Difference between revisions of "Plastic Scintillator Calculation"

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Avogadro's number <math> = \frac{6.022*10^{23}molecules}{mol}</math>
 
Avogadro's number <math> = \frac{6.022*10^{23}molecules}{mol}</math>
  
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Density of polyvinyl toluene (a common scintillator material) <math> = \frac{1.02grams}{cm^3}</math>
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Density of polyvinyl toluene (a common scintillator material) <math> = \frac{1.02grams}{cm^3}</math> (NOTE: this value is from Rexon RP 200 [http://www.rexon.com/RP_200.pdf])
  
 
  or is it <math>\rho_{BC408} = \frac{1.032grams}{cm^3}</math>  H/C = 11/10  [http://arxiv.org/abs/nucl-ex/0502006] (TF)
 
  or is it <math>\rho_{BC408} = \frac{1.032grams}{cm^3}</math>  H/C = 11/10  [http://arxiv.org/abs/nucl-ex/0502006] (TF)
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Probability of interaction (%) <math>= 1.1556*10^{-25}cm^2 * \frac{4.387*10^{22}molecules PVT}{cm^2} * 100% = 0.5070%</math>
 
Probability of interaction (%) <math>= 1.1556*10^{-25}cm^2 * \frac{4.387*10^{22}molecules PVT}{cm^2} * 100% = 0.5070%</math>
  
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Doing the same calculations using the NPOL3 for the material yields a probability of  
+
Doing the same calculations using the Bicron BC 408 PVT with anthracene [http://webh09.cern.ch/ajbell/Documents/Optical_Fibres/BICRON%20BC408.pdf] for the material yields a probability of  
  
  
 
[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]
 
[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]

Revision as of 03:34, 5 February 2009

Below is the calculations done to determine the probability of pair production depending on thickness of the scintillator.

Molecules per [math] cm^3 = \frac{grams CH_{2}}{cm^3} * \frac{mol}{gram} * {N[A]}[/math] (NOTE: [math] \frac{gram}{cm^3} [/math] is just the density of the scintillator material and N[A] is Avogadro's number)

Molecules per [math] cm^2 (K) = \frac{Molecules}{cm^3} * Thickness [/math]

Weighted cross-section [math] (\sigma_w) = (\sigma_{elec}C + \sigma_{nucleus}C) + 2(\sigma_{elec}H + \sigma_{nucleus}H)[/math]

Probability of interaction (%) [math]= \sigma_w * K * 100%[/math]


All cross sections listed here are pair production cross-sections

For carbon [math]\sigma_{nucleus} = 9.645*10^{-2} barns[/math] or [math]9.645*10^{-26}cm^2[/math]

For carbon [math]\sigma_{elec} = 1.030*10^{-2} barns[/math] or [math]1.030*10^{-26}cm^2[/math]

For hydrogen [math]\sigma_{nucleus} = 2.688*10^{-3} barns[/math] or [math]2.688*10^{-27}cm^2[/math]

For hydrogen [math]\sigma_{elec} = 1.716*10^{-3} barns[/math] or [math]1.716*10^{-27}cm^2[/math]

Avogadro's number [math] = \frac{6.022*10^{23}molecules}{mol}[/math]

Density of polyvinyl toluene (a common scintillator material) [math] = \frac{1.02grams}{cm^3}[/math] (NOTE: this value is from Rexon RP 200 [1]) 

or is it [math]\rho_{BC408} = \frac{1.032grams}{cm^3}[/math]  H/C = 11/10  [2] (TF)

For the sample calculation the thickness will be set to 1 cm just to get probability per cm


So entering all the numbers into the 4 initial equations gives the following answers:

Molecules per [math] cm^3 = \frac{1.02g PVT}{cm^3} * \frac{1 mol}{14 g} * \frac{6.022*10^{23}molecules}{mol} = \frac{4.387*10^{22}molecules PVT}{cm^3} [/math]

Molecules per [math] cm^2 (K) = \frac{4.387*10^{22}molecules PVT}{cm^3} * 1cm = \frac{4.387*10^{22}molecules PVT}{cm^2} [/math]

Weighted cross-section [math] (\sigma_w) = (1.030*10^{-26}cm^2 + 9.645*10^{-26}cm^2) + 2(1.716*10^{-27}cm^2 + 2.688*10^{-27}cm^2) = 1.1556*10^{-25}cm^2[/math]

Probability of interaction (%) [math]= 1.1556*10^{-25}cm^2 * \frac{4.387*10^{22}molecules PVT}{cm^2} * 100% = 0.5070%[/math]

Doing the same calculations using the Bicron BC 408 PVT with anthracene [3] for the material yields a probability of


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