the atomic scattering factor

Not all atoms scatter equally, and even a single atom does not scatter equally in all directions. The atomic scattering factor, written f (also called the form factor), is a number that says how strongly one isolated atom scatters a wave relative to a single electron. Roughly, a heavy atom with many electrons scatters strongly and a light atom weakly — because for X-rays it is the electrons that do the scattering, and more electrons means more scatterers working together.

Two facts pin f down. First, at zero scattering angle (straight through) every electron in the atom scatters exactly in step, so f equals the atomic number Z: carbon starts at f = 6, iron at f = 26, lead at f = 82 (in units of the single-electron scattering). Second, as the scattering angle grows, f falls off smoothly. Why the fall-off? Because the electron cloud has real size, comparable to the wavelength. At a finite angle, waves scattered from the near and far side of the cloud have a path difference and no longer add perfectly in step, so they partially cancel. The bigger the angle (the larger sin theta / lambda), the more they cancel, and the smaller f becomes.

This gentle decline with angle is why diffraction peaks generally get weaker toward higher angles, and why light atoms — especially hydrogen, with its lone electron — are hard to see by X-rays at all. It also explains why neutrons and electrons are complementary probes: neutrons scatter off nuclei (a scattering length that does not fall off with angle and does not track Z), and electrons scatter off the electrostatic potential, so each sees the atom differently. The X-ray f is the specific case of scattering by the electron cloud.