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)
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]