Slides from my talk to the School of Physics Optics Group in early 1998 (either March or April) with my physics honours thesis/project proposal into atomic form factors and x-ray - atom scattering.
a single atom • The types of scattering processes include – Elastic (Rayleigh) Scattering – Inelastic (Compton) Scattering – Photo Effect – Pair Production – Nuclear Thomson Scattering 2
[H0 + H′]ψ = Eψ • Scattering Wave Function as r → ∞ can be considered as an incident and scattered wave. ψ(r) = ψi (r) + ψs (r) ψ(r) = A eik·r + f(k, θ, φ) eikr r • f(k, θ, φ) is the scattering amplitude • Differential Cross Section dσ dΩ = |f(k, θ, φ)|2 4
on the atomic form factor • Scattering amplitude – form factor relationship depends on how atom-radiation interaction is modeled • Atomic Form Factors are used to determine diffraction, scattering and attenuation processes of X ray interactions with matter. 5
f = f0 + f′ + if′′ • Away from absorption edges (for a spherically symmetric atom) f0 (q) = eiqrρ(r)dr = 4π ∞ 0 ρ(r) sin qr qr r2dr • q = kf − ki = 2|k| sin θ 2 is the change in the photon’s momentum and θ is the scattering angle. • ρ(r) = ψ∗(r)ψ(r) is the electron density. • The real and imaginary components f′ and f′′ describe the situation when the photon energy is close to one of the atom’s energy levels – an absorption edge. 6
factors for low Z atoms. • Determine atomic form factors for low Z atoms and compare with existing theories and experimental results. • Investigate and develop the theory of anomalous X ray resonance scattering (EXAFS, XANES, DAFS) – effects of local interactions on the atomic form factor. 10
X Ray – Classical Radiation Field using electric dipole and/or electric quadrupole approximation • Investigate the effect of local interactions on the atomic form factor • Use a Dirac-Hartree-Fock computational approach to determine for multi-electron atoms the – Energy eigenvalues of the atom – Corresponding wave functions • Use these wave functions to determine the atomic form factors for the different atoms over a range of X ray energies. – Angular dependent component of the atomic form factor f0 – Energy dependent components of the atomic form factor f′ and f′′ 11