Self-Consistent Field and Some X-Ray Terms of the Sodium Atom

Abstract

Self-consistent field functions were found for neutral sodium, for which they are tabulated, and for the six internally ionized states $1s$, $2p$, $1s2s$, $2p2s$, $1s2p$, ${\mathrm{}\left(2p\right)\mathrm{}}^2$, these figures denoting in each case the quantum symbols of the missing electrons. With these functions the corresponding atomic energies were computed by the method of Fock and Slater. Applying a first-order correction for relativity and spin-orbit interaction, a close check is obtained between the observed and calculated frequency of Na $K\alpha$, the deviation being of the order of 0.1 percent. Finally the energy parameters of the Fock equations were computed to the first order in the exchange for the $2s$ and $2p$ electrons in the singly ionized states and are compared with the corresponding ionization energies, which they exceed by about 10 percent.