LB Thesis Thin Window Analysis - Revision history

Brenleyt: /* Thin Window Histograms */

2018-01-10T19:25:27Z

Thin Window Histograms

2018-01-10T19:25:00Z

Thin Window Histograms

2017-12-14T06:56:36Z

Thin Method Applied

2017-12-14T06:56:02Z

Thin Method Applied

2017-12-14T03:50:35Z

2017-12-14T03:42:41Z

Decay During the Measurement

2017-12-14T03:41:59Z

Decay During the Measurement

2017-12-14T03:41:34Z

Decay During the Measurement

2017-12-14T03:39:29Z

Decay During the Measurement

2017-12-14T03:25:07Z

Decay During the Measurement

@@ Line 38: / Line 38: @@
 To find the error in the signal, expand the window by 1 channel on each side and subtract the stats box integrals from these 2 different windows. In other words the intrinsic error will be
-<math> \sigma_{I} = \frac{I-I_{Expanded}}{I} </math>
+<math> \sigma_{I} = \frac{I_{Expanded}-I}{I} </math>
 ==Dealing With Background==

@@ Line 36: / Line 36: @@
 <math> Stats Box Integral = I </math>
-Since this is a counting experiment, the error in the signal will be given by
+To find the error in the signal, expand the window by 1 channel on each side and subtract the stats box integrals from these 2 different windows. In other words the intrinsic error will be
-<math> \sigma_{I} = \sqrt{I} </math>
+<math> \sigma_{I} = \frac{I-I_{Expanded}}{I} </math>
 ==Dealing With Background==

@@ Line 213: / Line 213: @@
 Now we can find the error in the true number activity with the dead time accounted for (here DTC stands for dead time correction)
-<math> \sigma_{A_{True}} = \sqrt{DTC^2 \times \sigma_{A}^2 + A^2 \times \sigma_{DTC}^2} = \sqrt{1.03^2 \times 2.85^2 + 1901.88^2 \times 0.003^2} = 6.42 Hz </math>
+<math> \sigma_{A_{True}^{DT}} = \sqrt{\frac{\sigma_{A_{True}^{DT}}^2}{(1-DT)^2} + \frac{A_{True}^2 \sigma_{DT}^2}{(1-DT)^4}} </math>
 So the true signal accounting for dead time is

@@ Line 284: / Line 284: @@
 Now we can find the error in the true number activity with the dead time accounted for (here DTC stands for dead time correction)
+<math> \sigma_{A_{True}^{DT}} = \sqrt{\frac{\sigma_{A_{True}^{DT}}^2}{(1-DT)^2} + \frac{A_{True}^2 \sigma_{DT}^2}{(1-DT)^4}} </math>
 So the true signal accounting for dead time is

@@ Line 9: / Line 9: @@
 Inner Se Pellet: 0.0523g
-Half Life of Se-81: 57.28 Minutes
+Half Life of Se-81: 57.28 +/-  0.02 Minutes
-Decay Constant: <math> 2.016838863 \times 10^{-4} \frac{1}{seconds} </math>
+Decay Constant: <math> 2.016838863 \times 10^{-4} \pm 1.173672523 \times 10^{-9} \frac{1}{seconds} </math>
 ==Thin Window Histograms==

@@ Line 79: / Line 79: @@
 The error in this value is dominated by the error in the measured value, so the error in the true activity can be found by
-<math> \sigma_{A_{True}} = \sqrt{\frac{t\times e^{\lambda t} \times \lambda \times \sigma_{A_{Measure}}}{e^{\lambda t}-1} + \frac{e^{\lambda t}(A t e^{\lambda t} - \lambda^2 - A t + A t \lambda)}{(e^{\lambda t}-1)^2} \times \sigma_{\lambda}^2} </math>
+<math> \sigma_{A_{True}} = \sqrt{(\frac{t\times e^{\lambda t} \times \lambda \times \sigma_{A_{Measure}}}{e^{\lambda t}-1})^2 + \frac{e^{\lambda t}(A t e^{\lambda t} - \lambda^2 - A t + A t \lambda)}{(e^{\lambda t}-1)^2} \times \sigma_{\lambda}^2} </math>
 ==Dead Time==