4 \pm 5.59 \times 10^2[/math] [math] 6.2979 \times 10^4 \pm 3.62 \times 10^2 [/math] [math] 3.7660 \times 10^4 \pm 2.33 \times 10^2 [/math]
Backtracked Signal (For Consistency)
.dat file entry 13.90 +/- 0.01 13.64 +/- 0.01 13.06 +/- 0.01 12.20 +/- 0.01 11.44 +/- 0.01 11.04 +/- 0.01 10.54 +/- 0.01

We can also trace these signals back in time to make sure that they somewhat match up with the previous signal that was seen.

Below is a plot that was made to help find the half life and the initial activity of the sample

170063 NickelFoil HLPlot DeadTimeCorrected.png

from here we can see that

[math] Slope = 5.63921 \times 10^{-6} \pm 1.75557 \times 10^{-8} [/math]

and the intercept is given by

[math] 13.9333 \pm 0.00643596 [/math]

By exponentiating the intercept, we can find the activity of the nickel foil at the time of the first measurement, which is

[math] 1.125007 \times 10^6 \pm 7.240 \times 10^3 [/math]

Now note that this measurement was taken 8 minutes after the selenium samples were measured. So we must correct the activity back 8 minutes.

[math] A_0 = 1.125007 \times 10^6 \times e^{5.40845 \times 10^{-6} \times 480} = 1.127931 \times 10^6 Hz [/math]

[math] \sigma_{A_0} = 7240 \times e^{5.40845 \times 10^{-6} \times 480} = 7258.82 Hz [/math]

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