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In this work, the controversy between the interpretations of recentmeasurements on dense aluminum plasma created with Linac coherent light sources(LCLS) X-ray free electron laser (FEL) and Orion laser has been addressed. Inboth kind of experiments, helium-like and hydrogen-like spectral lines are usedfor plasma diagnostics . However, there exist no precise theoreticalcalculations for He-like ions within dense plasma environment. The strong needfor an accurate theoretical estimates for spectral properties of He-like ionsin strongly coupled plasma environment leads us to perform ab initiocalculations in the framework of Rayleigh-Ritz variation principle in Hylleraascoordinates where ion-sphere potential is used. An approach to resolve thelong-drawn problem of numerical instability for evaluating two-electronintegrals with extended basis inside a finite domain is presented here. Thepresent values of electron densities corresponding to disappearance ofdifferent spectral lines obtained within the framework of ion-sphere potentialshow excellent agreement with Orion laser experiments in Al plasma and withrecent theories. Moreover, this method is extended to predict the criticalplasma densities at which the spectral lines of H-like and He-like carbon andargon ions disappear. Incidental degeneracy and level-crossing phenomena arebeing reported for the first time for two-electron ions embedded in stronglycoupled plasma. Thermodynamic pressure experienced by the ions in theirrespective ground states inside the ion-spheres are also reported.

Ab-initio calculations on two-electron ions in strongly coupled plasma environment