Does the atomic structure factor show atomic structure?

Numerical evidence for the monotonicity of the isotropic atomic form factor, F(k), is presented. It is shown that the structural features of F(k) can be considerably enhanced by taking its Laplacian, ∇2F(k). Roots and extrema of this function can be assigned to different atomic shells. Linear relationships between the position of the roots and extrema and the atomic number Z are found for the neutral atoms with Z≤92.