Nonrelativistic structure calculations of two-electron ions in a strongly coupled plasma environment

In this work, the controversy between the interpretations of recent measurements on dense aluminum plasma created with the Linac coherent light source (LCLS) x-ray free electron laser (FEL) and the Orion laser has been addressed. In both kinds of experiments, heliumlike and hydrogenlike spectral lines are used for plasma diagnostics. However, there exist no precise theoretical calculations for He-like ions within a dense plasma environment. The strong need for an accurate theoretical estimate for spectral properties of He-like ions in a strongly coupled plasma environment leads us to perform ab initio calculations in the framework of the Rayleigh-Ritz variation principle in Hylleraas coordinates where an ion-sphere potential is used. An approach to resolve the long-drawn problem of numerical instability for evaluating two-electron integrals with an extended basis inside a finite domain is presented here. The present values of electron densities corresponding to the disappearance of different spectral lines obtained within the framework of an ion-sphere potential show excellent agreement with Orion laser experiments in Al plasma and with recent theories. Moreover, this method is extended to predict the critical plasma densities at which the spectral lines of H-like and He-like carbon and argon ions disappear. Incidental degeneracy and level-crossing phenomena are being reported for two-electron ions embedded in strongly coupled plasma. Thermodynamic pressure experienced by the ions in their respective ground states inside the ion spheres is also reported.