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Abstract:
The dependence of the natural amplitudes of the harmonium atom in its ground state on the confinement strength omega is thoroughly investigated. A combination of rigorous analysis and extensive, highly accurate numerical calculations reveals the presence of only one positive-valued natural amplitude ("the normal sign pattern") for all omega >= 1/2 . More importantly, it is shown that unusual, weakly occupied natural orbitals (NOs) corresponding to additional positive-valued natural amplitudes emerge upon sufficient weakening of the confinement. These solitonic NOs, whose shapes remain almost invariant as their radial positions drift toward infinity upon the critical values of omega being approached from below, exhibit strong radial localization. Their asymptotic properties are extracted from the numerical data and their relevance to calculations on fully Coulombic systems is discussed. Published by AIP Publishing.
