Perturbation Energy Coefficients and Ionization Potentials of the Ground State of Three- to Ten-Electron Isoelectronic Atomic Series

Abstract

The well-known perturbation expansion, ${E_{\mathrm{nr}}}^{\mathrm{}\left(N\right)\mathrm{}}\mathrm{}\left(Z\right)=Z^2\Sigma \stackrel{\infty }{i=0\mathrm{}}{{\epsilon }_i}^{\mathrm{}\left(N\right)\mathrm{}}{Z}^{-i},$ of the eigenvalues of the nonrelativistic Schrödinger equation for $N$ electrons about a nucleus of charge $Z$, has been widely used in the past for the extrapolation and interpolation of atomic energies. The presence of many small effects not explicitly taken into account by the perturbation expansion analysis reduce such calculations to a process of empirical curve fitting of limited range and reliability. These small effects include relativistic effects, the mass polarization, and the Lamb terms; to a good approximation, these effect can also be expanded in a descending power series, but with a leading term containing $Z^8$. On the basis of three plausible assumptions, theoretical approximations make it possible, in a semiempirical fashion, to remove a major portion of these small effects from the experimental data. In this way accurate values for ${{\epsilon }_2}^{\mathrm{}\left(N\right)\mathrm{}}$ and good estimates for ${{\epsilon }_3}^{\mathrm{}\left(N\right)\mathrm{}}$ have been obtained for $3<~N<~10$. These coefficients have been used to disclose inaccuracies and to fill gaps in the existing atomic energy data and to estimate electron affinities.