Electron Wavefunctions and Densities for Atoms
  With a special `Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, $\sup_{y\in B(x,R)}|\nabla\psi(y)| \leq C(R) \sup_{y\in B(x,2R)}|\psi(y)|$ and obtain for the spherically averaged electron density, $\widetilde\rho(r)$, that $\widetilde\rho''(0)$ exists and is non-negative. 
Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof and Thomas   {\O}stergaard S{\o}rensen