ncrystal Use incoherent approximation in the epithermal energy region

Coherent scattering at high incident energies can be approximated by incoherent scattering, by means of replacing the sum over reciprocal space points with an integral (see, for instance V.F. Turchin, "Slow Neutrons", page 60)

This could be used to slightly improve the accuracy of the coherent scattering, by extending the sum with an integral (instead of extrapolating the last Bragg edge as 1/E), or to accelerate the code by taking into consideration a smaller number of planes without compromising the total scattering cross section:

$\frac{\lambda^2}{2V_{uc}} \sum_{hkl}^{\lambda \leq 2d_{hkl}} d_{hkl} \left|F\left(\vec{\tau}_{hkl} \right )\right|^2 \approx \frac{\lambda^2}{2V_{uc}} \sum_{hkl}^{\lambda \leq 2d_{hkl}^\text{cutoff} } d_{hkl}^\text{cutoff} \left|F\left(\vec{\tau}_{hkl} \right )\right|^2+\int_{}\left(\text{Incoherent model} \right )$

Oct 01 '21 13:10 marquezj

@marquezj the equation does not render here for me, can you upload an image instead?

Oct 24 '25 10:10 tkittel

I am trying to remember what we were discussing here, because the equation is just a concept: using the incoherent approximation for Bragg scattering in the epithermal limit, to reduce the artifacts when dcutoff is reduced:

It might be something along these lines (this is from "Low Energy Neutron Physics" by Gurevich and Tarasov):

Oct 24 '25 11:10 marquezj

Yeah ok, but that doesn't tell us how to estimate the contribution from any planes left out due to a dspacing cut-off, does it?

Oct 24 '25 12:10 tkittel