Pauli Principle for Heliumlike Atoms

Abstract

The layout of the periodic table of elements is governed by the Pauli exclusion principle. For heliumlike atoms in their ground state, for example, the two electrons must be of the opposite spin with zero probablility for the two electrons to have their spins pointing in the same direction. There are then no possibilities for the heliumlike atoms to exhibit paramagnetism in their ground state. In the density-functional theory (DFT), which is a topic of this book, the spin coupling is in some cases taken into consideration. Developments in the theory allow us to account for magnetism of many-electron atoms. For such a system, the magnetic properties of the ground state should be introduced so that the violations of the Pauli principle are unavoidable. The Pauli paramagnetism is “free electron” in nature and is treated in a similar way to the single particle approximations of DFT. Thus the parallel spin case might then arise as an artifact resulting in violations of the Pauli principle. This paper explains them briefly, and calculations for several heliumlike atoms are presented as illustrations. The final conclusion is that this error within DFT treatment is only substantial for H ⁻ ion. In the light of these results the generally accepted notion of no violations for heliumlike atoms other than H ⁻ is still valid within experimental error (Bethe and Salpeter, 1957; Goeke et al, 1987). Magnetic effects are expressible only as spin density defined as follows (Izuyama et al, 1963; Su and Wu, 1975)