# Angular dependence of x-ray and neutron scattering factors

Why are neutron scattering factors essentially independent of $2\theta$, whereas X-ray scattering factors drop off with increasing $2\theta$ ?

• Well, the interactions that lead to the scattering are different. Do you understand why the X-ray scattering factor drops off with increasing $2\theta$? If so, do those fields/potentials/forces apply to neutron scattering? – Jon Custer May 26 '15 at 15:03
• In X-ray scattering you have a dipolar electronic interaction, in neutron scattering presumably it is colour force. I don't really understand why there is a drop off in XRD. – J. LS May 26 '15 at 16:13
• Assume neutron scattering is sold hard spheres. Calculate the differential scattering cross section. You will find that it is flat vs either energy transferred or angle scattered (they are equivalent). For the x-Ray case there are many derivations online... – Jon Custer May 26 '15 at 16:41
• What search terms did you use ? I couldn't find anything which helped me to understand it – J. LS May 26 '15 at 17:00
• 'X-Ray scattering cross section' worked just fine for me. – Jon Custer May 26 '15 at 17:02

## 1 Answer

Scattering factors describe scattering of an atom

To predict how an object will diffract, you essentially have to do a 3D Fourier transform of the scattering density (https://chemistry.stackexchange.com/a/115815/72973). The scattering factor is derived from the scattering of a single atom (placed at the origin). For xray diffraction, the relevant density is that of the electrons. For neutron diffraction, it is that of the nucleus. See slide 11, https://www.embl-hamburg.de/biosaxs/courses/embo2012/slides/neutron-scattering-basics-trewhella.pdf

The fuzzier the scattering density, the higher the angular dependency

The Fourier transform of a Gaussian is a Gaussian again; a sharp Gaussian results in a broad transform, and vice versa. For X-ray diffraction, the electron density is fuzzy (same magnitude as the wavelength), so there is a large angular dependence. For neutron diffraction, the scattering density is very compact, leading to almost no angular dependence of the scattering factors.

• I would also point out that in a neutron scattering experiment there is little to no backscattering of neutrons simply due to the fact that a radioactive decay of the nuclei is needed to produce additional neutrons. This is not the case for x-ray photons as these can be produced by excited electrons. – Jeppe Nielsen Jul 7 at 2:46