Studi Energi Hartree-Fock dan Korelasi untuk Keadaan Singlet dan Triplet 1s2s dari Ion Mirip Helium

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.