513.001 Molecular and Solid State Physics

Atomic form factor of hydrogen

For the hydrogen atom in its ground state, the electron density is n(r) = (πa_o³)^-1exp(-2r/a_o), where a_o is the Bohr radius. Integrating this expression over all space yields 1 indicating that there is one electron.

The atomic form factor is the three-dimensional Fourier transform of the electron density. Show that the atomic form factor is f_G = 16/(4 + G²a_o²)².