LB 170063 Nickel Information With Dead Time: Difference between revisions
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||Rate (Hz) || <math> 1.009048 \times 10^6 \pm 1.2829 \times 10^4 </math> || <math>7.58401 \times 10^5 \pm 2.470 \times 10^3</math> ||<math> 4.15280 \times 10^5 \pm 1.248 \times 10^3 </math> || <math>1.84531 \times 10^5 \pm 8.58 \times 10^2 </math>||<math> 8.4720 \times 10^4 \pm 3.2115 \times 10^2</math> ||<math> 5.8017 \times 10^4 \pm 2.5233 \times 10^2 </math>|| <math> 3.5402 \times 10^4 \pm 1.9360 \times 10^2 </math> | ||Rate (Hz) || <math> 1.009048 \times 10^6 \pm 1.2829 \times 10^4 </math> || <math>7.58401 \times 10^5 \pm 2.470 \times 10^3</math> ||<math> 4.15280 \times 10^5 \pm 1.248 \times 10^3 </math> || <math>1.84531 \times 10^5 \pm 8.58 \times 10^2 </math>||<math> 8.4720 \times 10^4 \pm 3.2115 \times 10^2</math> ||<math> 5.8017 \times 10^4 \pm 2.5233 \times 10^2 </math>|| <math> 3.5402 \times 10^4 \pm 1.9360 \times 10^2 </math> | ||
|- | |- | ||
||True Rate (Integral Method) (Hz) || <math>1.040020 \times 10^6 \pm 1.3222 \times 10^4 </math> ||<math> 7.81679 \times 10^5 \pm 2.5458 \times 10^3</math> ||<math> 4.29155 \times 10^5 \pm 1.290 \times 10^3 </math> || <math> 1.90175 \times 10^5 \pm 8.8425 \times 10^2 </math>||<math> 8.7072 \times 10^4 \pm 3.29 \times 10^2 </math> || | ||True Rate (Integral Method) (Hz) || <math>1.040020 \times 10^6 \pm 1.3222 \times 10^4 </math> ||<math> 7.81679 \times 10^5 \pm 2.5458 \times 10^3</math> ||<math> 4.29155 \times 10^5 \pm 1.290 \times 10^3 </math> || <math> 1.90175 \times 10^5 \pm 8.8425 \times 10^2 </math>||<math> 8.7072 \times 10^4 \pm 3.29 \times 10^2 </math> || <math> 5.9793 \times 10^4 \pm 2.59 \times 10^2 </math> || <math> 3.6508 \times 10^4 \pm 2.00 \times 10^2 </math> | ||
|- | |||
||Number of Entries in Histogram || 566090 || 1015134 || 1428804 || 541498 || 984165 || 761238 ||494039 | |||
|- | |||
||<math> \frac{Entries}{Runtime} </math> || 1878.59 || 3368.93 || 4359.64 || 1803.62 || 3607.05 || 2531.63 || 1609.99 | |||
|- | |||
|| Percent Dead ||3.95 +/- 0.42 || 6.59 +/- 0.43 || 9.09 +/- 0.60 || 3.95 +/- 0.42 || 6.59 +/- 0.43 || 5.06 +/- 0.39 || 3.06 +/- 0.3 | |||
|- | |||
||True Rate (Hz) || <math> 1.082790 \times 10^6 \pm 1.4557 \times 10^4 </math> || <math> 8.36825 \times 10^5 \pm 4.764 \times 10^3 </math> || <math> 4.72065 \times 10^5 \pm 3.332 \times 10^3</math> || <math> 1.97995 \times 10^5 \pm 1.322 \times 10^3</math> || <math> 9.3214 \times 10^4 \pm 5.59 \times 10^2</math> || <math> 6.2979 \times 10^4 \pm 3.62 \times 10^2 </math> ||<math> 3.7660 \times 10^4 \pm 2.33 \times 10^2 </math> | |||
|- | |||
||Backtracked Signal (For Consistency) || || | |||
|- | |||
||.dat file entry || 13.90 +/- 0.01 || 13.64 +/- 0.01 || 13.06 +/- 0.01 || 12.20 +/- 0.01 || 11.44 +/- 0.01 || 11.04 +/- 0.01|| 10.54 +/- 0.01 | |||
|- | |- | ||
|} | |} | ||
We can also trace these signals back in time to make sure that they somewhat match up with the previous signal that was seen. | |||
Below is a plot that was made to help find the half life and the initial activity of the sample | |||
[[File:170063 NickelFoil HLPlot DeadTimeCorrected.png|200px]] | |||
from here we can see that | |||
<math> Slope = 5.63921 \times 10^{-6} \pm 1.75557 \times 10^{-8} </math> | |||
and the intercept is given by | |||
<math> 13.9333 \pm 0.00643596 </math> | |||
By exponentiating the intercept, we can find the activity of the nickel foil at the time of the first measurement, which is | |||
<math> 1.125007 \times 10^6 \pm 7.240 \times 10^3 </math> | |||
Now note that this measurement was taken 8 minutes after the selenium samples were measured. So we must correct the activity back 8 minutes. | |||
<math> A_0 = 1.125007 \times 10^6 \times e^{5.40845 \times 10^{-6} \times 480} = 1.127931 \times 10^6 Hz </math> | |||
<math> \sigma_{A_0} = 7240 \times e^{5.40845 \times 10^{-6} \times 480} = 7258.82 Hz </math> | |||
Latest revision as of 22:02, 6 December 2017
Below is a table with thin windows, original windows, and expanded windows for the nickel on sample 170063. The thin window method can be found at LB Thesis Thin Window Analysis.
| 5/25/17 | 5/26/17 | 5/27/17 | 5/29/17 | 5/30/17 | 5/31/17 | 6/1/17 | ||
| Thin Window |  |
 |
 |
 |
 |
 |
| |
| Original Window |  |
 |
 |
 |
 |
 |
| |
| Original Background | 329.6 +/- 8.6 | 708.3 +/- 12.8 | 1611 +/- 19.9 | 247.4 +/- 7.5 | 721 +/- 13.1 | 424.8 +/- 9.9 | 215.4 +/- 7.0 | |
| Integrated Background | 659.2 +/- 17.2 | 1416.6 +/- 25.6 | 3222 +/- 39.8 | 494.8 +/- 15 | 1442 +/- 26.2 | 849.6 +/- 19.8 | 430.8 +/- 14 | |
| Signal in Thin Window | 52350 +/- 228.80 | 97860 +/- 312.83 | 118500 +/- 344.24 | 47420 +/- 217.76 | 73100 +/- 270.37 | 54930 +/- 234.37 | 33720 +/- 183.63 | |
| Position on Detector A (cm) | 50 | 30 | 20 | 20 | 10 | 10 | 10 | |
| Efficiency (Percent) | 0.017000 +/- 0.000002 | 0.042200 +/- 0.000005 | 0.084700 +/0.000007 | 0.084700 +/0.000007 | 0.310000 +/- 0.000003 | 0.310000 +/- 0.000003 | 0.310000 +/- 0.000003 | |
| Signal in thin Window With Efficiency | 307941176.5 +/- 3864757.4 | 231895734.6 +/- 741812.3 | 139905549 +/- 406587.1067 | 55985832.4 +/- 257137.3 | 23580645.2 +/- 87216.4 | 17719354.8 +/- 75603. 4 | 10877419.4 +/- 59235.6 | |
| Integrated Background with Efficiency | 3877647.1 +/- 101177.5 | 3372857.1 +/- 60953.7 | 3804014.2 +/- 46990.42 | 584179.5 +/- 17709.6 | 465161.3 +/- 8451.6 | 274064.5 +/- 6387.1 | 13897.7 +/- 4516.1 | |
| Background Subtracted Signal | 304063529.4 +/- 3866081.6 | 228522877.5 +/- 744312.3 | 136101534.8 +/- 409293.5 | 55401652.9 +/- 257746.4 | 23115483.9 +/- 87624.9 | 17445290.3 +/- 75872.7 | 10863521.7 +/- 59407.5 | |
| Runtime (s) | 301.337 | 301.322 | 327.734 | 300.228 | 272.845 | 300.691 | 306.858 | |
| Rate (Hz) | [math]\displaystyle{ 1.009048 \times 10^6 \pm 1.2829 \times 10^4 }[/math] | [math]\displaystyle{ 7.58401 \times 10^5 \pm 2.470 \times 10^3 }[/math] | [math]\displaystyle{ 4.15280 \times 10^5 \pm 1.248 \times 10^3 }[/math] | [math]\displaystyle{ 1.84531 \times 10^5 \pm 8.58 \times 10^2 }[/math] | [math]\displaystyle{ 8.4720 \times 10^4 \pm 3.2115 \times 10^2 }[/math] | [math]\displaystyle{ 5.8017 \times 10^4 \pm 2.5233 \times 10^2 }[/math] | [math]\displaystyle{ 3.5402 \times 10^4 \pm 1.9360 \times 10^2 }[/math] | |
| True Rate (Integral Method) (Hz) | [math]\displaystyle{ 1.040020 \times 10^6 \pm 1.3222 \times 10^4 }[/math] | [math]\displaystyle{ 7.81679 \times 10^5 \pm 2.5458 \times 10^3 }[/math] | [math]\displaystyle{ 4.29155 \times 10^5 \pm 1.290 \times 10^3 }[/math] | [math]\displaystyle{ 1.90175 \times 10^5 \pm 8.8425 \times 10^2 }[/math] | [math]\displaystyle{ 8.7072 \times 10^4 \pm 3.29 \times 10^2 }[/math] | [math]\displaystyle{ 5.9793 \times 10^4 \pm 2.59 \times 10^2 }[/math] | [math]\displaystyle{ 3.6508 \times 10^4 \pm 2.00 \times 10^2 }[/math] | |
| Number of Entries in Histogram | 566090 | 1015134 | 1428804 | 541498 | 984165 | 761238 | 494039 | |
| [math]\displaystyle{ \frac{Entries}{Runtime} }[/math] | 1878.59 | 3368.93 | 4359.64 | 1803.62 | 3607.05 | 2531.63 | 1609.99 | |
| Percent Dead | 3.95 +/- 0.42 | 6.59 +/- 0.43 | 9.09 +/- 0.60 | 3.95 +/- 0.42 | 6.59 +/- 0.43 | 5.06 +/- 0.39 | 3.06 +/- 0.3 | |
| True Rate (Hz) | [math]\displaystyle{ 1.082790 \times 10^6 \pm 1.4557 \times 10^4 }[/math] | [math]\displaystyle{ 8.36825 \times 10^5 \pm 4.764 \times 10^3 }[/math] | [math]\displaystyle{ 4.72065 \times 10^5 \pm 3.332 \times 10^3 }[/math] | [math]\displaystyle{ 1.97995 \times 10^5 \pm 1.322 \times 10^3 }[/math] | [math]\displaystyle{ 9.3214 \times 10^4 \pm 5.59 \times 10^2 }[/math] | [math]\displaystyle{ 6.2979 \times 10^4 \pm 3.62 \times 10^2 }[/math] | [math]\displaystyle{ 3.7660 \times 10^4 \pm 2.33 \times 10^2 }[/math] | |
| Backtracked Signal (For Consistency) | ||||||||
| .dat file entry | 13.90 +/- 0.01 | 13.64 +/- 0.01 | 13.06 +/- 0.01 | 12.20 +/- 0.01 | 11.44 +/- 0.01 | 11.04 +/- 0.01 | 10.54 +/- 0.01 |
We can also trace these signals back in time to make sure that they somewhat match up with the previous signal that was seen.
Below is a plot that was made to help find the half life and the initial activity of the sample
from here we can see that
[math]\displaystyle{ Slope = 5.63921 \times 10^{-6} \pm 1.75557 \times 10^{-8} }[/math]
and the intercept is given by
[math]\displaystyle{ 13.9333 \pm 0.00643596 }[/math]
By exponentiating the intercept, we can find the activity of the nickel foil at the time of the first measurement, which is
[math]\displaystyle{ 1.125007 \times 10^6 \pm 7.240 \times 10^3 }[/math]
Now note that this measurement was taken 8 minutes after the selenium samples were measured. So we must correct the activity back 8 minutes.
[math]\displaystyle{ A_0 = 1.125007 \times 10^6 \times e^{5.40845 \times 10^{-6} \times 480} = 1.127931 \times 10^6 Hz }[/math]
[math]\displaystyle{ \sigma_{A_0} = 7240 \times e^{5.40845 \times 10^{-6} \times 480} = 7258.82 Hz }[/math]