Difference between revisions of "Neutron energy resolution in NaI detector"

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<math> E_n = \frac{m}{2}\left( \frac{d}{t_n} \right)^2 </math>
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<math> E_n = \frac{m}{2}\left( \frac{d}{t_n} \right)^2 </math>
  
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<math> \delta E_n = -2\ E_n \frac{\delta t_n}{t_n} = -\frac{2 \sqrt{2}}{\sqrt{m} d}\ E_n^{3/2} \delta t_n </math>
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<math> \delta E_n = -\frac{2 \sqrt{2}}{\sqrt{m} d}\ E_n^{3/2} \delta t_n </math>
  
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[[File:Na 22 timing.jpg | 400px]]
  
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* From NaI detector measurements <math>\delta t_n = 15\ ns</math>
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* <math> \delta t_n = 15\ ns</math>
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* $mc^2 = 938\ MeV$
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* <math> mc^2 = 938\ MeV </math>
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<math> d = 0.5\ m: \ \ \  ( \delta E_n/E_n ) = 0.83\ E_n^{1/2}\ MeV </math>
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<math> d = 0.7\ m: \ \ \  ( \delta E_n/E_n ) = 0.59\ E_n^{1/2}\ MeV </math>
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<math> d = 1.0\ m: \ \ \  ( \delta E_n/E_n ) = 0.42\ E_n^{1/2}\ MeV </math>
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<math> d = 1.5\ m: \ \ \  ( \delta E_n/E_n ) = 0.28\ E_n^{1/2}\ MeV </math>
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<math> d = 2.0\ m: \ \ \  ( \delta E_n/E_n ) = 0.21\ E_n^{1/2}\ MeV </math>
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[[File:NaI_energy_resolut.png | 450px]]
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[[File:NaI_energy_resolut_4.png | 450px]]

Latest revision as of 21:44, 28 April 2012

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[math] E_n = \frac{m}{2}\left( \frac{d}{t_n} \right)^2 [/math]

[math] \delta E_n = -\frac{2 \sqrt{2}}{\sqrt{m} d}\ E_n^{3/2} \delta t_n [/math]

Na 22 timing.jpg

  • [math] \delta t_n = 15\ ns[/math]
  • [math] mc^2 = 938\ MeV [/math]


[math] d = 0.5\ m: \ \ \   ( \delta E_n/E_n ) = 0.83\ E_n^{1/2}\ MeV [/math]
[math] d = 0.7\ m: \ \ \   ( \delta E_n/E_n ) = 0.59\ E_n^{1/2}\ MeV [/math]
[math] d = 1.0\ m: \ \ \   ( \delta E_n/E_n ) = 0.42\ E_n^{1/2}\ MeV [/math]
[math] d = 1.5\ m: \ \ \   ( \delta E_n/E_n ) = 0.28\ E_n^{1/2}\ MeV [/math]
[math] d = 2.0\ m: \ \ \   ( \delta E_n/E_n ) = 0.21\ E_n^{1/2}\ MeV [/math]

NaI energy resolut.png NaI energy resolut 4.png

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