<![CDATA[In this study, we calculate the energies of the 1s2s singlet and triplet states of an atom with nuclear charge Z by expressing them as a series expansion in ascending powers of 1/Z. The correlation energy, which represents the difference between the exact and mean-field descriptions of electron interactions, is determined by comparing the results obtained from the perturbation method with those calculated using the Hartree-Fock (HF) method. The Hartree-Fock energies are computed by solving an integro-differential equation, and the associated wave functions are obtained through the application of Laplace transformation techniques. To further support the calculation, the integral expressions for the Hartree-Fock energies per electron state are evaluated numerically using MATLAB. This approach enables a systematic analysis of electron correlation effects as a function of the nuclear charge, providing insights into the accuracy and limitations of mean-field approximations for two-electron atomic systems.]]>
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