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7:4. SIMPLE MODEL FOR NEUTRON SCATTERING LENGTHS

Explore solutions of the Schrodinger Equation, scattering cross sections, and a simple model for neutron scattering lengths using classical and Quantum Mechanics formalism. Derivations, boundary conditions, and transcendental equations explained.

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7:4. SIMPLE MODEL FOR NEUTRON SCATTERING LENGTHS

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

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

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

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

  5. Energies Ei ~ 0.025 eV Ei r 0 V0 ~ MeV V0 In Out Out R scattered neutron incident neutron 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. COMMENTS -- 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.

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