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

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Presentation transcript:

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

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

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

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

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

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

PLOT

-- 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

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