What is the total scattering cross-section?
The sum of elastic and inelastic scattering cross-sections. σ_total_scat = σ_el + σ_inel.
What is elastic scattering?
Scattering where incident particles are deflected but do not lose energy.
What is inelastic scattering?
Scattering in which incident particles lose energy.
What is the total interaction cross-section?
The sum of total scattering and absorption cross-sections: σ_total = σ_total_scat + σ_abs.
Define incident flux I₀.
Number of incident particles per unit area per unit time passing perpendicular to beam direction.
What is the attenuation law for beam intensity?
I = I₀ e^(−n σ x), where n is number density and x is target thickness.
I_0 is incident flux
What number of particles interact in a thin target?
I_tot = I₀ - I = I₀ (1 − e^(−n σ x)).
Scattering cross-section gives no information on…
direction of the scattered particles
what is dΩ?
sinθ dθ dφ
What is the differential scattering cross-section?
dσ/dΩ: probability per unit solid angle that a particle is scattered into direction (θ, φ).
visualise cross section σ as a geometric disc
consider particles scattered into solid angle dΩ
imagine them as originating from area of disc dσ
Why is the differential cross-section important?
It gives information about the angular distribution and the nuclear potential shape.
Fraction of particles scattered into dΩ for target with n particles per unit volume and thickness t
(I n t A dσ (θ,φ)) / (IA) = n t dσ (θ,φ) = n t (dσ (θ,φ))/dΩ dΩ
What is the relation between total scattering and differential cross-section?
σ_total_scat = ∫ (dσ/dΩ) dΩ over all solid angles.
Define solid angle.
dΩ = sinθ dθ dφ; Ω = ∫ sinθ dθ dφ.
What is the impact parameter b?
The distance at which the particle would pass by the target if no interaction occurred.
Expression linking impact parameter and differential cross-section?
dσ/dΩ = (b / sinθ) |db/dθ|.
What does a sharply peaked differential cross-section at small θ indicate?
Rutherford-like scattering; strong forward scattering.
How is σ_total measured experimentally?
From beam attenuation using I = I₀ e^(−n σ x).
How is σ_total_scat measured experimentally?
By detecting all particles scattered out of the beam direction.
What does beam attenuation assume about the target?
That the target is thin so that σ and n remain effectively constant.
Formula for interaction probability for thin target?
P = σ N, where N is nuclei per unit area.
What information can classical scattering give?
Insight into the form of the potential between particle and nucleus.
