  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.
