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.

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We report in this paper energy positions of the 2P˚_2s 2 2p 2 ( 1 D)nd 2 P, 2P˚_2s 2 2p 2 ( 1 D)nd 2 S, 2P˚_2s 2 2p 2 ( 1 D)ns 2 D, 2P˚_2s 2 2p 2 ( 1 S)nd 2 D, and 2P˚_2s 2 2p 3 ( 3 P)np 2 D Rydberg series in the photoionization spectra originating from 2P˚ metastable state of O+ ions. Calculations are performed up to n = 30 using the Modified Orbital Atomic Theory (MAOT). The present results are compared to the experimental data of Aguilar which are the only available values. The accurate data presented in this work may be a useful guideline for future experimental and other theoretical studies.

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.