Calculations of the energy levels of atoms and ions with Z ≤ 10 are carried out in this paper using the variational method. New wave function with two terms including correlation was performed to calculate excited (ns 2 ) 1 S e , (np 2 ) 1 D e , (nd 2 ) 1 G e , (nf 2 ) 1 I e , (nh 2 ) 1 M e and (ng 2 ) 1 K e states with (n ≤ 7). The results obtained show quantitatively the great significance of electron correlation effects in the doubly excited states. These results are in compliance with some experimental and theoretical data.

In this paper, we report the energies and resonant widths of the [(2s3s 1Se and 2s3s 3Se) (2s4s 1Se and 2s4s 3Se) (2s3p 1P0 and 2s3p 3P0) (2s4p 1P0 and 2s4p 3P0) (2p3p 1De and 2p3p 3De) (2p4p 1De and 2p4p 3De) (3s4s 1Se and 3s4s 3Se) (3s4p 1P0 and 3s4p 3P0) (3p4p 1De and 3p4p 3De) (3d4d 1Ge and 3d4d 1Ge)] Doubly Excited States of Helium isoelectronic series with nuclear charge Z (2 ≤ Z ≤ 10).Calculations are performedusing the Complex Rotation Method (CRM) in the framework of a variational procedure. The purpose of this study required a new correlated hydrogenic radial wave function combined with a Hylleraas wave function. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This proposed variational procedure, leads to accurate results in good agreement with available other theoretical results.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (Nℓ Nℓ) 2S+1Lᴨsystems.

Calculations of the energy levels of atoms and ions with Z ≤ 10 are carried out in this paper using a new wave function including a new method to calculate the correlation factor taking into account spherical harmonics through hypergeometric functions to calculate (1s22s) 2 S e , (1sns2) 2 S e , (1s2sns) 2 S e and (1s2snp) 2 P O states. The calculations concern the total energy, kinetic energy, Coulomb interaction between the atomic nucleus and the three electrons and the Coulomb interaction between electrons. The results that we have obtained confirm that a relatively theoretical procedure could be used for adequate calculations and understanding of electron correlation effects in doubly excited three-electron states. These results are in compliance with some experimental and theoretical data.

The () 1,3 , A e n N K T D doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2-9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.