1. 8:4. THE MASTER FORMULA OF NEUTRON SCATTERING 8:5. THE VARIOUS STRUCTURE FACTORS Chapter 8 - ELASTIC AND QUASIELASTIC/ INELASTIC NEUTRON SCATTERING

2. 8:4. THE MASTER FORMULA OF NEUTRON SCATTERING First Born Approximation: Fermi pseudo-potential: Calculate scattering element:

3. Heisenberg representation: Schrodinger equation: Calculate: Double differential scattering cross section: Master formula of neutron scattering: DERIVATIONS

4. 8:5. THE VARIOUS STRUCTURE FACTORS Define scattering density: Define dynamic structure factor: Fourier transform in time: Static structure factor: Density-density correlation: Differential scattering cross section: Fourier transform in space:

5. COMMENTS -- The first Born Approximation describes single-scattering well. This is the diffraction limit. -- Neutron Reflectometry involves multiple scatterings. The first Born Approximation does not describe reflectometry. This is the refraction limit. -- Both SANS and Neutron Reflectometry are elastic scattering methods. -- Elastic scattering probes structures while quasielastic/inelastic scattering probes dynamics in the sample (normal modes).