Two-Electron Systems in Generalized Exponential Cosine Screened Coulomb Potentials

We look at the ground state of two-electron systems placed in a dense quantum plasma environment where the three interactions between two particles of charges z$_{i}$ and z$_{j}$ placed at a distance r$_{ij}$ can be described by exponential-cosine-screened Coulomb potential (ECSCP) [1] V(r$_{ij})=$z$_{i}$z$_{j\, }$exp(-$\lambda $r$_{ij})$ cos($\delta $r$_{ij})$/r$_{ij}$ where $\lambda $ and $\delta $ are two positive real screening parameters related to the plasma frequency. The first calculations of the ground and first excited states of H$^{-}$, He and Li$^{+}$ where all three interactions between pairs of particles were represented by the same ECSCP, and with $\lambda = \delta $, were recently reported [2,3]. In the present work we show results for two-electron systems for which the interactions are described by generalized ECSCP with unequal parameters. Our calculations are performed with a rather versatile Configuration Interaction approach (see [3] and references therein), with correlated basis functions which explicitly depend on the three interparticle distances and which respect exactly all three cusp conditions. \\[4pt] [1] P. K. Shukla and B. Eliasson, Phys. Lett. A 372, 2897 (2008).\\[0pt] [2] A. Ghoshal and Y. K. Ho, J. Phys. B 42, \quad 075002 (2009).\\[0pt] [3] L. U. Ancarani and K. V. Rodriguez, Phys. Rev. A 89, 012507 (2014).