Critical Stability of a Model Two-Electron System With Tunable Interelectronic Repulsion

The stability of a model two-electron system with tunable interelectronic repulsion has been explored with respect to a scaling parameter $\kappa$. The complex scaling method within an orbital-based configuration expansion and the Ritz variational method with an explicitly correlated Hylleraas-type basis set are considered for this purpose. An estimation of critical scaling parameter ${\kappa }_c$, at which the bound state transforms into a shape resonance state, is reported. The position and width of the quasibound state for $\kappa >{\kappa }_c$ are calculated by adopting the complex scaling method. The onset of quantum phase transition in the vicinity of ${\kappa }_c$ is discussed through the estimation of geometrical properties such as radial moments.