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Chapter 9 – COHERENT AND INCOHERENT NEUTRON SCATTERING

Chapter 9 – COHERENT AND INCOHERENT NEUTRON SCATTERING. 9:1. COHERENT AND INCOHERENT CROSS SECTIONS. 9:2. SPIN INCOHERENCE. 9:3. COHERENT SCATTERING CROSS SECTION. 9:4. ISOTOPIC INCOHERENT SCATTERING CROSS SECTIONS. 9:7. CONTRAST FACTORS.

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Chapter 9 – COHERENT AND INCOHERENT NEUTRON SCATTERING

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  1. Chapter 9 – COHERENT AND INCOHERENT NEUTRON SCATTERING 9:1. COHERENT AND INCOHERENT CROSS SECTIONS 9:2. SPIN INCOHERENCE 9:3. COHERENT SCATTERING CROSS SECTION 9:4. ISOTOPIC INCOHERENT SCATTERING CROSS SECTIONS 9:7. CONTRAST FACTORS 9:11. TABULATED SCATTERING LENGTHS AND CROSS SECTIONS 9:12. NEUTRON TRANSMISSION 20:5. ESTIMATION OF INCOHERENT SCATTERING

  2. 9:1. COHERENT AND INCOHERENT CROSS SECTIONS Microscopic cross section (in barns): Standard deviation: Macroscopic cross section (in cm-1): incoherent part coherent part Q-dependent Q-independent

  3. scattering nucleus of spin I incident neutron of spin 1/2 number of degenerate states spin operators eigenvalues I + 1/2 2(I+1/2)+1=2I+2 I - 1/2 2(I-1/2)+1=2I 9:2. SPIN INCOHERENCE

  4. DERIVATIONS Average over spins: Coherent scattering length: Incoherent scattering length:

  5. 9:3. COHERENT SCATTERING CROSS SECTION Coherent cross section: With the fractions: Macroscopic (cm-1) and microscopic (barns) cross sections: 9:7. CONTRAST FACTORS Contrast factor:

  6. 9:4. ISOTOPIC INCOHERENT SCATTERING CROSS SECTIONS Spin incoherence cross section: Isotopic incoherence cross section:

  7. 9:11. TABULATED SCATTERING LENGTHS AND CROSS SECTIONS

  8. 9:12. NEUTRON TRANSMISSION St: total cross section Neutron transmission: d: sample thickness Total cross section: scattering absorption coherent incoherent

  9. 20:5. ESTIMATION OF INCOHERENT SCATTERING Incoherent scattering cross section: Including multiple scattering: Resuming the series: When incoherent scattering dominates: Way to estimate the incoherent cross section:

  10. REFERENCES V.F. Sears, “Neutron Scattering Lengths and Cross Sections”, Neutron News 3, 26-37 (1992). A scattering length density calculator can be found online at: http://www.ncnr.nist.gov/resources/sldcalc.html

  11. COMMENTS -- Coherent scattering probes the sample structure (Q-dependent). Incoherent scattering does not contain information about the structure (Q-independent). -- Scattering length densities and contrast factors can be estimated using the online calculator.

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