Difference between revisions of "A W thesis old"

From New IAC Wiki
Jump to navigation Jump to search
Line 149: Line 149:
  
  
−
====Error analysis====
+
=Error analysis=
  
 
'''Half-life'''
 
'''Half-life'''

Revision as of 18:50, 9 September 2014

898 keV signal table

[math]\sigma_Cut[/math]

[math]T_{1/2}[/math] Trig Signal BackG Subtracted Fit Parameters Signal Area Noise Area SNR
0.44 coin Run6980 898 raw.png Run6980 898 sub.png [math]\mu=[/math] 895.744 +/- 5.774e-4 [math]\sigma=[/math] 0.8189 +/- 0.0034 A= 0.0097 +/- 0.0013 B= 4.891e-9 +/- 6.707e-9 C= 2.543e-5 +/- 1.053e-4 0.0217 +/- 6.383e-4 4.643e-4 +/- 5.804e-5 46.678 +/- 0.0124
0.98 sing Run7022 898 raw.png Run7022 898 sub.png [math]\mu=[/math] 897.255 +/- 0.0047 [math]\sigma=[/math] 0.7277 +/- 0.0280 A=0.7027 +/- 0.0129 B= 8.448e-4+/- 4.457e-5 C=-0.7355 +/- 0.0408 1.2938 +/- 0.0381 0.3123 +/- 0.0390 4.143 +/- 0.6977
coin Run7023 898 raw1.png Run7023 898 sub1.png [math]\mu=[/math] 896.818 +/- 0.0075 [math]\sigma=[/math] 0.9856 +/- 0.0276 A= 0.0020 +/- 2.036e-5 B= 1.263e-8 +/- 7.797e-10 C= 1.095e-5 +/- 5.103e-7 0.0049 +/- 1.446e-4 9.518e-5 +/- 1.190e-5 51.591 +/- 0.0036
1.46 sing Run7107 898 raw.png Run7107 898 sub.png [math]\mu=[/math] 897.663 +/- 0.00987 [math]\sigma=[/math] 0.8348 +/- 0.0580 A=0.3925 +/- 0.1107 B=-2.696e-4 +/- 2.725e-7 C= 0.2633 +/- 1.939e-4 1.075 +/- 0.0316 0.0777 +/- 0.0097 13.827 +/- 0.3763
coin Run7108 898 raw.png Run7108 898 sub.png [math]\mu=[/math] 897.780 +/- 0.0025 [math]\sigma=[/math] 0.9737 +/- 0.0186 A= 1.679e-3 +/- 5.996e-7 B= 1.217e-8 +/- 7.211e-11 C= 1.098e-5 +/- 2.962e-8 3.987e-3 +/- 1.174e-4 8.732e-5 +/- 1.092e-5 45.661 +/- 0.0030
2.12 sing Run7203 898 raw.png Run7203 898 sub.png [math]\mu=[/math] 894.701 +/- 0.0127 [math]\sigma=[/math] 0.6371 +/- 0.0569 A=0.3740 +/- 6.200e-5 B= 8.285e-5+/- 4.503e-8 C=-0.0482+/- 5.103e-7 0.6212 +/- 0.0183 0.0723 +/- 0.0090 8.588 +/- 0.3858
coin Run7204 898 raw.png Run7204 898 sub.png [math]\mu=[/math] 890.896 +/- 0.0144 [math]\sigma=[/math] 1.137 +/- 0.0056 A= 7.293e-4 +/- 8.083e-9 B= 8.441e-7 +/- 6.284e-11 C= -7.342e-4 +/- 2.106e-7 0.00199 +/- 5.872e-5 8.296e-5 +/- 1.037e-5 24.032 +/- 0.0015
2.27 sing Run7235 898 raw2.png Run7235 898 sub2.png [math]\mu=[/math] 903.478 +/- 0.0064 [math]\sigma=[/math] 0.7121 +/-0.0877 A=0.2929 +/- 2.373e-4 B= -7.136e-4+/- 1.414e-9 C= 0.6715 +/- 1.777e-4 0.5609+/- 0.0165 0.0862 +/- 0.0108 6.505 +/- 0.3063
coin Run7236 898 raw.png Run7236 898 sub.png [math]\mu=[/math] 905.932 +/- 0.0050 [math]\sigma=[/math] 0.8066 +/- 0.0236 A= 5.888e-4 +/- 2.063e-7 B= 1.238e-6 +/- 4.497e-10 C= -1.106e-3 +/- 4.701e-7 1.170e-3 +/- 3.446e-5 5.310e-5 +/- 6.638e-6 22.033 +/- 8.137e-4


Re-Fit of Run 7203 without Event Cuts

[math]T_{1/2}[/math] Trig Signal BackG Subtracted Fit Parameters Signal Area Noise Area SNR
2.12 sing Run7203 898 raw nocut.png Run7203 898 sub nocut.png [math]\mu=[/math] 894.859 +/- 0.0377 [math]\sigma=[/math] 0.8294 +/- 0.0389 A= 0.1064 +/- 1.281e-4 B=4.131e-4 +/- 3e-9 C= -0.3439 +/- 1.047e-4 0.2214 +/- 0.0065 0.0900 +/- 0.0113 2.459 +/- 0.0082


Re-Fit of Run 7203 without Event Cuts and Scaled by 1.66

[math]T_{1/2}[/math] Trig Signal BackG Subtracted Fit Parameters Signal Area Noise Area SNR
2.12 sing Run7203 898 raw ratio3.png Run7203 898 sub ratio3.png [math]\mu=[/math] 894.901 +/- 0.0878 [math]\sigma=[/math] 0.8380 +/- 0.0389 A= 0.1774 +/- 4.505e-4 B=4.931e-5 +/- 9.842e-7 C= -2.231e-3 +/- 9.027e-4 0.3731 +/- 0.0110 0.1532 +/- 0.0192 2.435 +/- 0.1543



Signal, Noise, and Signal to Noise Ratio plots for 898 keV singles runs.

S N SNR 898 singles2.png SNR 898 singles2.png

Averaging over the last three noise values:

S N SNR 898 singles avg2.png SNR 898 singles avg2.png

Signal, Noise, and Signal to Noise Ratio plots for 898 keV coincidence runs.


S N SNR 898 coin.png SNR 898 coin.png

Averaging over the noise values:

S N SNR 898 coin avg.png SNR 898 coin avg.png

Signal to Noise Ratio (Singles and Coincidence): SNR 898 both.png

SNR 898 both2.png


1836 keV signal table

1836.1 keV Signal Table

[math]T_{1/2}[/math] Trig Signal BackG Subtracted Fit Parameters Signal Area Noise Area SNR
0.44 coin Run6980 1836 raw.png Run6980 1836 sub.png [math]\mu=[/math] 1833.43 +/- 0.0058 [math]\sigma=[/math] 1.447 +/- 0.0228 A= 0.0036 +/- 5.937e-7 B= 1.129e-6 +/- 9.991e-10 C=-2.041e-3 +/- 1.682e-6 0.0127 +/- 3.752e-4 1.937e-4 +/- 2.421e-5 65.781 +/- 0.0096
0.98 sing Run7022 1836 raw1.png Run7022 1836 sub.png [math]\mu=[/math] 1837.7 +/- 0.02 [math]\sigma=[/math] 1.126 +/- 0.0264 A=0.3115 +/- 9.318e-6 B=3.759e-5 +/- 2.793e-7 C=-6.575e-2 +/- 5.102e-4 0.8590 +/- 0.0253 0.0200 +/- 0.0025 42.920 +/- 0.6349
coin Run7023 1836 raw.png Run7023 1836 sub.png [math]\mu=[/math] 1835.86 +/- 0.01 [math]\sigma=[/math] 1.406 +/- 0.0201 A= 0.0018 +/- 2.541e-7 B= 4.930e-9 +/- 5.263e-11 C= 8.945e-6 +/- 8.814e-8 0.0063 +/- 1.853e-4 1.037e-4 +/- 1.297e-5 60.662 +/- 0.0047
1.46 sing Run7107 1836 raw.png Run7107 1836 sub.png [math]\mu=[/math]1838.65 +/- 0.0436 [math]\sigma=[/math] 1.117 +/- 0.0569 A=0.1757 +/- 3.782e-5 B=2.046e-4 +/- 1.5e-9 C=-3.713e-1 +/- 4.940e-5 0.4933 +/- 0.0145 0.0234 +/- 0.0029 21.115 +/- 0.3456
coin Run7108 1836 raw.png Run7108 1836 sub.png [math]\mu=[/math] 1838.003 +/- 0.0115 [math]\sigma=[/math] 1.854 +/- 0.0242 A= 9.717e-4 +/- 4.374e-7 B= 7.051e-7 +/- 1.119e-10 C=-1.291e-3 +/- 1.738e-7 0.0044+/- 1.286e-4 4.248e-5 +/- 5.309e-6 102.838 +/- 0.0033
2.12 sing Run7203 1836 raw.png Run7203 1836 sub.png [math]\mu=[/math] 1831.333 +/- 0.2887 [math]\sigma=[/math] 0.5219 +/- 0.0555 A= 0.1601+/- 1.321e-4 B=-1.429e-6 +/- 1.565e-10 C=2.260e-2 +/- 5.944e-7 0.2214 +/- 0.0065 0.0462 +/- 0.0058 4.796 +/- 0.1192
coin Run7204 1836 raw.png Run7204 1836 sub.png [math]\mu=[/math] 1824.26 +/- 0.0153 [math]\sigma=[/math] 1.570 +/- 0.0871 A= 5.842e-4 +/- 1.552e-5 B= -7.557e-7 +/- 6.718e-11 C= 1.405e-3 +/- 1.754e-7 0.0024 +/- 7.002e-5 1.802e-4 +/- 2.252e-5 13.198 +/- 0.0016
2.27 sing Run7235 1836 raw.png Run7235 1836 sub.png [math]\mu=[/math] 1850.08 +/- 0.0361 [math]\sigma=[/math] 1.238 +/- 0.1486 A=0.0741 +/- 3.058e-4 B=4.389e-4 +/- 5.774e-10 C=-8.040e-1 +/- 1.270e-4 0.2471+/- 0.0073 0.0451 +/- 0.0056 5.478 +/- 0.1354
coin Run7236 1836 raw.png Run7236 1836 sub.png [math]\mu=[/math] 1854.58 +/- 0.1587 [math]\sigma=[/math] 1.696+/- 0.1625 A= 3.873e-4 +/- 8.569e-7 B= -9.482e-7 +/- 7.143e-11 C= 0.0018 +/-3.216e-7 0.0017 +/- 5.083e-5 1.623e-5 +/- 2.028e-6 106.360 +/- 0.0012


Re-Fit of Run 7203 without Event Cuts

[math]T_{1/2}[/math] Trig Signal BackG Subtracted Fit Parameters Signal Area Noise Area SNR
2.12 sing Run7203 1836 raw nocut.png Run7203 1836 sub nocut.png [math]\mu=[/math]1831.55 +/- 1.74 [math]\sigma=[/math]0.6455 +/- 0.0693 A= 0.0658 +/- 0.0007 B= 7.775e-6+/- 1.615e-7 C= -7.311e-3 +/- 2.991e-4 0.1139 +/- 0.0034 0.0216 +/- 0.0027 5.282 +/- 0.0598



Re-Fit of Run 7236 without Event Cuts

[math]T_{1/2}[/math] Trig Signal BackG Subtracted Fit Parameters Signal Area Noise Area SNR
2.12 sing Run7236 1836 raw nocut.png Run7236 1836 sub nocut.png [math]\mu=[/math] 1860.48 +/- 0.0874 [math]\sigma=[/math]7.160 +/- 0.5751 A= 7.067e-5 +/- 1.151e-6 B= 8.389e-9+/- 1.764e-8 C= -1.293e-5 +/- 3.280e-5 0.0013 +/- 3.914e-5 0.0021 +/- 0.0003 0.6289 +/- 0.0007


Signal, Noise, and Signal to Noise Ratio plots for 1836 keV singles runs.

S N SNR 1836 singles.png SNR 1836 singles.png

Signal, Noise, and Signal to Noise Ratio plots for 1836 keV coincidence runs.

S N SNR 1836 coin.png SNR 1836 coin.png

Averaging over the noise values:

S N SNR 1836 coin avg.png SNR 1836 coin avg.png

Signal to Noise Ratio (Singles and Coincidence): SNR 1836 both.png



Error analysis

Half-life

898 keV Singles

Days [math]T_{1/2}[/math] Trig Energy Window Energy Calibration Linear Fit of Background Gaussian Integration of Signal Total Systematic Error
105 0.98 sing [math]\pm 0.1364[/math] [math] {+0.014} \atop { -0.025}[/math] [math] {+0.2468} \atop { -0.0025}[/math] [math]\pm 0.07[/math] [math] {+0.2974} \atop { -0.1759}[/math]
156 1.46 sing [math]\pm 0.2308[/math] [math] {+0.0071} \atop { -0.0212}[/math] [math] {+0.0065} \atop { -0.0063}[/math] [math] {+0.2908} \atop { -0.2601}[/math] [math] {+0.3758} \atop { -0.3622}[/math]
226 2.12 sing [math]\pm 0.1763[/math] [math] {+0.0562} \atop { -0.0774}[/math] [math] {+0.0128} \atop { -0.0122}[/math] [math]\pm 0.0174[/math] [math] {+0.2335} \atop { -0.2546}[/math]
242 2.27 sing [math]\pm 0.1326[/math] [math] {+0.0246} \atop { -0.0697}[/math] [math]\pm 0.01[/math] [math]\pm 0.062[/math] [math] {+0.1693} \atop { -0.2118}[/math]

898 keV Coincidence

Days [math]T_{1/2}[/math] Trig Energy Window Energy Calibration Linear Fit of Background Gaussian Integration of Signal Coincidence Energy Total Systematic Error
105 0.98 coin +/- 7.042e-4 [math] {+1.6e-5} \atop { -6.3e-5}[/math] + 7.358e-6, -7.092e-6 +/- 0.00018
156 1.46 coin +/- 6.383e-4 [math] {+1.5e-5} \atop { -1.3e-5}[/math] +2.004e-6, -1.990e-6 + 7.611e-5, -7.605e-5
226 2.21 coin +/- 6.912e-4 [math] {+2.0e-5} \atop { -5.9e-5}[/math] +8.041e-6, -7.859e-6 +/- 0.00013
242 2.27 coin +/- 2.179e-4 [math] {+2.0e-6} \atop { -4e-6}[/math] +4.436e-6, -4.365e-6 +/- 1.078e-5


1836.1 keV Singles

Days [math]T_{1/2}[/math] Trig Energy Window Energy Calibration Linear Fit of Background Gaussian Integration of Signal Total Systematic Error
105 0.98 sing [math]\pm 0.0991[/math] [math]\pm 0.0028[/math] [math] {+0.0051} \atop { -0.0049}[/math] [math]\pm 0.0197[/math] [math]\pm 0.1039[/math]
156 1.46 sing [math]\pm 0.0352[/math] [math] {+0.0141} \atop { -0.0071}[/math] [math] {+2.51e-6} \atop { -2.48e-6}[/math] [math]\pm 0.0240[/math] [math] {+0.0548} \atop { -0.0586}[/math]
226 2.12 sing [math]\pm 0.0571[/math] [math] {+0.0122} \atop { -0.0244}[/math] [math] {+0.0092} \atop { -0.0085}[/math] [math] {+0.0321} \atop { -0.0320}[/math] [math] {+0.0769} \atop { -0.0880}[/math]
242 2.27 sing [math]\pm 0.0480[/math] [math]\pm 0.0041[/math] [math] {+0.0055} \atop { -0.0054}[/math] [math] {+0.027} \atop { -0.0272}[/math] [math]\pm 0.059[/math]


1836.1 keV Coincidence

Days [math]T_{1/2}[/math] Trig Energy Window Energy Calibration Linear Fit of Background Gaussian Integration of Signal Coincidence Energy Cut Total Systematic Error
105 0.98 coin +/- 5.105e-4 [math] {+7.9e-5} \atop { -3.1e-5}[/math] +2.505e-6, -2.475e-6 +/- 8.97e-5
156 1.46 coin +/- 6.325e-4 [math] {+2.4e-5} \atop { -3.7e-5}[/math] +3.422e-6, -3.347e-6 +/-5.83e-5
226 2.12 coin
242 2.27 coin +/- 2.166e-4 [math] {+2.0e-6} \atop { -3e-6}[/math] +0.0020, -6.179e-6 +/-0.00012

=other

Run7204 Y88 898 signalnoise.png Run7204 Y88 898 signal.png

Run7235 Y88 898 signalnoise.png Run7235 Y88 898 signal.png

Run7236 Y88 898 signalnoise.png Run7236 Y88 898 signal.png

898 keV Signal and Background Noise Table

Run # Area of Signal Area of Background Signal to Noise Ratio
7203 130.17 120.59 1.08
7204 825.34 558.66 1.48
7235 194.38 60.23 3.23
7236 1429.75 436.93 3.27

A_W_thesis

Run7204 Y88 1836 signalnoise.png Run7204 Y88 1836 signal.png

Run7235 Y88 1836 signalnoise.png Run7235 Y88 1836 signal.png

Run7236 Y88 1836 signalnoise.png Run7236 Y88 1836 signal.png

1836.1 keV Signal and Background Noise Table

Run # Area of Signal Area of Background Signal to Noise Ratio
7203 83.29 24.73 3.37
7204 944.58 101.68 9.29
7235 82.25 20.90 3.94
7236 1849.86 97.64 18.95


Efficiency on 2/28/2014

Run Source Energy Expected rate (Hz) HpGe Det B Rate (ADC 7) (Hz) HpGe Eff (%)
7028 Ba-133 80.9971 1067.468 +/- 1.131 14.483 +/- 1.442 1.357
7028 Ba-133 276.3997 221.297 +/- 0.2345 4.239 +/- 0.9671 1.916
7028 Ba-133 302.8510 574.310 +/- 0.6085 9.523 +/- 0.5539 1.658
7028 Ba-133 356.0134 1941.418 +/- 2.057 27.130 +/- 1.316 1.397
7028 Ba-133 383.8480 278.416 +/- 0.2950 3.982 +/- 0.2440 1.430
7027 Na-22 511 1589.218 +/- 1.842 17.545 +/- 0.4560 1.104
7025 Cs-137 661.657 2548.022 +/- 2.222 25.622+/- 0.3286 1.006
7029 Mn-54 834.848 4032.782 +/- 0.0114 0.2911 +/- 0.1667 0.0072
7026 Co-60 1173.228 1876.619 +/- 0.2687 11.062 +/- 0.1215 0.589
7027 Na-22 1274.537 888.264 +/- 1.029 4.685 +/- 0.0825 0.527
7026 Co-60 1332.492 1878.167 +/- 0.2690 9.616 +/- 0.1181 0.512


Signal, Noise, and Signal to Noise Ratio plots for 898 keV singles runs.

SNR 898 singles plot.png Ratio 898 singles plot.png

Signal, Noise, and Signal to Noise Ratio plots for 898 keV coincidence runs.

SNR 898 coin plot.png Ratio 898 coin plot.png

Signal Diagram.png Signal Diagram 2.png


[math]\sigma_Fit[/math]

[math]T_{1/2}[/math] Trig Fit Parameters Signal Area Noise Area SNR
0.98 sing [math]\mu=[/math] 897.260 +/- 0.0047 [math]\sigma=[/math] 0.7074 +/- 0.0280 A=0.725 +/- 0.0129 B= 8.448e-4+/- 4.457e-5 C=-0.7355 +/- 0.0408 0.9938 +/- 0.0054 0.3039 +/- 0.0380 3.270 +/- 0.0243
coin [math]\mu=[/math] +/- [math]\sigma=[/math] +/- A= +/- B= +/- C= +/- +/- +/- +/-
2.27 sing [math]\mu=[/math] 903.482 +/- 0.0064 [math]\sigma=[/math] 0.6595 +/- 0.0877 A= 0.3199 +/- 0.0156 B= -7.248e-4+/- 9.968e-7 C= 6.816e-1 +/- 8.138e-4 0.5146 +/- 0.0073 0.0852 +/- 0.0107 6.037 +/- 0.0082
coin [math]\mu=[/math] +/- [math]\sigma=[/math] +/- A= +/- B= +/- C= +/- +/- +/- +/-

Fit method

Do the fit:

get parameters for line

Then fill 1 histogram with line

Then subtract 


TH1F *coin1=new TH1F("coin1","coin1",30,1800,1860);

ntuple->Draw("ADC7*0.604963-49.7001 >>coin1")

TH1F *lin1=new TH1F("lin1","line1",30,1800,1860);

for(int i=1800;i<1861;i++){
lin1->Fill(i,-2028+1.12*i)
}

TH1F *sub1=new TH1F("sub1","sub1",30,1800,1860);

sub1->Add(coin1,1);
sub1->Add(lin1,-1);

sub1->Draw();


A pdf of the Mathematica notebook used to calculate background area, gaussian area, and plot signal/noise vs. activity.

File:AW Background Noise custom4.pdf

All the ROOT fit parameters used to find the background and the resulting peaks.

File:Y-88 Fit Log Scaled&Cut.pdf

Integrating the gaussian of the HpGe detector signal.

File:AW Gaussian Integral2.pdf



[math] f(x)=A \textstyle \int_{\mu-2\sigma}^{\mu+2\sigma} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2} \operatorname{d}\!x +B x +C[/math]


A_W_thesis

Retrieved from "https://wiki.iac.isu.edu/index.php?title=A_W_thesis_old&oldid=94452"