On bound state computations in three- and four-electron atomic systems

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 which depend upon the six ($r_{12}, r_{13}, r_{14}, r_{23}, r_{24}, r_{34}$) and ten ($r_{12}, r_{13}, r_{14}, r_{15}, r_{23}, r_{24}, r_{25}, r_{34}, r_{35}$ and $r_{45}$) relative coordinates, respectively. The approach allows one to operate with the different number 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 $χ_1 = αβαβ+ βαβα- βααβ- αββα$ and $χ_2 = 2 ααββ+ 2 ββαα- βααβ- αββα- βαβα- αβαβ$. We also discuss the construction of variational wave functions for the excited $2^3S$-states in four-electron atomic systems.

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