3. Patterson function

3.1 Mathematical expression

To understand the process, let's explain its principle in the one-dimensional case. Let's imagine a one-dimensional mesh containing two atoms with abscissas x = α and x = β and atomic diffusion factors f ₁ and f ₂ . Consider two points with abscissas x and x + u and carry out the product of the electron density ρ at each of these points: ρ (x) · ρ (x + u)

Then let's calculate the average of this expression over the mesh of parameter a by varying x expressed in arbitrary units: $\begin{array}{ccc}P={\displaystyle {\int }_0^1\text{ρ}\left(x\right)}& \cdot & \text{ρ}\left(x+u\right)\cdot \text{d}x\end{array}$

...