The basic theory of neutron scattering

This last expression, (6.3), has been derived for fixed nuclei but the separation process into incoherent and coherent terms carries over into all kinds of neutron scattering theory. Moreover, it is particularly important for hydrogen. Remembering that the number of quantum states associated with a compound nuclear spin of J will be 27 -I- 1, we find that the average scattering length taken over the two spin states of hydrogen can be written  

8 b and so the proton is a strongly incoherent scatterer. On the other hand, the deuteron turns out to have 0 ° = 5.6 b and = 2.0b. Hence, to use neutron diffraction to identify the position of hydrogen in a crystal structure, it is more or less essential to prepare the deuterated version of the material, because, for H, the incoherent scattering gives an intense flat background to 

It will be seen that, if we separate out the parts of the equation that involve the neutron wave function, the rest of the equation is only a function of Q and (0. Van Hove [15] pointed out that this was a general property of neutron scattering cross-sections. Thus the expression for the cross-section can be reduced to the form of the scattering function which is a function of only two variables (in contrast to the three variables required to define the inelastic scattering cross-section). This relationship can be written  

---

The basic theory of neutron scattering from macromolecules has been given earlier and will not be repeated here. 

---