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Decomposition Rule of Energy Functional in the Density-Functional Theory: Applications to Affinity and Hyperfine Structure of Helium-Like Atoms |
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Der-Ruenn Su
Physics Department, National Taiwan University, Taipei, Taiwan 106, R.O.C. (Received July 9, 1997) |
Energy functionals in the density-functional theory (DFT) do not have
the linearity when the density is decomposed into separated parts in
an arbitrary way. We find a decomposition rule for these functionals
by a separation according to spin-up and spin-down densities. The
electron-spin dipole-dipole (DD) and hyperfine interactions (HI) are
used to treat helium-like atoms. Contrary to the expectation of
electrons with one spin-up and one spin-down from the Pauli principle,
our results indicate slight deviations therefrom, unavoidable though
small. From the nature of interactions, we conclude that there must
be Fermi-Coulomb and nuclear spin-holes in the electron distributions.
Investigations with the DD are a kind of symmetry-breaking to the
decomposition rule. This interaction also breaks the particle exchange
symmetry. The largest (16%) of these discrepancies for heliumlike atoms
is  .
It is suggested that magnetic effects between two electrons
here are still too small. After the HI is added and replaced by a
presumed smooth function, we obtained partial solutions in separated
spatial regions for various magnitudes of interaction strength. Finally,
a general fitting formula is given for this smoothed interaction. A
pattern of nucleus is thus proposed to be detectable. The physics of
counting electron numbers by density of states is discussed. Current
theory of 'one electron occupying one low energy state' is further
reviewed, reported, and related to previous works in addition to the
present methematical intuition.
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