COMPACT VARIATIONAL WAVE FUNCTIONS FOR BOUND STATES IN THREE-ELECTRON ATOMIC SYSTEMS
Frolov A.M., Wardlaw D.M.

Received: October 20, 2008

PACS: 31.15.ac, 31.15.ae

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The variational procedure to construct compact and accurate wave functions for three-electron atoms and ions is developed. The procedure is based on the use of six-dimensional Gaussoids written in the relative four-body coordinates r₁₂, r₁₃, r₂₃, r₁₄, r₂₄, and r₃₄. The nonlinear parameters in each basis function have been carefully optimized. Using these variational wave functions, we have determined the energies and other bound state properties for the ground 1²S-states in a number of three-electron atoms and ions. The three-electron atomic systems considered in this work include the neutral Li atom and nine positively charged lithium-like ions: Be⁺, B²⁺, C, Na⁸⁺, and Mg⁹⁺. Our variational wave functions are used to determine the hyperfine structure splitting and field shifts for some lithium-like ions. The explicit formulas of the Q^-1 expansion are derived for the total energies of these three-electron systems.