Intermediate Mechanics:Scattering

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Total Cross Section

$p r o b a b i l i t y = n t a r g e t s * n p r o j e c t i l e s * σ$

Where $σ$ is Area of the target divided by the Area of the total field.

$p r o b a b i l i t y = n t a r g e t s * n p r o j e c t i l e s * σ(θ) * ΔΩ$

$ΔΩ$ is the "Solid Angle"

$\Delta \Omega = \frac{A}{R^2}$

$\sigma(\theta) = \frac{b}{\sin \theta} \left| \frac{\, db}{\, d\theta} \right|$

$\sigma(\theta) = \left( \frac{k}{4 T} \right)^2 \frac{1}{\sin^4 \left( \frac{\theta}{2} \right)}$