The ground state of harmonium

TLDR: A detailed analysis of the ground state of the harmonium atom as a function of the confinement strength ω and quantifies the domains of the weakly and strongly correlated regimes in this system is presented in this article.

Abstract: A detailed analysis that benefits from a slate of new approximate numerical and exact asymptotic results produces highly accurate properties of the ground state of the harmonium atom as functions of the confinement strength ω and quantifies the domains of the weakly and strongly correlated regimes in this system. The former regime, which encompasses the values of ω greater than ωcrit≈4.011 624×10−2, is characterized by the one-electron density ρ(ω;r1) with a global maximum at r1=0. In contrast, the harmonium atom within the latter regime, which corresponds to ω<ωcrit, differs fundamentally from both its weakly correlated counterpart and Coulombic systems. Resembling a Wigner crystal of a homogeneous electron gas, it possesses a radially localized pair of angularly correlated electrons that gives rise to ρ(ω;r1) with a “fat attractor” composed of a cage critical point and a (1, −1) critical sphere. Allowing for a continuous variation in ω, the new compact representation of the ground-state wave function an...