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

Abstract

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 ${}^{1}S$-states in four-electron atomic systems include the two independent spin functions ${\chi }_1=\alpha \beta \alpha \beta +\beta \alpha \beta \alpha -\beta \alpha \alpha \beta -\alpha \beta \beta \alpha$ and ${\chi }_2=2\alpha \alpha \beta \beta +2\beta \beta \alpha \alpha -\beta \alpha \alpha \beta -\alpha \beta \beta \alpha -\beta \alpha \beta \alpha -\alpha \beta \alpha \beta$. We also discuss the construction of variational wave functions for the excited $2^{3}S$-states in four-electron atomic systems.

This paper was published in ZhETPh (JETP), v.137, 1 - 11 (2010). In this version only a few corrections have been made in formulas

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