We investigate the stability of two-electron ions interacting with Yukawa potentials with varying $Z$ using correlated exponential wave functions based on the Ritz variational method. The critical screening parameter ${\mu }_C$ as a function of the nuclear charge $Z$, the critical nuclear charge $Z_C$ as a function of the screening parameter $\mu$, and the ionization energies in terms of the screening parameter $\mu$ and $Z$ are reported. The critical charge for the bare Coulomb system ($Z$, $e$, $e$) obtained using 700-term correlated exponential wave functions is in reasonable agreement with the reported results in the literature. The critical screening parameter, critical nuclear charge, and ionization energy for the Yukawa system ($Z$, $e$, $e$) exhibit interesting behaviors. The possible existence of Borromean states and quasibound resonant states is also discussed.

• Received 3 January 2019

DOI:https://doi.org/10.1103/PhysRevA.99.042514