Http://quantumguru.f Iles.wordpress.com/2 013/04/59.pdf

Scattering in the static potential of extended charge distribution:
Formfactor F(q) = ∫ρ(r)e^{iqr}d³r
First order perturbation theory:
V = -∫ρ(r)e^{iqr}d³r / (4πε₀r)
Factorisation: point source × formfactor
Formfactor is an interference phenomenon, coherent scattering from all parts of the source.
Formfactor always reduces the corresponding point charge cross section.
Properties of form factors:
F(q) = ∫ρ(r)e^{iqr}d³r
Expansion: F(q) = 1 - (qR)²/6 + ...
RMS radius is given by the slope of the formfactor at vanishing momentum transfer.
Invariant Matrix element:
M = e²(LμL'μ) / q²
Electron tensor:
Lμ = γμ - (qμ/q²)(qγ)
Muon tensor:
L'μ = γμ - (qμ/q²)(qγ)
Pointlike e--proton scattering:
M = e²(LμL'μ) / q²
Cross section in lab frame:
dσ/dΩ = (α²/4E²)(1 + τ)(1 + τ - 2τsin²(θ/2))
Form factors of the nucleon:
Due to its finite size, the proton needs to be described by 2 form factors, one for the charge distribution and one for the distribution of the magnetic moments.
Generalized “Rosenbluth – formula” with so called Sachs - form factors:
dσ/dΩ = (α²/4E²)(GE² + τGM²)(1 + τ - 2τsin²(θ/2))
Electric form factor GE and Magnetic form factor GM.
Measurement of GE(Q²) and GM(Q²):
Rosenbluth - diagram
Q² = const!
tan(θ/2) = √(τ(1 + τ))/(1 + τ - 2τsin²(θ/2))
abzissa: 1/τ
slope: GE² / GM².