Chapter 9 – COHERENT AND INCOHERENT NEUTRON SCATTERING 9:1. COHERENT AND INCOHERENT CROSS SECTIONS 9:2. SPIN INCOHERENCE 9:3. COHERENT SCATTERING CROSS.

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Presentation transcript:

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

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

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

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

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

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

9:11. TABULATED SCATTERING LENGTHS AND CROSS SECTIONS Elementb Fermi  c Barn  i Barn  s Barn  a Barn H D C N F Na Si P S Cl

9:12. NEUTRON TRANSMISSION Total cross section: scatteringabsorption coherent incoherent  t : total cross section d: sample thickness Neutron transmission:

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:

V.F. Sears, “Neutron Scattering Lengths and Cross Sections”, Neutron News 3, (1992). A scattering length density calculator can be found online at: REFERENCES

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.