Fixed-shell statistical atomic models with piecewise exponentially decaying electron densities

Various versions of a statistical model of atoms are developed in which the numbers of electrons in different regions of an atom are fixed by certain postulates. It is assumed that the electron density can be represented by a sum of exponentially decreasing functions. The electronic energies and electronic densities of these new models are found to be comparable to the corresponding Hartree-Fock results and are substantial improvements over the original Thomas-Fermi statistical model and its various extensions. Densities of the new models are improvements over the modified statistical models of Wang and Par [Phys. Rev. A 16, 891 (1977)]. Some corrections to this reference are included.