Correlated n$^{1,3}$S states for two-electron atoms in screened potentials

We investigate two-electron atoms placed in a plasma environment, and consider both exponential cosine screened Coulomb potentials (ESCP) [1] and Debye-H\"{u}ckel or screened Coulomb potentials (SCP), for which the screening parameter $\lambda $ is related to the plasma frequency. Using highly correlated Hylleraas-type expansions, Ghoshal and Ho [2] have published the first calculations of the ground states of H$^{-}$ and He in ECSCP and SCP for a wide range of $\lambda $ values. We have confirmed these results with relatively simpler wave functions within a Configuration Interaction approach with explicitly correlated basis functions satisfying exactly all two-body Kato cusp conditions [3]. The main aim of the present contribution is to extend the findings of Ghoshal and Ho in various directions: (i) we evaluate the energy for the ground and the first $^{1,3}$S excited states, and provide analytical fits of the energy E($\lambda )$; (ii) we further extend the investigation to the iso-electronic series considering higher values of the nuclear charge Z and provide a double fit E($\lambda $,Z) -- thus a practical estimation tool for plasma applications; (iii) we make a systematic investigation of the $\lambda_{0}$ value for which the ground state ceases to exist. \\[4pt] [1] P K Shukla and B Eliasson 2008 Phys. Lett. A 372, 2897\\[0pt] [2] A Ghoshal and Y K Ho 2009 J. Phys. B 42, 075002; 42, 175006\\[0pt] [3] L U Ancarani and G Gasaneo 2007 Phys. Rev. A 75, 032706; 2008 Phys. Rev. A 77, 012705