Energies and wave functions for many-electron atoms.

Abstract

Screening constants \ensuremath{\sigma} are given for one-electron basis-set radial wave functions for atomic systems with 2\ensuremath{\le}Z\ensuremath{\le}18. The parameters \ensuremath{\sigma} for an individual screened electron (i) are dependent on the states of the screening electron (j), and the matrix of values ${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}\mathit{j}}$ is different from that suggested long ago by Slater [Phys. Rev. 36, 57 (1930)]. The matrix is slightly more complicated than Slater's, but the results for individual electron binding energies are much more accurate---even comparable in accuracy with Hartree-Fock (HF) values. The procedure is applied to compute both inner- and outer-shell binding energies, and a comparison is made with other similar calculations as well as with the HF and experimental values. The K-shell binding energies ${\mathit{E}}_{\mathit{K}}$ calculated with the new screening constants are in particularly close agreement with the results of HF calculations and with experimental values for elements for which accurate measurements can be made for gaseous atomic species. The quantities ${\mathit{E}}_{\mathit{K}}$ computed for C, N, and O atoms by the screening-constant method, while in agreement with HF calculations, differ from the values now being employed to evaluate the x-ray opacity of the interstellar gas. These currently used K threshold energies have not been measured for gaseous monatomic matter and are off by 2--6 %; the theoretical ${\mathit{E}}_{\mathit{K}}$ are very likely more accurate and should be adopted. A simple prescription is suggested for modifying the screening-constant wave functions for 2p states. Uncorrected, these functions, which are hydrogenic, fall off too fast at large r. Adding a single additional exponential term gives a much better fit to the HF functions, and a universal coefficient is suggested for this term. The prescription yields good agreement with HF values for 〈r〉 and 〈${\mathit{r}}^{2}$〉 for the species B to Ne; the computed diamagnetic susceptibility for Ne using the simple modified wave function agrees well with the experimental value.