Analytic Independent-Particle Model for Atoms

Abstract

A simple analytic electron-atom independent-particle model (IPM) potential for use in phenomenological studies is examined. The potential is given by $V(r)=\frac{2(N\ensuremath{\Upsilon}\ensuremath{-}Z)}{r}$, $\ensuremath{\Upsilon}=1\ensuremath{-}{[({e}^{\frac{r}{d}}\ensuremath{-}1)H+1]}^{\ensuremath{-}1}$, where $Z$ is the number of nuclear protons, $N$ the number of core electrons, and Rydberg units are used. The adjustable parameters $d$ and $H$ are evaluated using (1) Thomas-Fermi screening functions, (2) Herman and Skillman Hartree-Fock-Slater (HS-HFS) screening functions, (3) HS-HFS eigenvalues, (4) Hartree-Fock eigenvalues, and (5) experimental separation energies. Good agreements with HS-HFS eigenvalues and screening functions for electrons in neutral atoms is obtained if $H=d\ensuremath{\alpha}{N}^{0.4}$, where $d$ is adjusted for each element and $\ensuremath{\alpha}=1.05$ for HFS and 1.00 for HF models. The success in fitting energy values and screening functions suggests that the potential embodies exchange and possibly correlation effects. Applications of the model to excited states and elastic and inelastic collisions are discussed.