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The present work deals with an ab initio calculation of total energies of the doubly excited np 2 , nd 2 and nf 2 states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np 2 , nd 2 and nf 2 excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.

We report accurate energy resonances and natural widths belonging to the 1s 2 2s 2 1 S 0 → (2pnl) 1 P • and 1s 2 2s 2p 3 P 0 → 1s 2 2p [ 2 P • ] np 3 P transitions in the Photoionization spectra of the Be-like N 3+ , O 4+ , F 5+ and Ne 6+ ions. Calculations are performed in the framework of the Modified Orbital Atomic Theory (MAOT). Excellent agreements are obtained with available experimental and theoretical literature data. The present calculations provide benchmark data for the diagnostic and for the modeling of astrophysical and laboratory plasmas.

Resonance energies of the Cl II-[3s 2 3p 3 ( 2 D 5/2 )]nd and [3s 2 3p 3 ( 2 P 3/2 )]nd, Ar II-3s 2 3p 4 ( 1 D 2 )ns, nd and of the Kr II [4s 2 4p 4 ( 1 D 2 )]ns, nd and 4s 2 4p 4 ( 3 P 2 , 3 P 1 )]ns, 4s 2 4p 4 ( 3 D 2 )]ns, nd and 4s 2 4p 4 ( 3 D 2 , 1 S 0 )]ns, nd Rydberg series are reported. Natural widths of the Ar II-[3s 2 3p 4 ( 1 D 2 )]ns, nd series are also reported. Calculations are done in the framework of the Modified Atomic Orbital Theory (MAOT). Excellent agreements are obtained with available theoretical and experimental data. High lying accurate resonance energies up to n = 40 are tabulated. The possibility to use the MAOT formalism report rapidly with an excellent accuracy the position of the excitation resonances as well as their width within simple analytical formulae is demonstrated.