In the last three decades, intense experimental and theoretical studies of the properties of two-electron systems have been of great interest for physicists, in connection with the understanding of electron- electron correlation effects as well as in the ground state than in the doubly excited states of the helium isoelectronic series. For the doubly excited states, the correlation between the two electrons is understood as being analogous to the vibration and rotation of a flexible linear triatomic molecule. On the experimental side, transitions between the doubly excited-states have been observed in the Li atom, and the beam-foil spectroscopy has shown strong excitation of the preceding transitions. To simulate the oscillating term contained in the exact wave functions, it is necessary to use a sufficiently wide base of summable square wave functions for the test wave function. Thus, the values must depend on the vibrational parameters (α, β and γ) but also on the size of Ω. We investigate in this work, the energies for the (1s2ns) 2Se, (1s2np)2Po, (1s2sns) 2Se and (1s2snp) 2Po excited states of the lithium-like ions using using a new wave function including correlation. The calculations concern the total energy by use T is the kinetic energy; C is the Coulomb interaction between the atomic nucleus and the two electrons and W is the Coulomb interaction between electrons. The few differences noted between our results and those of other calculations can be explained by the fact that we have used in this work the largest sets of variational parameters.The results obtained are in compliance with recent theoretical calculations.
Keywords: wave function correlated, energy, excited states, correlation factor