1. 7:4. SIMPLE MODEL FOR NEUTRON SCATTERING LENGTHS CHAPTER 7 – NEUTRON SCATTERING THEORY 7:1. SOLUTION OF THE SCHRODINGER EQUATION 7:2. SCATTERING CROSS SECTIONS

2. 7:1. SOLUTION OF THE SCHRODINGER EQUATION Incident plane wave Scattered spherical wave

3. Schrodinger Equation: Eigenvalue (energy): Hamiltonian: Eigenfunction: Scattering amplitude: incident plane wave scattered spherical wave DERIVATIONS

4. 7:2. SCATTERING CROSS SECTIONS  r Incident neutron current: Scattered neutron current: Scattering cross section:

5. EiEi Energies r incident neutron scattered neutron V0V0 R Out InOut 0 E i ~ 0.025 eV V 0 ~ MeV 7:4. SIMPLE MODEL FOR NEUTRON SCATTERING LENGTHS

6. DERIVATIONS Schrodinger Equation: Solution outside of the well: Solution inside of the well: Boundary condition: Obtain: Combine to obtain transcendental equation:

7. PLOT

8. -- Scattering is not a quantum mechanics problem (there are no bound states). It is a classical mechanics problem. -- However, the Quantum Mechanics formalism is well suited to describe scattering. COMMENTS