ON BOUND STATE COMPUTATIONS IN THREE- AND FOUR-ELECTRON ATOMIC SYSTEMS
Frolov A.M., Wardlaw D.M.

Received: October 30, 2009

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A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r₁₂, r₁₃, r₁₄, r₂₃, r₂₄, r₃₄) and ten (r₁₂, r₁₃, r₁₄, r₁₅, r₂₃, r₂₄, r₂₅, r₃₄, r₃₅ and r₄₅) relative coordinates. The approach allows operating with different numbers of electron spin functions. In particular, the trial wave functions for the ¹S states in four-electron atomic systems include the two independent spin functions χ₁ = α β α β + β α β α - β α α β - α β β α and χ₂ = 2 α α β β + 2 β β α α - β α α β - α β β α - β α β α - α β α β. We also discuss the construction of variational wave functions for the excited 2³S states in four-electron atomic systems.