New real space correlated-basis-functions approach for the electron correlations of the semiconductor inversion layer

Based on the real space Correlated-Basis-Functions theory and the collective oscillation behavior of the electron gas with effective Coulomb interaction, the many body wave function is obtained for the quasi-two-dimensional electron system in the semiconductor inversion layer. The pair-correlation function and the correlation energy of the system have been calculated by the integro-differential method in this paper. The comparison with the other previous theoretical results is also made. The new theoretical approach and its numerical results show that the pair-correlation functions are definitely positive and satisfy the normalization condition.