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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) 2Se, (1sns2) 2Se, (1s2sns) 2Se and (1s2snp) 2PO 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.

Correlation Factor Taking into Account Spherical Harmonics Through Hypergeometric Functions to Calculate Energies of Li-Like Ions