Independent-particle-model potentials for ions and neutral atoms withZ≤18

The atomic independent-particle model of Green, Sellin, and Zachor (GSZ) is used to obtain potentials for electrons in ions of light elements ($Z\le 18$). The two parameters of such potentials are obtained by the ab initio procedure of Bass, Green, and Wood (BGW). Here the expectation of the exact Hamiltonian with respect to a Slater determined of one-electron wave functions corresponding to GSZ potentials is minimized. Total energies determined by this modified Hartree-Fock procedure are found to be in excellent agreement with Hartree-Fock values (usually within a hundred parts per million). Potential parameters obtained in this way are found to be strongly dependent on both the atomic number and the number of electrons in the ion. Several other simple analytic potentials are treated in a similar way and it is found that the two-parameter GSZ and Gaspar potentials yield energies substantially lower than one-parameter potentials of the forms used earlier by Bohr and Tietz.