The theoretical framework of neutron scattering

The theory of thermal neutron scattering has for its objective the interpretation of the experimental observables in terms of the microscopic, quantum-like, properties of the scattering sample. It is as well then to understand exactly what is being measured in neutron spectroscopy. (The theory is fully developed in Appendix 2.) 

The observable is the rate of change of the cross section with respect to the final energy, Eu and solid angle, d 2. This is the double differential scattering cross section, (d o/d f d/2 ), with units, bam eV steradian, where  

The changes that occur during the scattering process must now be related to how the initial state of the system (scattering atom plus neutron) is transformed into the final state of the system. 

The nature of the neutrons in the incident beam is represented by their initial wavefunction, y/,, which at long distances from the scattering nucleus will be a simple plane wave. At short distances from the nucleus the influence of its nuclear potential perturbs the incident wavefunction into the final wavefunction, n,f- The form of the final wavefunction is dependent on the energy of the neutron and is determined by solving the 

Schrodinger equation. The final waveflinetions ean be isotropic in nature, and have spherical (S) wave solutions, or strongly anisotropic, like the P-wave and D-wave solutions (similar to the electron wavefunctions in the Coulombic field of the nucleus). However, the energies of thermal neutrons, about 200-4000 cm are too low to require P- or D-wave solutions and only spherical wave solutions need be considered. The sample, of N atoms, is represented by its initial state, i (final state, f) wavefimctions, (q. What is needed is an understanding of how the final states, in changing fi-om the initial states, relate 

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