Basic neutron scattering

You may recall the Bragg law from your high school physics

$$n\lambda=2d\sin(\theta),$$

giving the scattering condition for a wave of wavelength $\lambda$ against a series of lattice planes with lattice spacing $d$, rotated the angle $\theta$ off the lattice plane normal. $n$ is an integer giving the spectral order of the scattered wave. In neutron science one often refers to the scattering vector, $\vec{\kappa}$ of a given reflection, where

$$\kappa=\vert\vec{\kappa}\vert=\frac{2\pi}{d}.$$

This gives us the scattering vector formulation of the Bragg law

$$\kappa=2k\sin(\theta),$$

where $k=\frac{2\pi}{n\lambda}$. The Bragg law / scattering condition is illustrated in Figure 1.

Figure 1: Illustration of the Bragg Law.

Most of the neutron processes we will study in this paper are elastic, meaning that the wavelength of the neutron is unaltered by the process.