Difference between revisions of "Se170063 Pure Se Wide Gauss Window Expansion"

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|| || 400 <t< 640 sec || 1100 < t < 1360 sec || 1875 < t < 2150 || 2650 < t < 2930 sec || 3400 < t < 3690 sec || 4120 < t < 4400 sec || 4840 < t < 5130 sec  
 
|| || 400 <t< 640 sec || 1100 < t < 1360 sec || 1875 < t < 2150 || 2650 < t < 2930 sec || 3400 < t < 3690 sec || 4120 < t < 4400 sec || 4840 < t < 5130 sec  
 
|-  
 
|-  
||Original Window Counts ||564700 ||536100 ||497100  ||432200 ||380500 ||319900
+
||Original Window Counts ||564700 ||536100 ||497100  ||432200 ||380500 ||319900 || 289400
 
|-
 
|-
|| Original Window Background (Integrated) ||  85711 || 86719 || 78500.2 ||73399.5 || 76327.6 || 61106.5
+
|| Original Window Background (Integrated) ||  85711 || 86719 || 78500.2 ||73399.5 || 76327.6 || 61106.5 || 57459.7
 
|-
 
|-
||Original Window Difference || 478989 || 449381 || 418599.8 || 358800.5 || 304172.4 || 243572.4
+
||Original Window Difference || 478989 || 449381 || 418599.8 || 358800.5 || 304172.4 || 243572.4 || 231940.3
 
|-
 
|-
||Expanded Window Counts ||587300 ||558100 || 517500 || 451400 ||398700 || 336000
+
||Expanded Window Counts ||587300 ||558100 || 517500 || 451400 ||398700 || 336000 ||304500
 
|-
 
|-
||Expanded Window Background ||  108563 || 108152 || 98915.2 ||92183.5 || 93245 || 77423.5
+
||Expanded Window Background ||  108563 || 108152 || 98915.2 ||92183.5 || 93245 || 77423.5 || 72660.2
 
|-
 
|-
||Expanded Window Difference ||478737  || 449948 || 418584.8 || 359216.5 || 305455 || 258576.5
+
||Expanded Window Difference ||478737  || 449948 || 418584.8 || 359216.5 || 305455 || 258576.5 || 231839.8
 
|-
 
|-
||Error in counts || 252* || 567 || 15* || 416 || 1282.6 ||15004.1 ||  
+
||Error in counts || 252* || 567 || 15* || 416 || 1282.6 ||15004.1 || 100.5 *
 
|-
 
|-
||.dat file entry || 7.598793988 +/- 0.0005261081152 || 7.454944728 +/- 0.0012617356 || 7.327899514 +/- 0.0000358337 || 7.1557322 +/- 0.0011594187 || 6.955469002 +/- 0.0042166876 || 6.768379905 +/- 0.0616001649
+
||.dat file entry || 7.598793988 +/- 0.0005261081152 || 7.454944728 +/- 0.0012617356 || 7.327899514 +/- 0.0000358337 || 7.1557322 +/- 0.0011594187 || 6.955469002 +/- 0.0042166876 || 6.768379905 +/- 0.0616001649 || 6.684354367 +/- 0.0004333011
 
|-
 
|-
 
|}
 
|}
 +
 +
 +
Using this method there seemed to be a problem with the background. When finding the error in the counts, sometimes the value was negative. Below is the example of the last timed run where 4840 < t < 5130
 +
 +
[[File:170063 NegativeCountError OGWindow.png|200px]]
 +
 +
Here you can see that the total number of counts in the window is 289400, while the integral of the background, which is found in the terminal is 57459.7. So we have a difference of 231940.3 counts. The expanded window is shown below.
 +
 +
[[File:170063 NegativeError ExpWindow.png||200px]]
 +
 +
Now here it is shown that the total number of counts within the window is 304500 counts, while on the terminal we can see that the integral of the background is 72660.2 counts, which gives a difference of 231839.8 counts. Subtracting these two numbers to find the error in the number of counts, we find that
 +
 +
<math> Expanded Counts - Original Counts = 231839.2 - 231940.3 = -100.8 counts </math>
 +
 +
This result is slightly troubling, but it did not occur in the ash + se sample at all. It seems that the macro may be overcompensating for the background.
 +
 +
Below is a plot of the activity vs. time to get the half life and initial activity
 +
 +
[[File:170063 WindowExp WideGauss PureSeHL.png|200px]]
 +
 +
The root window gives a slope of -0.000211997 +/- 1.3423e^-7. This gives us a half life of
 +
 +
54.49 +/- 0.03 Minutes
 +
 +
We can find the initial activity by using the constant value given, which is 7.72506 +/- 0.000255985.
 +
 +
<math> A_t = e^{7.72506} = 2264.39 Hz </math>
 +
 +
<math> \sigma_{A_t} =  e^{7.72506}*\sigma_{A_t} = 0.58 Hz </math>
 +
 +
Now we can correct for the efficiency, which will be the same factor as the mixed (which should cancel)
 +
 +
<math> A_{t'} = \frac{A_t}{\epsilon} = \frac{2264.39}{0.0070} = 323484.28 Hz </math>
 +
 +
while the error is
 +
 +
<math> \sigma_{A_{t'}} = \frac{A_t * \sigma_{\epsilon}}{\epsilon^2} = 508.33 Hz </math>
 +
 +
Now we must trace this signal back to t = 0 for the mixture (since that is what it will be compared to). The mixture was measured 400 seconds prior to the pure sample, which gives
 +
 +
<math> A_0 = A_{t'}*e^{\lambda*400} = 352112.00 Hz </math>
 +
 +
while the error is
 +
 +
<math> \sqrt{e^{2\lambda t}\sigma_{A_t}^2 + A_{t}^2t^2e^{2\lambda t}\sigma_{\lambda}^2 } = 553.64 Hz </math>

Latest revision as of 13:56, 26 October 2017

In this example I only weighted the histogram by the mass of the sample, which in the case of the pure selenium sample is 0.0971g.

400 <t< 640 sec 1100 < t < 1360 sec 1875 < t < 2150 2650 < t < 2930 sec 3400 < t < 3690 sec 4120 < t < 4400 sec 4840 < t < 5130 sec
Original Window Counts 564700 536100 497100 432200 380500 319900 289400
Original Window Background (Integrated) 85711 86719 78500.2 73399.5 76327.6 61106.5 57459.7
Original Window Difference 478989 449381 418599.8 358800.5 304172.4 243572.4 231940.3
Expanded Window Counts 587300 558100 517500 451400 398700 336000 304500
Expanded Window Background 108563 108152 98915.2 92183.5 93245 77423.5 72660.2
Expanded Window Difference 478737 449948 418584.8 359216.5 305455 258576.5 231839.8
Error in counts 252* 567 15* 416 1282.6 15004.1 100.5 *
.dat file entry 7.598793988 +/- 0.0005261081152 7.454944728 +/- 0.0012617356 7.327899514 +/- 0.0000358337 7.1557322 +/- 0.0011594187 6.955469002 +/- 0.0042166876 6.768379905 +/- 0.0616001649 6.684354367 +/- 0.0004333011


Using this method there seemed to be a problem with the background. When finding the error in the counts, sometimes the value was negative. Below is the example of the last timed run where 4840 < t < 5130

170063 NegativeCountError OGWindow.png

Here you can see that the total number of counts in the window is 289400, while the integral of the background, which is found in the terminal is 57459.7. So we have a difference of 231940.3 counts. The expanded window is shown below.

170063 NegativeError ExpWindow.png

Now here it is shown that the total number of counts within the window is 304500 counts, while on the terminal we can see that the integral of the background is 72660.2 counts, which gives a difference of 231839.8 counts. Subtracting these two numbers to find the error in the number of counts, we find that

[math] Expanded Counts - Original Counts = 231839.2 - 231940.3 = -100.8 counts [/math]

This result is slightly troubling, but it did not occur in the ash + se sample at all. It seems that the macro may be overcompensating for the background.

Below is a plot of the activity vs. time to get the half life and initial activity

170063 WindowExp WideGauss PureSeHL.png

The root window gives a slope of -0.000211997 +/- 1.3423e^-7. This gives us a half life of

54.49 +/- 0.03 Minutes

We can find the initial activity by using the constant value given, which is 7.72506 +/- 0.000255985.

[math] A_t = e^{7.72506} = 2264.39 Hz [/math]

[math] \sigma_{A_t} = e^{7.72506}*\sigma_{A_t} = 0.58 Hz [/math]

Now we can correct for the efficiency, which will be the same factor as the mixed (which should cancel)

[math] A_{t'} = \frac{A_t}{\epsilon} = \frac{2264.39}{0.0070} = 323484.28 Hz [/math]

while the error is

[math] \sigma_{A_{t'}} = \frac{A_t * \sigma_{\epsilon}}{\epsilon^2} = 508.33 Hz [/math]

Now we must trace this signal back to t = 0 for the mixture (since that is what it will be compared to). The mixture was measured 400 seconds prior to the pure sample, which gives

[math] A_0 = A_{t'}*e^{\lambda*400} = 352112.00 Hz [/math]

while the error is

[math] \sqrt{e^{2\lambda t}\sigma_{A_t}^2 + A_{t}^2t^2e^{2\lambda t}\sigma_{\lambda}^2 } = 553.64 Hz [/math]