Difference between revisions of "LB DetLimits Thesis"

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The detection limit was found by using "fixed fit" activity values (half life curves with the slope forced to be the accepted half life) and its associated error (|Data Fit - Fixed Fit|). Once those values have been found, then an average value was taken between irradiations with similar beam times. Normalization constants were found for the two averaged values for the activity by computing
 
The detection limit was found by using "fixed fit" activity values (half life curves with the slope forced to be the accepted half life) and its associated error (|Data Fit - Fixed Fit|). Once those values have been found, then an average value was taken between irradiations with similar beam times. Normalization constants were found for the two averaged values for the activity by computing
  
−
<math> Normalization = \frac{A_{Avg}}{A_{Measured}} </math>  
+
<math> Normalization = \frac{A_{Avg}}{A_{Fixed}} </math>  
  
 
Once the average was found, the next step was to normalize the activities to the longest beam time with
 
Once the average was found, the next step was to normalize the activities to the longest beam time with
  
−
<math> A_{t_{Norm}} = A_{Measured} \times \frac{(1-e^{-\lambda_{el} \times t_{Norm}})}{(1-e^{-\lambda \times t_{irr}})} </math>
+
<math> A_{t_{Norm}} = A_{Fixed} \times \frac{(1-e^{-\lambda_{el} \times t_{Norm}})}{(1-e^{-\lambda \times t_{irr}})} </math>
  
 
Where <math> t_{Norm} </math> is the longest irradiation time and <math> t_{irr} </math> is the actual irradiation time.
 
Where <math> t_{Norm} </math> is the longest irradiation time and <math> t_{irr} </math> is the actual irradiation time.

Revision as of 02:15, 26 July 2018

Analysis

The detection limit was found by using "fixed fit" activity values (half life curves with the slope forced to be the accepted half life) and its associated error (|Data Fit - Fixed Fit|). Once those values have been found, then an average value was taken between irradiations with similar beam times. Normalization constants were found for the two averaged values for the activity by computing

[math] Normalization = \frac{A_{Avg}}{A_{Fixed}} [/math]

Once the average was found, the next step was to normalize the activities to the longest beam time with

[math] A_{t_{Norm}} = A_{Fixed} \times \frac{(1-e^{-\lambda_{el} \times t_{Norm}})}{(1-e^{-\lambda \times t_{irr}})} [/math]

Where [math] t_{Norm} [/math] is the longest irradiation time and [math] t_{irr} [/math] is the actual irradiation time.

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