Plastic Scintillator Calculation

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

Molecules per cm3=gramsCH2cm3∗molgram∗N[A] (NOTE: gramcm3 is just the density of the scintillator material and N[A] is Avogadro's number)

Molecules per cm2(K)=Moleculescm3∗Thickness

Weighted cross-section (σw)=(σelecC+σnucleusC)+2(σelecH+σnucleusH)

Probability of interaction (%) =σw∗K∗100


All cross sections listed here are pair production cross-sections

For carbon σnucleus=9.645∗10−2barns or 9.645∗10−26cm2

For carbon σelec=1.030∗10−2barns or 1.030∗10−26cm2

For hydrogen σnucleus=2.688∗10−3barns or 2.688∗10−27cm2

For hydrogen σelec=1.716∗10−3barns or 1.716∗10−27cm2

Avogadro's number =6.022∗1023moleculesmol

Molecular formula for PVT =C10H11

Density of polyvinyl toluene (a common scintillator material) =1.02gramscm3 (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 cm3=1.02gPVTcm3∗1mol131g∗6.022∗1023moleculesmol=4.689∗1021moleculesPVTcm3

Molecules per cm2(K)=4.689∗1021moleculesPVTcm3∗1cm=4.689∗1021moleculesPVTcm2

Weighted cross-section (σw)=(10∗(1.030∗10−26cm2+9.645∗10−26cm2))+(11∗(1.716∗10−27cm2+2.688∗10−27cm2))=1.116∗10−24cm2

Probability of interaction (%) =1.116∗10−24cm2∗4.689∗1021moleculesPVTcm2∗100

Doing the same calculations using the Bicron BC 408 PVT with anthracene [3] for the material yields a probability of 0.5294

A different way to calculate probability of interaction

I checked out a few of the physics material supply sites and most of them list with their products the amounts of each individual atom per cm3. Therefore there is a quicker way to calculate the probability of interaction which is listed below.


Probability of interaction per cm thickness=((NumCarbonAtomscm3∗(σelecC+σnucleusC))+(NumHydrogenAtomscm3∗(σelecH+σnucleusH)))∗100

Using this method of calculation for Rexon RP 200 yields a probability =0.5234cm

Using this method for Bicron BC 408 yields a probabiltiy =0.5303cm


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