Correlation Effects in Two- and Three-Electron Systems

Correlation effects in the lithium isoelectronic series (1s)²2s²S have been studied by computing the expectation values of a number of one- and two-electron operators. Calculations were performed using both Hartree-Fock and configuration interaction wave functions. The operators considered are ΣrᵢN (N=-2, -1, 2, 4), δ³(rᵢ), pᵢ², Σi>j^δ³(rᵢⱼ), Σi>j^(rᵢ·rⱼ), and Σi>j^(pᵢ·pⱼ). Computations were performed for Z=3, 4, 5, and 8. For comparison purposes the same expectation values were computed from configuration interaction wave functions of comparable accuracy for the two-electron systems (1s)²¹S with Z=2, 3, 4, 5, and 8. The results of the two-electron computations show reasonable agreement with more accurate computations and with empirical estimates. For the three-electron systems the main conclusions are: (a) Correlation has little effect on the one-electron expectation values, (b) the expectation values of Σi>j^(rᵢ·rⱼ) and Σi>j^(pᵢ·pⱼ) are proportionately larger for three- than for two-electron systems, and (c) the configuration interaction approach probably gives poor estimates of the expectation value of Σi>j^δ³(rᵢⱼ) even though this value appears to converge as the number of terms in the wave function is increased.