Relativistic and correlation effects for bound levels of atomic systems with three electrons

Abstract

A theoretical apparatus is developed which allows accurate calculation of atomic energy levels whose dominant configurations are of the three-electron, one p-hole and two-electron, or one-electron type. Correlation effects are incorporated through a configuration interaction expansion of Slater determinants in which the radials are found by solving the Hartree-Fock-Slater equation. The relativistic effects are incorporated by using the low- Z Pauli approximation for the Hamiltonian. The discussion is made general enough so that results for configurations with more than three electrons can be generated (with a substantial amount of algebraic manipulation) and approximations to the Hamiltonian, other than that of Pauli, can be considered (with a small amount of algebraic manipulation). The one p-hole two-electron theory is then applied to Na I, Mg II, and Cs I to obtain the fine structure of the energetically lowest D doublets. For Na I, Mg II, Cs I, the calculated values are (in cm −1), −0.038, −0.42, and +102.41, respectively. The observed values are (in cm −1), −0.050, −0.87, and +97.59, respectively. The three-electron theory is applied to the N = 13 isoelectronic series (up to Ca) to explain the doublet D fine structure associated with the 3 s3 p 2 configuration. A substantial improvement over the single configuration, nonrelativistic results is obtained.