Plastic Scintillator Calculation

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

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

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

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

Probability of interaction [math]\displaystyle{ = \sigma_w * K }[/math]

All cross sections listed here are pair production cross-sections

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

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

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

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

Density of polyvinyl toluene (a common scintillator material) [math]\displaystyle{ = /frac{1.02grams}{cm^3} }[/math]

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