coherentElastic.rst

Coherent Elastic

In crystalline solids consisting of coherent scatterers [i.e. materials with relatively large bound coherent scattering cross sections], the so-called "zero-phonon term" leads to interference scattering from the various planes of atoms of the crystal making up the solid. There is no energy loss/gain in such events, and are described using the coherent elastic cross section formula:

$$\sigma^{coh}(E,E',\mu) = \frac{\sigma_{coh}}{E}~\sum_{E_i>E}f_i~\mathrm{e}^{-2WE_i}~\delta(\mu-\mu_0)~\delta(E-E')$$

where

$$\mu_0=1-\frac{2E_i}{E}.$$

Here, E is the incident neutron energy, E′ is the secondary neutron energy, μ is the scattering cosine in the laboratory reference system, σ_coh is the characteristic bound coherent scattering cross section of the material, W is the Debye-Waller Coefficient (which is a function of temperature), E_i are the locations in energy of the Bragg-edges, and f_i are the related to crystallographic structures.

For select materials, LEAPR prepares the coherent elastic scattering data and writes the data into the MF=7/MT=2 ENDF-6 section. THERMR may then take those Bragg peak locations and weights, calculate the cross section, and write the output coherent elastic cross sections to the MF=3 file of the output PENDF.