  An approximate analytical solution of the Thomas-Fermi equation for neutral
atoms is obtained, using the Ritz variational method, which reproduces
accurately the numerical solution, in the range $0\leq x\leq50$, and its
derivative at $x=0$. The proposed solution is used to calculate the total
ionization energies of heavy atoms. The obtained results are in good agreement
with the Hartree-Fock ones and better than those obtained from previously
proposed trial functions by other authors.
