Contactium: A strongly correlated model system.

At the limit of an infinite confinement strength ω, the ground state of a system that comprises two fermions or bosons in harmonic confinement interacting through the Fermi–Huang pseudopotential remains strongly correlated. A detailed analysis of the one-particle description of this "contactium" reveals several peculiarities that are not encountered in conventional model systems (such as the two-electron harmonium atom, ballium, and spherium) involving Coulombic interparticle interactions. First of all, none of the natural orbitals (NOs) { ψ n (ω ; r) } of the contactium is unoccupied, which implies nonzero collective occupancies for all the angular momenta. Second, the NOs and their non-ascendingly ordered occupation numbers { ν n } turn out to be related to the eigenfunctions and eigenvalues of a zero-energy Schrödinger equation with an attractive Gaussian potential. This observation enables the derivation of their properties, such as the n − 4 / 3 asymptotic decay of ν n at the n → ∞ limit (which differs from that of n − 8 / 3 in the Coulombic systems), the independence of the confinement energy v n = ⟨ ψ n (ω ; r) | 1 2 ω 2 r 2 | ψ n (ω ; r) ⟩ of n , and the n − 2 / 3 asymptotic decay of the respective contribution ν n t n to the kinetic energy. Upon suitable scaling, the weakly occupied NOs of the contactium turn out to be virtually identical to those of the two-electron harmonium atom at the ω → ∞ limit, despite the entirely different interparticle interactions in these systems. [ABSTRACT FROM AUTHOR]