Checking the math in PAP eq39

Treating each electron individually and neglecting absorption effects we can estimate the thickness from eq 8.

We must also be assuming an element is only contained in 1 layer:

$p(\rho z)=N\cdot (\rho z-L)^2\cdot (\rho z-R)^2\label{eq39}\tag{39}$ $= N\cdot (\rho z^2-2\rho zL+L^2)(\rho z^2-2\rho zR+R^2)$ $=N\cdot (\rho z^4-2\rho z^3R-\rho z^2R^2-2\rho z^3L+ 4\rho z^2RL-2\rho zR^2L-\rho z^2L^2-2\rho zRL^2+L^2R^2)$ $=N\cdot (\rho z^4-2\rho z^3(R+L)+\rho z^2(R^2+4RL+L^2)- 2\rho z(R^2L+RL^2)+L^2R^2)$

with N such that:

$\int^R_0 p(\rho z)d\rho z=1$

reference to eq39: \ref{eq39},

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Austin Fox's personal website.

Checking the math in PAP eq39

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