Difference between revisions of "Se170063"

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=Sample Description=
 
=Sample Description=
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The sample was placed in an aluminum cylinder that was to be irradiated. The target components consisted of a nickel foil on the front of the cylinder with 2 pure selenium pellets under the foil, but still outside the cylinder. Inside the target there was burnt sagebrush ash, which was burned with a blowtorch, and selenium. Below are the masses of the components
+
The sample was placed in an aluminum cylinder that was to be irradiated. The target components consisted of a nickel foil on the front of the cylinder with 2 pure selenium pellets under the foil, but still outside the cylinder. Inside the target there was burnt sagebrush ash, which was place in an oven, and selenium. Below are the masses of the components
  
 
Nickel Foil: 0.2783g
 
Nickel Foil: 0.2783g
Line 18: Line 18:
 
The Calibration for Detector A was done on the morning of 5/23/17 with the MPA software using the thorium rods (as the calibration was fairly close already) and the correction values were found to be Det A Intercept = -12.208800 slope =1.021270
 
The Calibration for Detector A was done on the morning of 5/23/17 with the MPA software using the thorium rods (as the calibration was fairly close already) and the correction values were found to be Det A Intercept = -12.208800 slope =1.021270
  
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+
Se170063 Thin Window Analysis
 
=Efficiency=
 
=Efficiency=
  
Line 24: Line 24:
  
 
=Nickel Information=
 
=Nickel Information=
 +
 +
[[Se170063 Nickel Investigation]]
  
 
=Activity and Half Life=
 
=Activity and Half Life=
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The window used during this investigation was [110,118]. I used the script on daq1 /data/IAC/Se/May2017/5_25_17/Eff.C which fits lines of interest to a Gaussian function plus a constant. Once this function is found, the constant is integrated across the window of interested, then subtracted out of the original equation. After that the Gaussian is integrated across the window which gives the total number of counts for the peak of interest (in this case it is the 93 keV line of Se-81). To find the error in the counts, I increased the value for the standard deviation by a factor of 3 and integrated that function across the region of interest and subtracted that value from the original number of counts. Below is an example of a spectrum seen when using Eff.C
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[[Se170063 Activity And Half Life]]
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[[File:170063 SeSoilMix Spectrum.png|200px]]
 
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Once the raw number of counts and the error has been obtained, before entering the value into a .dat file a few modifications were made to that number. The first and simplest modification is to convert the number of counts into activity simply by dividing by the time duration of the measurement. In other words
 
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<math>A(t) = \frac{N(t)}{t} </math>
 
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Since the radioactive decay equation is given by
 
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−
<math>A(t) = A_0e^{-\lambda*t}</math>
 
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So to get a linear equation, simply take the natural log of both sides, which gives
 
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(1) <math>\ln{(A(t))} = \ln{(A_0)} - \lambda*t </math>
 
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So we take the natural log of the activity and input that value into the .dat file. To propagate the error we take the error in the number of counts and divide by the time to put the error in units of Hertz. After that, since we are taking the natural log, we must use the standard error propagation formula, which is given by
 
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(2) <math>\sigma_{\ln{A}} = \sqrt{(\frac{\partial \ln{A}}{\partial A})^2 * \sigma_A^2 } = \frac{1}{A}*\sigma_A = \frac{t}{N}*\frac{\sigma_N}{t} = \frac{\sigma_N}{N} </math>
 
  
 +
The method that has given the most acceptable results is given in [[Se170063 Thin Window Analysis]]
  
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Once the activity and its associated error have been computed, put the values into a .dat file with 3 columns. The first column is the time elapsed for the measurement, the second column is the natural log of the activity, and finally the third column is the associated error found as outlined above.
 
  
 +
Compare Rates between Two pure SE samples Irradiated at same time and measured using same detector with samples at the same location
  
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Once the .dat file has been created, simply change the script /data/IAC/Se/May2017/5_25_17/LB_WeightedFit.C to read in the new .dat file and run the script on ROOT. Doing so will give a plot such as the one below
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[[Se_5-25-17-RateCompare_OuterSe]]
  
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[[File:170063 PureSe HalfLife Plot.png|200px]]
+
=Alternative Method=
  
 +
[[Se170063 Activity and HL Alternate]]
  
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This plot gives parameters of the linear equation (1). The next step in the process is to find the half life of the sample. To do so recall that
+
=Corrected Alternative method=
 +
The files used for this analysis are in the directory /data/IAC/Se/May2017/5_25_17/Se_Activity_SysOffset_Mix
  
−
<math> t_{\frac{1}{2}} = \frac{\ln{2}}{\lambda} = \frac{\ln{2}}{0.000207} = 3,348.54  Seconds \rightarrow 55.8090  Minutes </math>
+
To begin, I have corrected the mixture to have a factor of 0.62, which is the mystery factor throwing of all of these analyses. The histogram is also weighted by the mass. The weight added to the histogram is
  
 +
<math> h1 -> Fill(evt.Chan,\frac{1}{0.0523*0.62}) </math>
  
−
Now we must propagate the error in the half life. Even though the error in the decay constant says that it is zero in the plot, by looking at the root output, it can be seen that the error is actually
+
So the true number of counts has indeed been weighted here. Now I want to try to test every different method that was suggested. So first I am going to weight the mixture by the mystery factor of 0.62, and leave my Gaussian fits as wide as they were previously. The gaussians will probably be made more compact if the mystery factor does not alleviate the problem. The first step is to find the number of counts within the window of interest. Below is the process I used to determine the number of counts and the error associated with it. First begin by plotting the histogram using the ROOT program Eff.C, which is shown below.
  
−
<math> 5.91816*10^{-9} s^{-1} </math> (See if this can be fixed)
+
[[File:170063 Spec Weighted.png|200px]]
  
−
To propagate the error, use the standard propagation of error formula
+
Now take the integral given in the stats box and subtract the background to get the number of counts. Here the number of counts would be
  
−
<math> \sigma_{t_{\frac{1}{2}}} = \sqrt{(\frac{\partial t_{\frac{1}{2}}}{\partial \lambda})^2 * \sigma_\lambda ^2} = \frac{\ln{2}}{\lambda^2}*\sigma_\lambda = 0.095446 s^{-1} \rightarrow 0.001591  Minutes^{-1}</math>
+
<math> 927800 - 47670 = 880130  Counts </math>
  
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which gives us a half life of
+
Now I can convert this error into an activity by dividing by the time, which is 300 seconds in this case. After that take the natural log of the quotient.
  
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<math> t_{\frac{1}{2}} = 55.8090 \pm 0.0016 </math> Minutes
+
<math> \ln{\frac{880130}{300}} = 7.984042428 </math>
  
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The accepted value of the half life of Se-81 is  
+
Now to find the error we can notice that the standard deviation here is 0.6238. The procedure is to expand the window by one or two standard deviations and find the difference in the number of counts in the original window. Due to the binning here I have decided to expand the window by 1 channel on each side, which is roughly 2 standard deviations. A picture is given below.
  
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<math> 57.28 \pm 0.02 Minutes </math>
+
[[File:170063 Spec ExpandedWindow.png|200px]]
  
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Note that these two values do not overlap. This means that there could be some systematic error within the measurement systems.
+
Now we do a similar method to find the number of counts within this window.
  
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Now, to find the activity of the sample when it was measured, we use the other parameter given by ROOT. Note that the value given is
+
<math> 1017000 - 46810 = 970190 Counts </math>
  
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<math> \ln{A_{measure}} </math>
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Now take the difference between the original window's number of counts and the expanded window's number of counts.
  
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This means we must exponentiate to get the initial activity parameter to continue
+
<math> 970190 - 880130 = 90060 Counts </math>
  
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<math> e^{\ln{A_{measure}}} = e^{5.34637} = 209.845 Hz </math>
+
Now to propagate this error we must divide this number by the original number of counts.
  
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The associated error to the activity at the time of measurement can be found as well. Since we are exponentiating and the exponential function is its own derivative, the error can be written as
+
<math> \frac{90060}{880130} = 0.1023257928 </math>
  
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<math> \sigma_{A_t} = e^{\ln{A_t}}*\sigma_{\ln{A_t}} = 0.003 Hz </math>
+
This method was repeated for the next set of runs that make the data file. The numbers are in a table below.
  
 +
{| border="3"  cellpadding="5" cellspacing="0"
 +
|| || 0 <t< 300 sec || 730 < t < 1020 sec || 1480 < t < 1775 || 2250 < t < 2550 sec || 3050 < t < 3300 sec || 3775 < t < 4050 sec || 4480 < t < 4770 sec
 +
|-
 +
||Original Window Counts ||  880200 || 716200 ||617100 || 545800 ||394100 || 362000 || 346300
 +
|-
 +
|| Original Window Background (Integrated) || 381379 ||  267608 || 215260 || 189665 || 143921 || 137541 || 128197
 +
|-
 +
||Original Window Difference || 498821 || 448592 || 401850 || 356135|| 250179 || 224459 || 218103
 +
|-
 +
||Expanded Window Counts || 970900 || 782600 || 671300 || 593100 || 426700 ||395400 ||378100
 +
|-
 +
||Expanded Window Background || 468138 || 333633 || 269025 || 236476 || 173353 ||170089 || 159644
 +
|-
 +
||Expanded Window Difference || 502762 || 448967 || 402275 || 356624 ||253347 || 225311 || 218456
 +
|-
 +
||Error in counts || 3941 || 375 || 425 || 489 || 3168 || 852 || 353 ||
 +
|-
 +
||.dat file entry ||  7.416220118 +/- 0.0079006297 || 7.343988145 +/- 0.0008359489264 || 7.216858801 +/- 0.0010576086 || 7.079282677 +/- 0.0013730748 || 6.908471023 +/- 0.012662933 || 6.704677244 +/- 0.0037957934 || 6.622841784 +/- 0.0016185014
 +
|-
 +
|}
  
−
which means that the activity of the Pure Selenium sample at the beginning of the measurement was
+
Below is the graph that contains the information about the initial activity and the half life
  
−
<math>A_t = 209.845 \pm 0.003 Hz </math>
+
[[File:170063 WindowExpand WideGauss HLPlot.png|200px]]
  
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Now note that the pure sample was measured second in the split run file. This means that the activity at the beginning of the measurement must be backtracked to when the mixture of ash and selenium was measured, which was 400 seconds prior. To do this, solve the radioactive decay equation for the initial activity.
+
The slope of the line is -0.00019198 +/- 4.13511e^-7, which gives a half life of
  
−
<math> A_0 = A_t*e^{\lambda*t} = (209.845)*e^{0.00207*400} = 227.960 Hz </math>
+
<math> t_{\frac{1}{2}} = \frac{\ln{2}}{\lambda}\rightarrow 60.18 minutes </math>
  
 +
While the error is
  
−
Now to propagate the error using the standard error propagation formula using 0.5 seconds for the uncertainty in the time.
+
<math> \sigma_{t_{\frac{1}{2}}} = \frac{\ln{2}*\sigma_{\lambda}}{\lambda^2} \rightarrow 0.13 minutes </math>
  
−
<math> \sigma_{A_0} = \sqrt{(\frac{\partial A_0}{\partial A_t})^2\sigma_{A_t}^2 + (\frac{\partial A_0}{\lambda})^2\sigma_{\lambda}^2 + (\frac{\partial A_0}{\partial t})^2\sigma_{t}} = \sqrt{e^{2\lambda t}\sigma_{A_t}^2 + A_{t}^2t^2e^{2\lambda t}\sigma_{\lambda}^2 + A_t^2\lambda^2e^{2\lambda t}\sigma_t^2}  = \sqrt{1.06209\times 10^{-5} + 2.91212 \times 10^{-7} + 5.56669 \times 10^{-4} } = 0.024 </math>
+
The constant value given by the plot is 7.4918 +/- 0.000927611, which gives an initial activity of
  
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Which means that the activity of the Pure selenium sample, corrected to be the activity at the same time that the mixture was measure is
+
<math> A_0 = e^{7.4918} = 1793.28 Hz </math>
  
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<math>A_0 = 227.960 \pm 0.024 Hz </math>
+
and an error of
  
 +
<math> e^{7.4918}*\sigma_{A} = 1.66 Hz </math>
  
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Now moving on to the Se-Torch Ash mixture, we can apply a similar analysis to find the initial activity.
+
Now correcting for the efficiency we have
  
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Below is the plot for the half life of the mixture
+
<math> A_0^' = \frac{A_0}{\epsilon} = \frac{1793.28}{0.007} = 256182.8571 Hz </math>
  
−
[[File:170063 Mix HalfLifePlot.png|200px]]
+
While the error is
  
−
Now to find the half life use
+
<math> \sigma_{A_0^'} = \frac{A_0}{\epsilon^2}*\sigma_{\epsilon} = 402.57 Hz </math>
  
−
<math> t_{\frac{1}{2}} = \frac{\ln{2}}{\lambda} = \frac{\ln{2}}{0.000181} = 3829.54  Seconds \rightarrow 63.8257  Minutes </math>
+
Below are the related pages for this sample using this method of window expansion:
  
−
Propagating the error in the half life gives
+
[[Se170063 Nickel Foil Wide Gauss Window Expansion]]
  
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<math> \sigma_{t_{\frac{1}{2}}} = \sqrt{(\frac{\partial t_{\frac{1}{2}}}{\partial \lambda})^2 * \sigma_\lambda ^2} = \frac{\ln{2}}{\lambda^2}*\sigma_\lambda = 0.2397 s^{-1} \rightarrow 0.004  Minutes^{-1}</math>
+
[[Se170063 Pure Se Wide Gauss Window Expansion]]
  
 
=Runlist=
 
=Runlist=

Latest revision as of 17:54, 9 November 2017

PAA_Selenium/Soil_Experiments#Selenium_Sample_Analysis

Sample Description

The sample was placed in an aluminum cylinder that was to be irradiated. The target components consisted of a nickel foil on the front of the cylinder with 2 pure selenium pellets under the foil, but still outside the cylinder. Inside the target there was burnt sagebrush ash, which was place in an oven, and selenium. Below are the masses of the components

Nickel Foil: 0.2783g

Outer Se Pellets: 0.0971g

Sage Ash: 0.5111g

Inner Se Pellets: 0.0523g

Energy

LB May Calibration 2017

The Calibration for Detector A was done on the morning of 5/23/17 with the MPA software using the thorium rods (as the calibration was fairly close already) and the correction values were found to be Det A Intercept = -12.208800 slope =1.021270

Se170063 Thin Window Analysis

Efficiency

LB May 2017 Det A Efficiency

Nickel Information

Se170063 Nickel Investigation

Activity and Half Life

Se170063 Activity And Half Life

The method that has given the most acceptable results is given in Se170063 Thin Window Analysis


Compare Rates between Two pure SE samples Irradiated at same time and measured using same detector with samples at the same location

Se_5-25-17-RateCompare_OuterSe

Alternative Method

Se170063 Activity and HL Alternate

Corrected Alternative method

The files used for this analysis are in the directory /data/IAC/Se/May2017/5_25_17/Se_Activity_SysOffset_Mix

To begin, I have corrected the mixture to have a factor of 0.62, which is the mystery factor throwing of all of these analyses. The histogram is also weighted by the mass. The weight added to the histogram is

[math] h1 -\gt Fill(evt.Chan,\frac{1}{0.0523*0.62}) [/math]

So the true number of counts has indeed been weighted here. Now I want to try to test every different method that was suggested. So first I am going to weight the mixture by the mystery factor of 0.62, and leave my Gaussian fits as wide as they were previously. The gaussians will probably be made more compact if the mystery factor does not alleviate the problem. The first step is to find the number of counts within the window of interest. Below is the process I used to determine the number of counts and the error associated with it. First begin by plotting the histogram using the ROOT program Eff.C, which is shown below.

170063 Spec Weighted.png

Now take the integral given in the stats box and subtract the background to get the number of counts. Here the number of counts would be

[math] 927800 - 47670 = 880130 Counts [/math]

Now I can convert this error into an activity by dividing by the time, which is 300 seconds in this case. After that take the natural log of the quotient.

[math] \ln{\frac{880130}{300}} = 7.984042428 [/math]

Now to find the error we can notice that the standard deviation here is 0.6238. The procedure is to expand the window by one or two standard deviations and find the difference in the number of counts in the original window. Due to the binning here I have decided to expand the window by 1 channel on each side, which is roughly 2 standard deviations. A picture is given below.

170063 Spec ExpandedWindow.png

Now we do a similar method to find the number of counts within this window.

[math] 1017000 - 46810 = 970190 Counts [/math]

Now take the difference between the original window's number of counts and the expanded window's number of counts.

[math] 970190 - 880130 = 90060 Counts [/math]

Now to propagate this error we must divide this number by the original number of counts.

[math] \frac{90060}{880130} = 0.1023257928 [/math]

This method was repeated for the next set of runs that make the data file. The numbers are in a table below.

0 <t< 300 sec 730 < t < 1020 sec 1480 < t < 1775 2250 < t < 2550 sec 3050 < t < 3300 sec 3775 < t < 4050 sec 4480 < t < 4770 sec
Original Window Counts 880200 716200 617100 545800 394100 362000 346300
Original Window Background (Integrated) 381379 267608 215260 189665 143921 137541 128197
Original Window Difference 498821 448592 401850 356135 250179 224459 218103
Expanded Window Counts 970900 782600 671300 593100 426700 395400 378100
Expanded Window Background 468138 333633 269025 236476 173353 170089 159644
Expanded Window Difference 502762 448967 402275 356624 253347 225311 218456
Error in counts 3941 375 425 489 3168 852 353
.dat file entry 7.416220118 +/- 0.0079006297 7.343988145 +/- 0.0008359489264 7.216858801 +/- 0.0010576086 7.079282677 +/- 0.0013730748 6.908471023 +/- 0.012662933 6.704677244 +/- 0.0037957934 6.622841784 +/- 0.0016185014

Below is the graph that contains the information about the initial activity and the half life

170063 WindowExpand WideGauss HLPlot.png

The slope of the line is -0.00019198 +/- 4.13511e^-7, which gives a half life of

[math] t_{\frac{1}{2}} = \frac{\ln{2}}{\lambda}\rightarrow 60.18 minutes [/math]

While the error is

[math] \sigma_{t_{\frac{1}{2}}} = \frac{\ln{2}*\sigma_{\lambda}}{\lambda^2} \rightarrow 0.13 minutes [/math]

The constant value given by the plot is 7.4918 +/- 0.000927611, which gives an initial activity of

[math] A_0 = e^{7.4918} = 1793.28 Hz [/math]

and an error of

[math] e^{7.4918}*\sigma_{A} = 1.66 Hz [/math]

Now correcting for the efficiency we have

[math] A_0^' = \frac{A_0}{\epsilon} = \frac{1793.28}{0.007} = 256182.8571 Hz [/math]

While the error is

[math] \sigma_{A_0^'} = \frac{A_0}{\epsilon^2}*\sigma_{\epsilon} = 402.57 Hz [/math]

Below are the related pages for this sample using this method of window expansion:

Se170063 Nickel Foil Wide Gauss Window Expansion

Se170063 Pure Se Wide Gauss Window Expansion

Runlist

Table with dates and filename and locations on daq1

LB_May_2017_Irradiation_Day#10.25_Se_Soil_Mix

PAA_Selenium/Soil_Experiments#Selenium_Sample_Analysis

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