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Wigner molecules: natural orbitals of strongly correlated two-electron harmonium.

Explicit asymptotic expressions for natural orbitals and their occupancies are derived for the harmonium atom at the strong-correlation limit at which the confinement strength omega tends to zero. Unlike in systems with moderate correlation effects, the occupancies at the omega-->0 limit (derived from occupation amplitudes with alternating sign patterns) are vanishingly small and asymptotically independent of the angular momentum, forming a geometric progression with the scale factor proportional to omega(1/3) and the common ratio of ca. 0.0186. The radial components of the natural orbitals are given by products of polynomials and Gaussian functions that, as expected, peak at approximately half of the equilibrium interelectron distance.